Paper Citation Record · LEDGER

Black holes and their shadows in $F(R)$ gravity

As of 13 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 2 inbound Pith citation observations for arXiv:2412.13775.

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

pith.paper-citation-record.v1
2412.13775 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T12:56:22.782789Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T23:01:59.731638Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-30T23:05:07.478759Z

Reference resolution

43 of 43 outbound references displayed

verified exact3
verified fuzzy5
unresolved26
parse uncertain8
malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 853e7595-a4dc-4be1-a791-1b8a0e3f4803 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T12:56:23.809848Z

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Observation be15a071-c74a-4ee4-a974-1f21f9fdfc3d · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T12:56:23.794319Z

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Observation 6c250f76-e1fb-4efa-94a9-0db61570e397 · outbound

This paper cites Can Magrans s/n, 08193 Barcelona, Spain.

Black holes and their shadows in $F(R)$ gravity Can Magrans s/n, 08193 Barcelona, Spain

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.584143Z

Source-reported events for the cited work

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Observation 7954404a-7f47-49a1-b9a8-269dcbf0f556 · outbound

This paper cites For this purpose, we derive the ﬁeld equation for t he corresponding theory when the general spherically symmetric and static conﬁguration is c onsidered.

Black holes and their shadows in $F(R)$ gravity For this purpose, we derive the ﬁeld equation for t he corresponding theory when the general spherically symmetric and static conﬁguration is c onsidered

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:56:23.767804Z

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Observation bb4219ce-9429-4174-8980-dcb376e900a6 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T12:56:23.751589Z

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Observation f89e487b-cffd-4ebc-a307-033a6e41a702 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 6

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Observation 4f523237-761a-42bf-a9d6-e0601fd1ab5e · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T12:56:23.720577Z

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Observation e6daf562-1d6b-4b23-8ce2-7ed11131c722 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T12:56:23.705930Z

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Observation 08a1ed0e-ff38-42f2-8333-1c14c4ae4548 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 9

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Observation 24409b3c-2fc8-431a-aea9-f2afb2e902cd · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 10

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T12:56:23.675256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5e6c0063-7c50-49d9-9570-e36a355b7d65 · outbound

This paper cites (15) Here A ≡ ν′′ + 2ν′2 − 1 r2 , B ≡ ν′ − 1 r , C ≡ ν′ + 1 r , (16) Eq.

Black holes and their shadows in $F(R)$ gravity (15) Here A ≡ ν′′ + 2ν′2 − 1 r2 , B ≡ ν′ − 1 r , C ≡ ν′ + 1 r , (16) Eq

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:56:23.659374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 565646c2-157e-412a-9e82-6ba4eac54c55 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 12

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Source-reported events for the cited work

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Observation 0f7080fb-0cf6-4e0f-b4ae-0292c04ddc01 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 13

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T12:56:23.627278Z

Source-reported events for the cited work

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Observation b4550020-c754-40d6-acb5-a62faf473d68 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 14

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T12:56:23.610673Z

Source-reported events for the cited work

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Observation a6bef526-0d32-4432-9dbf-c7cfe339ccbd · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 15

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T12:56:23.593409Z

Source-reported events for the cited work

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Observation 39dabbf1-6be7-45ca-b7ae-5ba06d662af0 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 16

Resolution: parse uncertain; raw_fallback, observed 2026-08-11T12:56:23.577144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 926d01bc-5156-43dd-897a-6275946b2b6c · outbound

This paper cites (18) By assuming FR 2 ∝ rα with a constant α, we ﬁnd 0 = α4 − 2α3 + 8α2 − 4α , (19) whose solution is given by, α = 0 , 2 3 + β0 , 2 3 + β±.

Black holes and their shadows in $F(R)$ gravity (18) By assuming FR 2 ∝ rα with a constant α, we ﬁnd 0 = α4 − 2α3 + 8α2 − 4α , (19) whose solution is given by, α = 0 , 2 3 + β0 , 2 3 + β±

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:56:23.559851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4813a187-b517-42df-aab0-e6d20528b7b9 · outbound

This paper cites (33) Here f 0 R and f 1 R are constants.

Black holes and their shadows in $F(R)$ gravity (33) Here f 0 R and f 1 R are constants

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:56:23.543151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 650f2773-c136-410f-8da9-518614c05d82 · outbound

This paper cites dot” or “˙.

Black holes and their shadows in $F(R)$ gravity dot” or “˙

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:56:23.527092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 70d70063-ee54-4af7-8838-54fe96e80610 · outbound

This paper cites First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole.

Black holes and their shadows in $F(R)$ gravity First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.665771Z

Source-reported events for the cited work

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Observation 9dfda7a3-d1c4-4293-9e9e-123bae9860f7 · outbound

This paper cites Event Horizon Telescope observations exclude compact objects in baseline mimetic gravity.

Black holes and their shadows in $F(R)$ gravity Event Horizon Telescope observations exclude compact objects in baseline mimetic gravity

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.671108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30a443aa-6938-4674-92c3-1ade99c69c26 · outbound

This paper cites Nojiri and S.

Black holes and their shadows in $F(R)$ gravity Nojiri and S

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.676411Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1a7422d-676b-4088-b691-0c2041c2e746 · outbound

This paper cites Nojiri and S.

Black holes and their shadows in $F(R)$ gravity Nojiri and S

Reference 23

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Source-reported events for the cited work

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Observation cf61ee9b-9992-44ec-8a63-61a30b37ae31 · outbound

This paper cites Nojiri and G.

Black holes and their shadows in $F(R)$ gravity Nojiri and G

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.686259Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5390f830-6d3e-4f70-b3bf-ac1ac27f1c32 · outbound

This paper cites Asymptotic safety casts its shadow.

Black holes and their shadows in $F(R)$ gravity Asymptotic safety casts its shadow

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.690825Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation febdc138-7c4e-4a8a-bef0-3cf7a5da21a8 · outbound

This paper cites Calculating black hole shadows: Review of analytical studies.

Black holes and their shadows in $F(R)$ gravity Calculating black hole shadows: Review of analytical studies

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.696381Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a3e77eb-c5bc-4008-b02d-743dda16b49f · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 27

Resolution: verified exact; raw_fallback, observed 2026-08-11T12:56:23.195864Z

Source-reported events for the cited work

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Observation f2e734dc-9d1e-4f9a-b458-9de2159752d6 · outbound

This paper cites an unresolved cited work.

Black holes and their shadows in $F(R)$ gravity Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.706983Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0eca9ec9-8177-4b21-9814-ae9130b8cc90 · outbound

This paper cites Curvature Quintessence.

Black holes and their shadows in $F(R)$ gravity Curvature Quintessence

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.711690Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10c0bd5f-50f9-4be3-a203-3954ea9edf55 · outbound

This paper cites Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration.

Black holes and their shadows in $F(R)$ gravity Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.716869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22591846-58e5-420e-a6f1-a23fa3b6261e · outbound

This paper cites Extended Theories of Gravity.

Black holes and their shadows in $F(R)$ gravity Extended Theories of Gravity

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.722141Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e4d34c6-b91c-442f-ab72-6de043950d87 · outbound

This paper cites Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models.

Black holes and their shadows in $F(R)$ gravity Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.727121Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43348641-1ffd-4912-9723-d11dd66995c1 · outbound

This paper cites Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution.

Black holes and their shadows in $F(R)$ gravity Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.732295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 929b978c-ba8d-4789-a467-6db2930b8033 · outbound

This paper cites Beyond Einstein Gravit y: A Survey of Gravitational Theories for Cosmology and Astrophysics,.

Black holes and their shadows in $F(R)$ gravity Beyond Einstein Gravit y: A Survey of Gravitational Theories for Cosmology and Astrophysics,

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.737331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ca572ed-b6bb-48ec-a8ea-9bfb64d6ee8e · outbound

This paper cites Spherically symmetric solutions of modified field equations in f(R) theories of gravity.

Black holes and their shadows in $F(R)$ gravity Spherically symmetric solutions of modified field equations in f(R) theories of gravity

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.742373Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e46ca71-5556-4b22-a1ec-bfa8fbfa25ec · outbound

This paper cites Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach.

Black holes and their shadows in $F(R)$ gravity Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:56:22.970308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c722a42d-1feb-43cf-ad6e-2097b5116e77 · outbound

This paper cites Black Holes in f(R) theories.

Black holes and their shadows in $F(R)$ gravity Black Holes in f(R) theories

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.752237Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bae9f91a-1479-4e90-afce-fae68990fc9a · outbound

This paper cites Axially symmetric solutions in f(R)-gravity.

Black holes and their shadows in $F(R)$ gravity Axially symmetric solutions in f(R)-gravity

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:56:22.928886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 231127ec-01b6-447f-a78e-3cfb997c36fc · outbound

This paper cites Static Spherically Symmetric Solutions in F(R) Gravity.

Black holes and their shadows in $F(R)$ gravity Static Spherically Symmetric Solutions in F(R) Gravity

Reference 39

Resolution: malformed identifier; no resolver link, observed 2026-08-11T12:56:22.762304Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b58f4dc-751b-4e1f-b9d4-5f09e31cc70b · outbound

This paper cites New Spherically Symmetric Solutions in f(R)-gravity by Noether Symmetries.

Black holes and their shadows in $F(R)$ gravity New Spherically Symmetric Solutions in f(R)-gravity by Noether Symmetries

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.767443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a10b8f5-5804-46a0-a567-d92152a4ae38 · outbound

This paper cites Non-trivial black hole solutions in $\mathit{f(R)}$ gravitational theory.

Black holes and their shadows in $F(R)$ gravity Non-trivial black hole solutions in $\mathit{f(R)}$ gravitational theory

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.772486Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0022300a-0637-40ab-bea3-253e562f9773 · outbound

This paper cites Testing the rotational nature of the supermassive object M87* from the circularity and size of its first image.

Black holes and their shadows in $F(R)$ gravity Testing the rotational nature of the supermassive object M87* from the circularity and size of its first image

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.777475Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b9aad0d-5516-43b4-b006-864debcf3cc4 · outbound

This paper cites Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$.

Black holes and their shadows in $F(R)$ gravity Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-11T12:56:22.782789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation f79f4930-3f26-42c6-afe2-a7941ceb236a · inbound

Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity cites this paper.

Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity Black holes and their shadows in $F(R)$ gravity

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-20T23:09:12.514887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4214bd63-9c95-4a08-8430-f47e12d59086 · inbound

Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity cites this paper.

Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity Black holes and their shadows in $F(R)$ gravity

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-06-30T23:05:07.480241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.