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Paper Citation Record · LEDGER

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

As of 17 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 6 inbound Pith citation observations for arXiv:2501.00361.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.00361 v6

Coverage vector

measured 62 of 62 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:05:43.343372Z

measured 68 of 68 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 6 of 6 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T04:38:28.978649Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-23T06:12:38.636178Z

Reference resolution

62 of 62 outbound references displayed

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  • verified fuzzy43
  • unresolved19
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7cb3fc1b-e3e1-4ce6-a826-9530a56164d6 · outbound

This paper cites (3.71)–(3.73), the images ofRc fs(b, α, θ0,1) in Figs.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach (3.71)–(3.73), the images ofRc fs(b, α, θ0,1) in Figs

Reference 1

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Source-reported events for the cited work

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Observation 3f1274ea-53c0-4e46-a4b1-5a8b915df280 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 2

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Source-reported events for the cited work

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Observation a06eba6f-a003-4a8f-a9cd-bfa99c1af7f0 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 3

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Source-reported events for the cited work

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Observation bb2c5b5c-cdee-4041-82a2-18862de198fa · outbound

This paper cites Highland of Innovation Talent.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Highland of Innovation Talent

Reference 4

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Source-reported events for the cited work

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Observation 59e32a58-eae4-4149-b290-4375652235ee · outbound

This paper cites As in references, the entire geodesic path is in a plane, which implies that we can rotate coordinates to setθ(λ) =π/2.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach As in references, the entire geodesic path is in a plane, which implies that we can rotate coordinates to setθ(λ) =π/2

Reference 5

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation b769fa8f-dd95-41c6-819a-a3749b19f04b · outbound

This paper cites Because of dφ dr =− 1 m X 2 dφ dX ̸= 0 for r m ∈[2,+∞),(A21) one end of the geodesic is at infinity, and the other is behind the horizon of the BH.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Because of dφ dr =− 1 m X 2 dφ dX ̸= 0 for r m ∈[2,+∞),(A21) one end of the geodesic is at infinity, and the other is behind the horizon of the BH

Reference 6

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verified fuzzy
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Source-reported events for the cited work

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Observation f316ca2f-7750-44ed-93fc-b68f1e31d217 · outbound

This paper cites 2 3 arcsin r 1− b2 cri b2 !# ,(A22) X2 = 1 6 − 1 3 cos.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach 2 3 arcsin r 1− b2 cri b2 !# ,(A22) X2 = 1 6 − 1 3 cos

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation b0f61cf2-274b-4d49-89da-0a7f02711038 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 8

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation c4ec0611-10ac-40a1-8c1b-26ea3418f5f0 · outbound

This paper cites X1 + (X2 −X 1)sn2 ±(φ−φ 0) r X3 −X 1 2 + F ϑlarI m r0 , klar !#−1 ,(A54) r=m.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach X1 + (X2 −X 1)sn2 ±(φ−φ 0) r X3 −X 1 2 + F ϑlarI m r0 , klar !#−1 ,(A54) r=m

Reference 9

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f7446896-2007-43a1-927d-8627d687b100 · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 10

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 21ec9f91-0d27-4c61-a92a-da8d7167a410 · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 11

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f0367222-4ed9-4926-af63-9bcc7f88426c · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 12

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 9be64ca4-0b23-41b4-aed2-70553b9c486e · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 13

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation c83ac81b-11af-4090-80b2-cf2b833c1bd8 · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 14

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation fea04ffd-aef7-4932-a205-a8a368700339 · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 15

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 46287d31-7f2c-49a2-9b7c-bc01c46558ef · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 16

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation ceca7443-c5f9-4fb5-9dc2-2aaeabf12dcc · outbound

This paper cites Akiyamaet al.,First M87 Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First M87 Event Horizon Telescope Results

Reference 17

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation b3fed8b6-8f8f-44bd-815f-ff72aaa42826 · outbound

This paper cites Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results

Reference 18

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 1ee71972-0a84-4a95-ac3f-45f67eaad390 · outbound

This paper cites Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results

Reference 19

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 11ed6d25-b61e-4399-a427-4e579d27eef3 · outbound

This paper cites Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results

Reference 20

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 2568a542-38a0-461d-acae-9e34fc3e9160 · outbound

This paper cites Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results

Reference 21

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 83e4a5a3-24eb-4f6f-8123-ad53a6e89119 · outbound

This paper cites Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results

Reference 22

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 27a3fba9-3d6a-495c-8fd0-771e000eed12 · outbound

This paper cites Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Akiyamaet al.,First Sagittarius A* Event Horizon Telescope Results

Reference 23

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 29397d94-a6bd-4633-9e6b-89cb48c31ac4 · outbound

This paper cites Zeng, H.-Q.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Zeng, H.-Q

Reference 24

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 6c979760-a0d6-44fd-b746-6b8859c159bb · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 25

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unresolved
raw_fallback, observed 2026-08-10T23:05:43.745213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 3657ee26-deca-4adf-bf5d-7d5a83b1b688 · outbound

This paper cites Guo, K.-J.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Guo, K.-J

Reference 26

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation bb43b589-15e4-482c-862c-88e46c62736d · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.726534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.221059Z digest=sha256:6b4f7d081b1e61e0255eddfdb8e0b97e1bc0171bce98ba6d275dd8280fb0f632

Observation e6e90ed4-47d4-4995-a4f3-9126abb2225b · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.716641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.224611Z digest=sha256:86b1754e4f85885a8c03c4aa6e37bb35e10f46d64abe0adae169636bcdd51141

Observation 4321d222-56e1-40b0-9239-0265022fbbeb · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.706207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.228161Z digest=sha256:6484093f2e2f42ac7f39d9c86f08dbefe3e7daedd5c5bb6177aa416893463bb6

Observation 6ef1d9e4-c40f-4c2e-93b7-32cb935c6182 · outbound

This paper cites Chandrasekhar,The Mathematical Theory of Black Holes(Oxford University Press, Oxford, 1992).

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Chandrasekhar,The Mathematical Theory of Black Holes(Oxford University Press, Oxford, 1992)

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.696224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation d33fb60a-41f8-47b4-8666-ecc48da26511 · outbound

This paper cites Cadez and U.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Cadez and U

Reference 31

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verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.686063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.235505Z digest=sha256:472458d05a84338450f319238be5db99aebd8973387e74bc92b2dc675be4307d

Observation 73aed53f-1673-47f7-9665-ad45ebc13276 · outbound

This paper cites Hackmann and C.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Hackmann and C

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.676886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.238729Z digest=sha256:6375681a8950006b444dc49219ac1bba06a47232f9c2042126a9f4b8a46609ef

Observation 3cdb26a8-b250-4383-a0ce-68d6e40127bb · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.667580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.242338Z digest=sha256:65aecbdc07489e44a939e8cbcb97659283624ac08a06510486c67b36e59638af

Observation fb08a4b1-50ef-47d4-858c-488e257978b9 · outbound

This paper cites Mu˜ noz,Orbits of massless particles in the Schwarzschild metric: Exact solutions, Am.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Mu˜ noz,Orbits of massless particles in the Schwarzschild metric: Exact solutions, Am

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.658409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.245828Z digest=sha256:ccecc8c0fc43556e915f9aa54127e56379c4fc85ff018a368581aa77d035f3aa

Observation 6e1af809-ab53-4e59-a4e2-997c311d31c3 · outbound

This paper cites Saurabh and K.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Saurabh and K

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.649208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.249328Z digest=sha256:1dfb219ea0eb2d9d7a96931caea4020020bcc4b1e88fd4ab829347ddca382c59

Observation 7e039ce3-5cde-4a86-b8fd-36ee6621c1d3 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.639452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.252749Z digest=sha256:7f02f2753f30df8ebcfaf8e977d814d1abd4bb4e728398f2a9cc8625b7ecf77e

Observation 0e14a16c-1247-4519-b3ea-2f645806431e · outbound

This paper cites Jusufi and Saurabh,Black hole shadows in Verlinde’s emergent gravity, Mon.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Jusufi and Saurabh,Black hole shadows in Verlinde’s emergent gravity, Mon

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.630188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.256583Z digest=sha256:8cf32571e3c7dd094ab36928a612af710f84516f0f372d9867efa146a8f89229

Observation 2cd1b99c-3d92-4eed-8f4e-135707342863 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.619849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.260032Z digest=sha256:96ec2c7dd61491bf11eb396bf868c5609581563b1b44e30d9a31cee7d3d41198

Observation bc62815c-25d7-46f9-9e3a-9c96c8a08e03 · outbound

This paper cites Narayan, M.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Narayan, M

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.610785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.263397Z digest=sha256:fb735a529ae459ddd3507fef7b683d2bfa4291e07249a020cb8b7cb7f9d49d9e

Observation c232a8a5-a043-470c-a862-a8f53cfae759 · outbound

This paper cites Jaroszynski and A.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Jaroszynski and A

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.601540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.266656Z digest=sha256:ad1ea709fe4bee6a0ec7d2cde63110cc8e9704773330bad0e8dcb512f3d2ad14

Observation 2865874b-fcd5-4e02-8413-14fc72f46392 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.591935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.270031Z digest=sha256:7aeb5b7d3c2d0cda831cebaf356ea7091c91e2d87139c05bbcdcc0e0f224fc95

Observation b4ce80cf-b4ad-4b27-8675-c33b17008a9e · outbound

This paper cites Younsi, K.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Younsi, K

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.581725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.273356Z digest=sha256:62e54aef359b6aba931832ae7558843747ba85d723b1d4d79c06d0fcd428e8dd

Observation 30776537-8846-44ab-89f5-cb90322dc7c0 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.571822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.276801Z digest=sha256:8dcc4a05939f0ba19dc067082d3be91cf7cf0304837caae2ad0fe19eca778192

Observation b5768a04-8ab5-448c-9456-c731b1a1d06e · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.561721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.280027Z digest=sha256:075e2d32f9bbe78227712ed1154dd295d4f1f60804b5c3d3b111decced891d59

Observation 2fa1235a-8fa3-4afe-adaa-c26219c54ec1 · outbound

This paper cites Luminet,Image of a spherical black hole with thin accretion disk, Astron.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Luminet,Image of a spherical black hole with thin accretion disk, Astron

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.551836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.283502Z digest=sha256:9150ce5de7d070326298e8293f6a2cfeb7abd2055c34168652487d717351b527

Observation 60ce7935-2694-4b7b-9d05-0404f1ae0095 · outbound

This paper cites Gyulchev, P.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Gyulchev, P

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.542539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.286747Z digest=sha256:1dc41302128998a0f61b375d8263b01089563f40ac7416a7900fe10f50d9c6c0

Observation 51bcfa99-1543-400d-92bf-332a2ade5fb4 · outbound

This paper cites Gyulchev, P.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Gyulchev, P

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.532920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.290258Z digest=sha256:217603714825c1b4d81fc7e03282aa421aa2678be83f55271cb31201782d997c

Observation 9413e534-32f2-4d77-98fc-9ca6a73c4641 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.523629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.293843Z digest=sha256:5590596117215ea5c0f708fee2b42b4706266c9450917e68fa6131f5f2b261c0

Observation 3ec3145c-e282-4c29-9293-caf3fe2785f7 · outbound

This paper cites Rahaman, T.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Rahaman, T

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.514087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.297582Z digest=sha256:581ee43f6760646254bb6c39b181ff1d8f57f3c0c698f5f87f16137cf224766e

Observation eae43abb-0b1a-43d2-a2d2-b3999c20015f · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.503917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.301155Z digest=sha256:cb82612e8e4583fbc13ad6409c90ce43f26540680c61565fabcd1e0459583f60

Observation 6c132ec4-1104-4d41-be1f-8c52a0f4f36d · outbound

This paper cites Guo, Y.-X.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Guo, Y.-X

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.493799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.304373Z digest=sha256:64a955316e0c46eaf91e90cf0c6e19d4c27b9a1b8a2acbdbbb17edf44a00d180

Observation a5e88a33-49f3-472a-a2e8-2a5e161ab9f8 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.483790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.308243Z digest=sha256:c741151588c9ecd5e7ba88859ae048382757523c1e122e398b97d40e757e55eb

Observation 252610f7-6bd3-453b-afb3-421450e27564 · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.474179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.311758Z digest=sha256:e4de1b071f3b8469f59bd7570f52d483a4af490be1a4ab6f4402259849422e62

Observation 4b0d4ded-941f-4422-ab07-af5877813f2f · outbound

This paper cites Tian and Z.-H.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Tian and Z.-H

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.464496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.315002Z digest=sha256:b5fe4e265318791bcc11a5f45a14b0dfba269fc9c58a5060f86634181be92cc9

Observation 0b0eaa65-c71b-47f4-8ab0-721fd089d567 · outbound

This paper cites Gyulchev, J.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Gyulchev, J

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.454316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.318614Z digest=sha256:2b3d24a87d39ffd2f97be2e7cd1dca7cd17f511007f51a0641c3c3d91eb16349

Observation 161aba99-5512-4505-9423-4b4182cdd12a · outbound

This paper cites M¨ uller,Analytic observation of a star orbiting a Schwarzschild black hole, Gen.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach M¨ uller,Analytic observation of a star orbiting a Schwarzschild black hole, Gen

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.443824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.322411Z digest=sha256:805f3a5598789a1842bbfdbe2b932e6929d90b58719c508f59dae7695670873e

Observation fbc66a6f-4403-4918-90d3-cedd8140a5e9 · outbound

This paper cites Bambi and E.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Bambi and E

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.432985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.325894Z digest=sha256:f64ed6fe9c8383d76f67d4ed8ad31ffaf03dc58d1186342e696a728f2acb686d

Observation 5917b3d0-22aa-4249-af6f-84a5691bedf3 · outbound

This paper cites Bambi,A code to compute the emission of thin accretion disks in non-Kerr space-times and test the nature of black hole candidates, Astrophys.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Bambi,A code to compute the emission of thin accretion disks in non-Kerr space-times and test the nature of black hole candidates, Astrophys

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.421265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.329407Z digest=sha256:aa3569da2bed0bdf130a53ea8b7b343a8db28a6dfebf2c7d1d9c7eec87f5e83b

Observation 61cad9e1-7dbb-4c01-807b-b4399629c165 · outbound

This paper cites Huang,Lectures on General Relativity(Science Press, Beijing, 2023) (in Chinese).

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Huang,Lectures on General Relativity(Science Press, Beijing, 2023) (in Chinese)

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.408941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.332811Z digest=sha256:9da1dd1f6eac5caee46a215b1af95fd3e74332c72be086a5caa1bcad669abbf0

Observation a5a6dc5f-5320-43df-9f80-178384104eea · outbound

This paper cites Abramowitz and I.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Abramowitz and I

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:05:43.396607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.336219Z digest=sha256:2f19bd32291653e6eb0a6a3832097cacef3f1a452963ef7e0d2af108aefc5b8a

Observation b8f299b7-5474-42b3-8337-8f4808563c3d · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.386069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.339706Z digest=sha256:d8dec9de215200642540389240435b62e8c0bf07a0ad7aa898e5c8f0ab5df675

Observation 0f6886bb-179d-47bf-a336-39a05937d77c · outbound

This paper cites an unresolved cited work.

Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:05:43.375446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T23:05:43.343372Z digest=sha256:aa811f452d454374967c4b84eb3b317a205382f5a2d88e51a8c346bd4cd077a9

Pith citing papers

Observation de36af32-57c6-4ec2-b281-2041fcb14bc6 · inbound

Shadow of the Scalar Hairy Black Hole with Inverted Higgs Potential cites this paper.

Shadow of the Scalar Hairy Black Hole with Inverted Higgs Potential Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

Reference 80

Resolution
verified exact
arxiv_id, observed 2026-05-23T06:12:38.639455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-05-23T06:09:14.669705Z digest=sha256:7f81ac1a53061969d9e81a197e2549231c89f8b32dbaf28c442197e7b6d6a6f5

Observation fdd5ca09-36f0-4b9a-bdd3-8ddb165f63dd · inbound

Static Dark Fluid Thin Shells in Schwarzschild-de Sitter Spacetimes: Stability and Black Hole Shadows cites this paper.

Static Dark Fluid Thin Shells in Schwarzschild-de Sitter Spacetimes: Stability and Black Hole Shadows Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

Reference 87

Resolution
unresolved
no resolver link, observed 2026-08-02T20:49:50.847585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-02T20:49:50.847585Z digest=sha256:a897382e60f91441cb826221e2362842ab466093f0d3cc18463a0c3402181e23

Observation c26c60e2-c7d5-49b3-808b-b5fa1f169a62 · inbound

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics cites this paper.

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

Reference 30

Resolution
verified exact
arxiv_id, observed 2026-05-11T16:01:05.868581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-05-09T18:57:17.004672Z digest=sha256:842054ebe109868aa7b5a737554297b11d668471c662fbda601ed90551d3d193

Observation 7c5dd3b0-2d75-42e6-8c64-252b79aeb760 · inbound

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics cites this paper.

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

Reference 30

Resolution
verified exact
arxiv_id, observed 2026-05-12T07:51:27.615343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-05-12T01:51:40.922299Z digest=sha256:80ecb26c70ea29d4e35d5365fd31a9e8ec70e537334dc07efe47cbe366298d1b

Observation 4bf03372-4a2a-4408-a684-07171a9bbd7a · inbound

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics cites this paper.

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

Reference 30

Resolution
verified exact
arxiv_id, observed 2026-05-14T21:39:28.950520Z

Source-reported events for the cited work

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source=pdf_text observed=2026-05-14T21:38:19.473597Z digest=sha256:54b864e37fae8d7429af491b8e540b484a41aec1e9fb2d47adcca8e1f9f13d6c

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Construction of an analytic multi-component accretion environment and its application to Kerr black hole imaging cites this paper.

Construction of an analytic multi-component accretion environment and its application to Kerr black hole imaging Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach

Reference 27

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no resolver link, observed 2026-08-14T04:38:28.978649Z

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source=pdf_text observed=2026-08-14T04:38:28.978649Z digest=sha256:92332a33e4ffd374f9d29a86bca4e4a6b70c73fdf99bf4503f0f2443fb33f096