Paper Citation Record · LEDGER

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma

As of 18 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2508.00624.

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

pith.paper-citation-record.v1
2508.00624 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-22T00:39:12.671191Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

43 of 43 outbound references displayed

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verified fuzzy28
unresolved13
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External citation measurements

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Outbound references

Observation 7eaf8c32-6574-4539-9c71-339180aedeea · outbound

This paper cites In the presence of a plasma with the distribution specified in (6) it reads r4 + 2mE2 C E2 − E2 C r3 − K E2 − E2 C r2 + 2mK E2 − E2 C r = 0.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma In the presence of a plasma with the distribution specified in (6) it reads r4 + 2mE2 C E2 − E2 C r3 − K E2 − E2 C r2 + 2mK E2 − E2 C r = 0

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:51.997483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e2e11486-0746-4a7c-9a0b-59df77d99622 · outbound

This paper cites As first step we take (40) and write down the conditional equation for the roots.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma As first step we take (40) and write down the conditional equation for the roots

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.988039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 697ad537-a156-48b5-b397-d7d084e87b73 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:40:51.989605Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 731e523c-6a3b-47b2-a0d2-ca274f4cb3b7 · outbound

This paper cites II C we encountered several elliptic integrals.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma II C we encountered several elliptic integrals

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:51.981694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9fc493d6-fdfc-4c0c-96e6-2cc120ace1f1 · outbound

This paper cites First M87 Event Horizon Telescope results.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma First M87 Event Horizon Telescope results

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:51.985545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bae0fc65-9971-4b42-8c6f-a507251cb205 · outbound

This paper cites First Sagittarius A ∗ Event Horizon Telescope results.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma First Sagittarius A ∗ Event Horizon Telescope results

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:52.009044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 77a043f9-e1bc-4f54-becd-a0ec4f03cd0f · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:50.977098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ab12905a-68e9-460d-a13c-a28ccf0b8c8e · outbound

This paper cites First M87 Event Horizon Telescope results.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma First M87 Event Horizon Telescope results

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:51.009232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0b6577e2-f76f-4fae-bd2d-3d6bd6d1a571 · outbound

This paper cites First M87 Event Horizon Telescope results.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma First M87 Event Horizon Telescope results

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.994559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 51366c93-aff8-4bac-8e54-d7e8c5a9f3b2 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:50.991130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bc0b8c68-3140-44e2-a0ea-241fc5e10f47 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:51.012301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1260994a-1808-4c67-b914-2ad754244703 · outbound

This paper cites Perlick, Ray Optics, Fermat’s Principle, and Appli- cations to General Relativity , Lecture Notes in Physics Monographs (Springer, Berlin, 2000).

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Perlick, Ray Optics, Fermat’s Principle, and Appli- cations to General Relativity , Lecture Notes in Physics Monographs (Springer, Berlin, 2000)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.997547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c1df5ed7-3f92-4365-98ca-3c2892c51b75 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:50.973920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f451e310-a64f-4a7e-aee0-35caa890391b · outbound

This paper cites Er and S.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Er and S

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:51.022005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4be8f143-ff2b-401d-9391-52b6d8ef3745 · outbound

This paper cites Feleppa, V.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Feleppa, V

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.980786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 64b7def4-ce1c-4bd2-98a0-bb3214f0fbbc · outbound

This paper cites Perlick, O.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Perlick, O

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:51.018836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a37240de-970d-488d-9688-a6bc77c254cf · outbound

This paper cites Perlick and O.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Perlick and O

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:51.015305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9bcaf9ab-196c-463f-a149-4111c0df6b8c · outbound

This paper cites Bezdˇ ekov´ a, V.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Bezdˇ ekov´ a, V

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:51.025139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a00415a6-06f4-459e-8b74-22ec50661c45 · outbound

This paper cites Perlick and O.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Perlick and O

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:51.006211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 71032e83-d6a9-4002-82b1-5432ea570c45 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:51.003234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation de145e71-9b22-415b-a045-5e1a2db71eed · outbound

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

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Luminet, Image of a spherical black hole with thin accretion disk, Astron

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:51.000692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8ff59ded-158e-4b08-85ad-8b549d6badb8 · outbound

This paper cites Johannsen and D.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Johannsen and D

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:51.993364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 849965f4-b45d-49a7-a406-93d56405f388 · outbound

This paper cites Aratore, O.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Aratore, O

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.984084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d7fc34f6-2f8b-40db-b07e-9bda5e42a9fb · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:40:52.016594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 309bd1aa-e5fb-474a-b97e-a3f5bedb3a1a · outbound

This paper cites Lockhart and S.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Lockhart and S

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:52.012765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1e2072a5-2708-4cf8-a6e0-e0e085f2830c · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:40:52.004850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 712bd546-9e84-49fc-ad49-6bd0d7b3abf5 · outbound

This paper cites Falcke, F.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Falcke, F

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:52.001423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b23066ee-0a7f-4610-8554-813cefe064b9 · outbound

This paper cites Desire, A.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Desire, A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.970607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5dc59e92-6a13-45b0-b861-dca28fd4df40 · outbound

This paper cites Gravitational shadow and emission spectrum of thin accretion disks in a plasma medium.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Gravitational shadow and emission spectrum of thin accretion disks in a plasma medium

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-22T00:40:51.034811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation db4d6cdd-fb92-45a0-b5f3-44da78a83fee · outbound

This paper cites Perlick, Influence of a plasma on the shadow of a black hole, Astron.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Perlick, Influence of a plasma on the shadow of a black hole, Astron

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.938719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ba39a0a1-b793-4955-9fa8-4b014bccd902 · outbound

This paper cites Mino, Perturbative approach to an orbital evolution around a supermassive black hole, Phys.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Mino, Perturbative approach to an orbital evolution around a supermassive black hole, Phys

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.935017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1fcb1715-0460-43b6-b11c-d4fb33e1ed52 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:50.946444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6324e1f4-1a09-4820-a35b-d01c8dd9b0ad · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:50.942535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6c6104e7-1e99-45f5-8a90-a66cb3ce5e9a · outbound

This paper cites Hancock, Elliptic Integrals, 1st ed., edited by M.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Hancock, Elliptic Integrals, 1st ed., edited by M

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.964166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d0ae7e96-ba68-407a-a5b4-39b862ff41d0 · outbound

This paper cites Grenzebach, V.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Grenzebach, V

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.967626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 15e3a3db-6afb-4adb-9936-0b0a752adefb · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:40:52.027664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0ddb57ae-c388-440d-95aa-7724f034b510 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:40:52.020563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1ac01354-001b-47c1-97e6-a55f7c4f9609 · outbound

This paper cites Frittelli and E.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Frittelli and E

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:52.024207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ad3c0205-3242-4512-91d5-b8cc192eba02 · outbound

This paper cites Perlick, Exact gravitational lens equation in spheri- cally symmetric and static spacetimes, Phys.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Perlick, Exact gravitational lens equation in spheri- cally symmetric and static spacetimes, Phys

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:40:52.031669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 02f1a0b9-17af-43e7-8577-aa3c79c68e2d · outbound

This paper cites Bezanson, A.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Bezanson, A

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.956775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6e189d60-ee05-4dc5-bb53-a255d773d767 · outbound

This paper cites M¨ uller and M.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma M¨ uller and M

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-22T00:45:50.950073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fa6be17d-5374-4106-bf3a-3d6fea895901 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-05-22T00:45:50.953529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 81bb111c-928e-40cf-8fd8-949d5249f258 · outbound

This paper cites an unresolved cited work.

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma Unresolved cited work

Reference 43

Resolution: parse uncertain; raw_fallback, observed 2026-05-22T00:45:50.960703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.