Paper Citation Record · LEDGER

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity

As of 20 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2506.10414.

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pith.paper-citation-record.v1
2506.10414 v3

Coverage vector

measured 44 of 44 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

44 of 44 outbound references displayed

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External citation measurements

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Outbound references

Observation e11fbefd-9268-4191-968e-529ef1bcdfb1 · outbound

This paper cites First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole

Reference 1

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Observation 1368ec6a-3c33-4b36-a9f9-2f004e02e483 · outbound

This paper cites Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant

Reference 2

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Observation fc5a8c9d-e8de-40e9-8241-bc768d8f9c64 · outbound

This paper cites Angular radius of the black hole shadow for large distance ro >> mis αsh = 3 √ 3m ro.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Angular radius of the black hole shadow for large distance ro >> mis αsh = 3 √ 3m ro

Reference 3

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Observation 67b1013d-9f6d-483e-afa6-81eaba24561c · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 4

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Observation 421f1981-80a4-4003-b1f5-aecf5e16a5cd · outbound

This paper cites The Cosmological Constant Problem and Quintessence.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity The Cosmological Constant Problem and Quintessence

Reference 5

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Observation 1d8cc348-ffc3-4593-a748-33711c0b4841 · outbound

This paper cites The Case for a Positive Cosmological Lambda-term.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity The Case for a Positive Cosmological Lambda-term

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.675503Z

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Observation f2fbc8ac-8907-4674-9f26-2427f30950a7 · outbound

This paper cites A new recipe for $\Lambda$CDM.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity A new recipe for $\Lambda$CDM

Reference 7

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Observation a265f7aa-3d59-4a2a-a8d0-b0372f9eec23 · outbound

This paper cites Particle Dark Matter: Evidence, Candidates and Constraints.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Particle Dark Matter: Evidence, Candidates and Constraints

Reference 8

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Observation 18f8379f-265c-4cf0-b300-0f38e254b117 · outbound

This paper cites How Cold is Cold Dark Matter?.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity How Cold is Cold Dark Matter?

Reference 9

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Observation 3589571f-8643-4a7d-b1a0-198c8a981b84 · outbound

This paper cites Dark Matter properties through cosmic history.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Dark Matter properties through cosmic history

Reference 10

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Observation 04b6077a-7c74-424a-90d3-484c84737095 · outbound

This paper cites Challenges for $\Lambda$CDM: An update.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Challenges for $\Lambda$CDM: An update

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:53.000766Z

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Observation ac525a89-d168-4485-a225-af56e6e8880a · outbound

This paper cites Probing the cold nature of dark matter.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Probing the cold nature of dark matter

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:53.056297Z

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Observation 34b51e92-d9f3-466f-b4cc-bd1a6370c581 · outbound

This paper cites Effect of the modified gravity on the large scale structure formation.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Effect of the modified gravity on the large scale structure formation

Reference 13

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Observation 26d39d7b-e931-42a1-96c4-559508c0c44a · outbound

This paper cites Dark matter as scalaron in $f(R)$ gravity models.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Dark matter as scalaron in $f(R)$ gravity models

Reference 15

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Observation 07c1f07c-7ce3-4085-adbe-3a60215cf2a6 · outbound

This paper cites Light deflection angle through velocity profile of galaxies in $f(R)$ model.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Light deflection angle through velocity profile of galaxies in $f(R)$ model

Reference 17

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Observation 359d0f07-a838-4493-b107-fffcbe92267b · outbound

This paper cites Snepppen, Scientific reports 11, 14247 (2021).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Snepppen, Scientific reports 11, 14247 (2021)

Reference 18

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Observation 575b4d84-6e11-439c-90a5-c5b02d50aa4e · outbound

This paper cites Akiyama, A.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Akiyama, A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.326004Z

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Observation c22b9afb-c42e-4786-a50d-1e143634b5b9 · outbound

This paper cites Synge, Monthly Notices of the Royal Astronomical So- ciety 131, 463 (1966).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Synge, Monthly Notices of the Royal Astronomical So- ciety 131, 463 (1966)

Reference 20

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Observation 35222921-69af-4e5b-8d6e-0efb56b4b75f · outbound

This paper cites Perlick and O.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Perlick and O

Reference 22

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Observation 5ea8bf3e-24fc-42d0-8b06-b580c62da460 · outbound

This paper cites Takahashi, The Astrophysical Journal 611, 996 (2004).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Takahashi, The Astrophysical Journal 611, 996 (2004)

Reference 23

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 24

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 25

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Observation ff31acb2-4a03-494e-8717-1b98f244950a · outbound

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 26

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Observation 5a16827e-50ba-4322-bcc3-45ec7bf4d526 · outbound

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

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

Reference 27

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Observation c9380b9e-eb83-48ef-b7f5-46073c726369 · outbound

This paper cites Schwarzschild, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften , 189 (1916).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Schwarzschild, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften , 189 (1916)

Reference 28

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 29

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Observation 182e288e-16b8-47cd-8193-11b8aac4a9c4 · outbound

This paper cites Schutz, A first course in general relativity (Cambridge university press, 2022).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Schutz, A first course in general relativity (Cambridge university press, 2022)

Reference 30

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Observation dcb7e9a3-67b5-4dc1-978d-b11c3be76b18 · outbound

This paper cites Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley and Sons, New York, 1972).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley and Sons, New York, 1972)

Reference 31

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This paper cites Sitzungs- berichte der k ˜A¶niglich preussischen akademie der wissenschaften zu berlin,.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Sitzungs- berichte der k ˜A¶niglich preussischen akademie der wissenschaften zu berlin,

Reference 32

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Observation 2cce0aff-4ffa-4de1-b752-440ebfc4ab83 · outbound

This paper cites The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions

Reference 33

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Observation 5ca8195c-9011-40d5-956d-6b92462494ba · outbound

This paper cites Chaotic Shadows of Black Holes: A Short Review.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Chaotic Shadows of Black Holes: A Short Review

Reference 34

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Observation f26b6f2e-6044-425d-aaa6-b24fb5762b72 · outbound

This paper cites Kottler, Annalen der Physik 361, 401 (1918).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Kottler, Annalen der Physik 361, 401 (1918)

Reference 35

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 36

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 38

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Observation 5163c7c5-fb05-490c-abe5-c968d72b678d · outbound

This paper cites Photon Rings around Kerr and Kerr-like Black Holes.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Photon Rings around Kerr and Kerr-like Black Holes

Reference 39

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 40

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Observation 8f1f76e4-bf4c-4172-b915-4b56f83d4473 · outbound

This paper cites Extended galactic rotational velocity profiles in $f(R)$ gravity background.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Extended galactic rotational velocity profiles in $f(R)$ gravity background

Reference 41

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Observation da3a0c3c-0f0a-442f-94b3-de3540df3da8 · outbound

This paper cites Unified $f(R)$ gravity at local scales.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unified $f(R)$ gravity at local scales

Reference 42

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Observation 23482edd-df5f-4363-837d-0c38a293e884 · outbound

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Nojiri and S

Reference 43

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Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Nojiri and S

Reference 44

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Observation 0892b76b-57b3-41e6-a319-da5949c7e277 · outbound

This paper cites Capozziello, K.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Capozziello, K

Reference 45

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Observation ec47ff00-de1f-45b9-a921-5adc24053a3d · outbound

This paper cites De Felice and S.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity De Felice and S

Reference 46

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Observation fa73745a-62ea-406c-ad74-55c9ae03d357 · outbound

This paper cites Nojiri, S.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Nojiri, S

Reference 47

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