Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T23:05:43.343372Z
Paper Citation Record · LEDGER
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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T23:05:43.343372Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-14T04:38:28.978649Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-23T06:12:38.636178Z
62 of 62 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 7cb3fc1b-e3e1-4ce6-a826-9530a56164d6 · outbound
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
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.
Observation 3f1274ea-53c0-4e46-a4b1-5a8b915df280 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 2
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.
Observation a06eba6f-a003-4a8f-a9cd-bfa99c1af7f0 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 3
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.
Observation bb2c5b5c-cdee-4041-82a2-18862de198fa · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Highland of Innovation Talent
Reference 4
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.
Observation 59e32a58-eae4-4149-b290-4375652235ee · outbound
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
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.
Observation b769fa8f-dd95-41c6-819a-a3749b19f04b · outbound
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
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.
Observation f316ca2f-7750-44ed-93fc-b68f1e31d217 · outbound
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
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.
Observation b0f61cf2-274b-4d49-89da-0a7f02711038 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 8
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.
Observation c4ec0611-10ac-40a1-8c1b-26ea3418f5f0 · outbound
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
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.
Observation f7446896-2007-43a1-927d-8627d687b100 · outbound
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
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.
Observation 21ec9f91-0d27-4c61-a92a-da8d7167a410 · outbound
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
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.
Observation f0367222-4ed9-4926-af63-9bcc7f88426c · outbound
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
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.
Observation 9be64ca4-0b23-41b4-aed2-70553b9c486e · outbound
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
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.
Observation c83ac81b-11af-4090-80b2-cf2b833c1bd8 · outbound
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
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.
Observation fea04ffd-aef7-4932-a205-a8a368700339 · outbound
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
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.
Observation 46287d31-7f2c-49a2-9b7c-bc01c46558ef · outbound
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
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.
Observation ceca7443-c5f9-4fb5-9dc2-2aaeabf12dcc · outbound
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
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.
Observation b3fed8b6-8f8f-44bd-815f-ff72aaa42826 · outbound
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
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.
Observation 1ee71972-0a84-4a95-ac3f-45f67eaad390 · outbound
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
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.
Observation 11ed6d25-b61e-4399-a427-4e579d27eef3 · outbound
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
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.
Observation 2568a542-38a0-461d-acae-9e34fc3e9160 · outbound
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
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.
Observation 83e4a5a3-24eb-4f6f-8123-ad53a6e89119 · outbound
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
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.
Observation 27a3fba9-3d6a-495c-8fd0-771e000eed12 · outbound
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
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.
Observation 29397d94-a6bd-4633-9e6b-89cb48c31ac4 · outbound
Reference 24
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.
Observation 6c979760-a0d6-44fd-b746-6b8859c159bb · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 25
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.
Observation 3657ee26-deca-4adf-bf5d-7d5a83b1b688 · outbound
Reference 26
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.
Observation bb43b589-15e4-482c-862c-88e46c62736d · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 27
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.
Observation e6e90ed4-47d4-4995-a4f3-9126abb2225b · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 28
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.
Observation 4321d222-56e1-40b0-9239-0265022fbbeb · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 29
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.
Observation 6ef1d9e4-c40f-4c2e-93b7-32cb935c6182 · outbound
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
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.
Observation d33fb60a-41f8-47b4-8666-ecc48da26511 · outbound
Reference 31
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.
Observation 73aed53f-1673-47f7-9665-ad45ebc13276 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Hackmann and C
Reference 32
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.
Observation 3cdb26a8-b250-4383-a0ce-68d6e40127bb · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 33
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.
Observation fb08a4b1-50ef-47d4-858c-488e257978b9 · outbound
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
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.
Observation 6e1af809-ab53-4e59-a4e2-997c311d31c3 · outbound
Reference 35
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.
Observation 7e039ce3-5cde-4a86-b8fd-36ee6621c1d3 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 36
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.
Observation 0e14a16c-1247-4519-b3ea-2f645806431e · outbound
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
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.
Observation 2cd1b99c-3d92-4eed-8f4e-135707342863 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 38
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.
Observation bc62815c-25d7-46f9-9e3a-9c96c8a08e03 · outbound
Reference 39
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.
Observation c232a8a5-a043-470c-a862-a8f53cfae759 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Jaroszynski and A
Reference 40
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.
Observation 2865874b-fcd5-4e02-8413-14fc72f46392 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 41
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.
Observation b4ce80cf-b4ad-4b27-8675-c33b17008a9e · outbound
Reference 42
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.
Observation 30776537-8846-44ab-89f5-cb90322dc7c0 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 43
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.
Observation b5768a04-8ab5-448c-9456-c731b1a1d06e · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 44
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.
Observation 2fa1235a-8fa3-4afe-adaa-c26219c54ec1 · outbound
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
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.
Observation 60ce7935-2694-4b7b-9d05-0404f1ae0095 · outbound
Reference 46
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.
Observation 51bcfa99-1543-400d-92bf-332a2ade5fb4 · outbound
Reference 47
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.
Observation 9413e534-32f2-4d77-98fc-9ca6a73c4641 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 48
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.
Observation 3ec3145c-e282-4c29-9293-caf3fe2785f7 · outbound
Reference 49
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.
Observation eae43abb-0b1a-43d2-a2d2-b3999c20015f · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 50
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.
Observation 6c132ec4-1104-4d41-be1f-8c52a0f4f36d · outbound
Reference 51
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.
Observation a5e88a33-49f3-472a-a2e8-2a5e161ab9f8 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 52
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.
Observation 252610f7-6bd3-453b-afb3-421450e27564 · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 53
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.
Observation 4b0d4ded-941f-4422-ab07-af5877813f2f · outbound
Reference 54
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.
Observation 0b0eaa65-c71b-47f4-8ab0-721fd089d567 · outbound
Reference 55
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.
Observation 161aba99-5512-4505-9423-4b4182cdd12a · outbound
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
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.
Observation fbc66a6f-4403-4918-90d3-cedd8140a5e9 · outbound
Reference 57
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.
Observation 5917b3d0-22aa-4249-af6f-84a5691bedf3 · outbound
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
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.
Observation 61cad9e1-7dbb-4c01-807b-b4399629c165 · outbound
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
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.
Observation a5a6dc5f-5320-43df-9f80-178384104eea · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Abramowitz and I
Reference 60
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.
Observation b8f299b7-5474-42b3-8337-8f4808563c3d · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 61
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.
Observation 0f6886bb-179d-47bf-a336-39a05937d77c · outbound
Black hole images under spherical-shell and circular-annulus accretion models in Schwarzschild spacetime: a semianalytical approach Unresolved cited work
Reference 62
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.
Observation de36af32-57c6-4ec2-b281-2041fcb14bc6 · inbound
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
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.
Observation fdd5ca09-36f0-4b9a-bdd3-8ddb165f63dd · inbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c26c60e2-c7d5-49b3-808b-b5fa1f169a62 · inbound
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
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.
Observation 7c5dd3b0-2d75-42e6-8c64-252b79aeb760 · inbound
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
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.
Observation 4bf03372-4a2a-4408-a684-07171a9bbd7a · inbound
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
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.
Observation fa23200a-ac98-476d-9eed-467c1cf0a1bc · inbound
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
Source-reported events for the cited work
Unavailable: canonical work link unavailable.