Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
The geometry of photon surfaces
As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 30 inbound Pith citation observations for arXiv:gr-qc/0005050.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:40:19.357836Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-04T04:19:34.866205Z
Reference resolution
0 of 0 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation 1d1eddeb-0950-4a4a-9177-eca16e9d0eaf · inbound
Massive particle surfaces and black hole shadows from intrinsic curvature cites this paper.
Massive particle surfaces and black hole shadows from intrinsic curvature The geometry of photon surfaces
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-05-22T23:32:15.263470Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 51939dbd-385e-4156-81be-9ef51567c357 · inbound
Deflection of Light due to Kerr Sen Black Hole in Heterotic String Theory using Material Medium Approach cites this paper.
Deflection of Light due to Kerr Sen Black Hole in Heterotic String Theory using Material Medium Approach The geometry of photon surfaces
Reference 49
- Resolution
- verified exact
- local_arxiv, observed 2026-05-22T20:42:05.339289Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 35e64791-72b2-41b6-967f-0d06214f8a97 · inbound
Black Hole Solutions in Dark Photon Models with Higher Order Corrections cites this paper.
Black Hole Solutions in Dark Photon Models with Higher Order Corrections The geometry of photon surfaces
Reference 42
- Resolution
- verified exact
- local_arxiv, observed 2026-05-22T17:11:49.980852Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation e06e8699-2511-4de9-8eed-0688f35254b1 · inbound
Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres cites this paper.
Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres The geometry of photon surfaces
Reference 40
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T16:40:19.357836Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 84799745-e41c-4000-b865-100fa8f36402 · inbound
Semi-Analytic Trajectory Analysis of Light in Generic Static Spacetimes cites this paper.
Semi-Analytic Trajectory Analysis of Light in Generic Static Spacetimes The geometry of photon surfaces
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T15:20:02.828629Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 98879cb4-4834-4449-a560-980401ddf052 · inbound
Topological charge and black hole photon spheres in massive gravity cites this paper.
Topological charge and black hole photon spheres in massive gravity The geometry of photon surfaces
Reference 19
- Resolution
- verified exact
- local_arxiv, observed 2026-05-18T18:52:48.362874Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation be6aa8b1-75c3-460d-b6c5-5fd956bde120 · inbound
Supertranslations in the bulk of spacetime cites this paper.
Supertranslations in the bulk of spacetime The geometry of photon surfaces
Reference 99
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T14:35:41.747124Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 84e5c422-911d-49cf-bb0f-32383e431fe9 · inbound
Optical and orbital characterization of spherically symmetric static black holes of self-gravitating new nonlinear electrodynamics model cites this paper.
Optical and orbital characterization of spherically symmetric static black holes of self-gravitating new nonlinear electrodynamics model The geometry of photon surfaces
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-07-15T12:04:34.107907Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 20fb8cb4-6b2f-4b0a-9c25-cb5647c18fde · inbound
Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes cites this paper.
Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes The geometry of photon surfaces
Reference 12
- Resolution
- verified exact
- arxiv_id, observed 2026-05-10T07:37:04.731179Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 20207b40-6b39-402d-b93a-0a94666f0a06 · inbound
Photon Propagation and Black Hole Imaging in Kruglov Nonlinear Electrodynamics cites this paper.
Photon Propagation and Black Hole Imaging in Kruglov Nonlinear Electrodynamics The geometry of photon surfaces
Reference 56
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T20:01:09.170961Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 5cec1be2-9d8e-41c6-9d5e-e589e63082de · inbound
Photon Propagation and Black Hole Imaging in Kruglov Nonlinear Electrodynamics cites this paper.
Photon Propagation and Black Hole Imaging in Kruglov Nonlinear Electrodynamics The geometry of photon surfaces
Reference 56
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T04:41:01.127349Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 13bc4991-eecd-4f30-a54c-7568b47884a5 · inbound
Photon Propagation and Black Hole Imaging in Kruglov Nonlinear Electrodynamics cites this paper.
Photon Propagation and Black Hole Imaging in Kruglov Nonlinear Electrodynamics The geometry of photon surfaces
Reference 56
- Resolution
- unresolved
- no resolver link, observed 2026-07-12T18:30:37.013457Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ddac788f-7716-46a2-8f37-ed5835768a22 · inbound
A Complete Invariant Analysis of the Kerr Spacetime and its Photon Region cites this paper.
A Complete Invariant Analysis of the Kerr Spacetime and its Photon Region The geometry of photon surfaces
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T21:01:10.099651Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 40c86d76-7afa-42f6-9847-08c2e9d31170 · inbound
Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing cites this paper.
Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing The geometry of photon surfaces
Reference 5
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T22:51:23.283411Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 5f655c1c-2c06-4ff3-a07a-9545581a83f8 · inbound
Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing cites this paper.
Photon Surfaces in Higher-Curvature Gravity: Implications for Quasinormal Modes and Gravitational Lensing The geometry of photon surfaces
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T15:40:41.999975Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 10faf456-a72c-4f4a-8f80-7830d8dde0fc · inbound
Scalar-Electromagnetic Couplings as Source of Deformed Black Hole: From Shadows to Thermodynamic Topology cites this paper.
Scalar-Electromagnetic Couplings as Source of Deformed Black Hole: From Shadows to Thermodynamic Topology The geometry of photon surfaces
Reference 42
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T16:31:06.898662Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation e5e45f4b-2727-4b6c-9704-bc06f1182440 · 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 The geometry of photon surfaces
Reference 7
- Resolution
- verified exact
- arxiv_id, observed 2026-05-13T01:57:04.944042Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ce5c410c-d1ea-4a6c-8d91-0bc9b32ed75a · 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 The geometry of photon surfaces
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-05-20T23:09:12.482992Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation f1d7b2a6-b561-41d3-b7bd-9ca13390a53e · 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 The geometry of photon surfaces
Reference 14
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T23:05:07.474293Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 0a7fffef-a1ce-49f1-ba2a-943a81f87f13 · inbound
Regular black hole solutions and the quark chemical potential at the QCD phase transition cites this paper.
Regular black hole solutions and the quark chemical potential at the QCD phase transition The geometry of photon surfaces
Reference 35
- Resolution
- verified exact
- local_arxiv, observed 2026-06-29T16:13:36.551069Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 0bd3fd97-18a9-4986-b612-33256f004d9d · inbound
Probing Effective Field Theory Corrections with Quasinormal Modes and Gravitational Lensing in Reissner-Nordstr\"om Black Holes cites this paper.
Probing Effective Field Theory Corrections with Quasinormal Modes and Gravitational Lensing in Reissner-Nordstr\"om Black Holes The geometry of photon surfaces
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-06-29T11:23:20.798346Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 8892d2e8-dde0-42a8-bfa3-de6b125eb319 · inbound
A perturbative geometric approach for photon spheres, massive particle surfaces and black hole shadows with mass variations cites this paper.
A perturbative geometric approach for photon spheres, massive particle surfaces and black hole shadows with mass variations The geometry of photon surfaces
Reference 36
- Resolution
- verified exact
- local_arxiv, observed 2026-06-28T18:52:29.885682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 4d6e30c5-dbb4-42b7-97e7-86131bb18532 · inbound
Polarization-Dependent Photon Propagation, Quasinormal Modes, and Gravitational Lensing in Higher-Curvature Effective Theories cites this paper.
Polarization-Dependent Photon Propagation, Quasinormal Modes, and Gravitational Lensing in Higher-Curvature Effective Theories The geometry of photon surfaces
Reference 17
- Resolution
- verified exact
- local_arxiv, observed 2026-07-04T04:19:34.867634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 6b23c930-68bc-4ab1-a1af-8442d7c20803 · inbound
Photon surfaces extension in general spherical dust collapse cites this paper.
Photon surfaces extension in general spherical dust collapse The geometry of photon surfaces
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-06-26T17:09:36.153491Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation a1d08799-f596-4896-8b36-0c41ee45e64c · inbound
Revisit Static Aether: Exact Vacuum Solution in Einstein-Aether Theory and Its Analytic Extension cites this paper.
Revisit Static Aether: Exact Vacuum Solution in Einstein-Aether Theory and Its Analytic Extension The geometry of photon surfaces
Reference 39
- Resolution
- verified exact
- local_arxiv, observed 2026-07-01T17:35:51.411386Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 28d9ed30-3af4-44cb-a387-8a45769e4e30 · inbound
Analytical Study of Deflection Angle and Time Delay in Kerr Spacetime with Modified Propagation cites this paper.
Analytical Study of Deflection Angle and Time Delay in Kerr Spacetime with Modified Propagation The geometry of photon surfaces
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T19:55:50.251506Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4bfd16e6-1b1f-41c0-a84b-78b860d7b312 · inbound
Shadow of the generalized Vaidya black hole cites this paper.
Shadow of the generalized Vaidya black hole The geometry of photon surfaces
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T17:57:53.784782Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0ba3d145-8c9d-4bda-9b7f-ebeab7217246 · inbound
Gravitational wave echoes as probes of the maximum mass of strange stars in quadratic curvature-matter coupled gravity cites this paper.
Gravitational wave echoes as probes of the maximum mass of strange stars in quadratic curvature-matter coupled gravity The geometry of photon surfaces
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T12:55:53.126203Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9ee6bb04-92e6-4d48-a101-88c5436d3b5f · inbound
Quantum-Corrected Thermodynamics, Dirac Perturbations, Geodesic Structure, and Topological Phases of Black Holes with Non-Minimal Logarithmic Coupling cites this paper.
Quantum-Corrected Thermodynamics, Dirac Perturbations, Geodesic Structure, and Topological Phases of Black Holes with Non-Minimal Logarithmic Coupling The geometry of photon surfaces
Reference 88
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T06:51:10.427587Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 28bef2dd-7023-44f9-9775-2d7c6d535430 · inbound
Spin precession in the strong deflection limit cites this paper.
Spin precession in the strong deflection limit The geometry of photon surfaces
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T02:10:39.599444Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.