Paper Citation Record · LEDGER

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass

As of 15 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 4 inbound Pith citation observations for arXiv:2509.10667.

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

pith.paper-citation-record.v1
2509.10667 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:00:06.329833Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T17:09:57.756756Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-14T21:39:28.710481Z

Reference resolution

43 of 43 outbound references displayed

verified exact2
verified fuzzy6
unresolved35
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External citation measurements

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Outbound references

Observation 865b8a40-d15b-4bdf-88f2-c6e6bb84fcd1 · outbound

This paper cites General Relativity and Gravitation: A Centennial Perspective.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass General Relativity and Gravitation: A Centennial Perspective

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:00:07.103810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2e6002a9-97a6-4615-a06d-c42acf58a85a · outbound

This paper cites On the gravitational field of a mass point according to Einstein's theory.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass On the gravitational field of a mass point according to Einstein's theory

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.070378Z

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Observation c76b5b3f-47c5-46a1-aefd-da7e1677c7a5 · outbound

This paper cites The Confrontation between General Relativity and Experiment.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass The Confrontation between General Relativity and Experiment

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.077684Z

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Observation 8edb5cd9-0f55-4845-9786-a57fb28def20 · outbound

This paper cites Quantum Gravity: A Brief History of Ideas and Some Prospects.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Quantum Gravity: A Brief History of Ideas and Some Prospects

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.083459Z

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Unavailable: canonical work link unavailable.

Observation 118ef154-518a-4b40-9789-83e76cc4c542 · outbound

This paper cites The deepest problem: some perspectives on quantum gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass The deepest problem: some perspectives on quantum gravity

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.090519Z

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Unavailable: canonical work link unavailable.

Observation e24cf855-b9ff-4260-943f-539bffaa401c · outbound

This paper cites Gravitational vacuum polarization.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Gravitational vacuum polarization

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.102355Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52edbf80-5bfb-4f72-ae77-41db0baf85cb · outbound

This paper cites On gauge invariance and vacuum polarization,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass On gauge invariance and vacuum polarization,

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.109363Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b83f8499-61bd-4880-b349-55a5aacadc39 · outbound

This paper cites Black Stars, Not Holes,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Black Stars, Not Holes,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:00:07.253884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9dfbaea0-9cd8-4179-9a44-047ee2996f07 · outbound

This paper cites Stellar equilibrium in semiclassical gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Stellar equilibrium in semiclassical gravity

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.130404Z

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Unavailable: canonical work link unavailable.

Observation 0f98688e-10f5-4967-a53c-7bb502a747e4 · outbound

This paper cites an unresolved cited work.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.135862Z

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Unavailable: canonical work link unavailable.

Observation 531b837a-e114-4d1e-982e-89b6575e9fd1 · outbound

This paper cites Gravitational vacuum polarization I: Energy conditions in the Hartle--Hawking vacuum.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Gravitational vacuum polarization I: Energy conditions in the Hartle--Hawking vacuum

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.144828Z

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Unavailable: canonical work link unavailable.

Observation 2ccb95d5-c4b7-4d9f-8dbe-3a96e87aaede · outbound

This paper cites Gravitational vacuum polarization II: Energy conditions in the Boulware vacuum.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Gravitational vacuum polarization II: Energy conditions in the Boulware vacuum

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.153709Z

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Unavailable: canonical work link unavailable.

Observation 73685fa4-4d29-4369-9c81-46474dd1fe73 · outbound

This paper cites Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.162349Z

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Observation e4d20610-1fa2-4309-a8fc-6f56230d67ff · outbound

This paper cites Self-gravitating anisotropic fluids. I: Context and overview.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Self-gravitating anisotropic fluids. I: Context and overview

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.169601Z

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Observation 0d385a84-ec27-43af-853d-75cdbfe8430c · outbound

This paper cites Relativistic equations for adiabatic, spherically symmetric gravitational collapse,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Relativistic equations for adiabatic, spherically symmetric gravitational collapse,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:00:07.213652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9143017b-35bd-4fe5-a937-151ce896586c · outbound

This paper cites Gravitational Energy in Spherical Symmetry.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Gravitational Energy in Spherical Symmetry

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.179915Z

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Observation dd961335-5ec4-4267-8f97-5a10c6af0a36 · outbound

This paper cites Geometric wormhole throats.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Geometric wormhole throats

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.187092Z

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Observation 7be2b45e-53a4-496a-8410-a6b3fc1b8342 · outbound

This paper cites Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.191988Z

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Observation 6601a13d-f870-47af-9974-e51d6bf28506 · outbound

This paper cites Semiclassical constant-density spheres in a regularized Polyakov approximation.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Semiclassical constant-density spheres in a regularized Polyakov approximation

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.196560Z

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Observation 505f3491-bed6-43c2-af31-a0491c1c89e7 · outbound

This paper cites Semiclassical relativistic stars.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Semiclassical relativistic stars

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.201601Z

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Unavailable: canonical work link unavailable.

Observation 4882fe1a-28d4-4b5c-bd9e-a3c2167acef4 · outbound

This paper cites Ultracompact horizonless objects in order-reduced semiclassical gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Ultracompact horizonless objects in order-reduced semiclassical gravity

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.209080Z

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Unavailable: canonical work link unavailable.

Observation dd9b3219-bf7a-4500-bd45-840b8491af8b · outbound

This paper cites Arrechea,Hydrostatic equilibrium in the semiclassical approximation.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Arrechea,Hydrostatic equilibrium in the semiclassical approximation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:00:07.189953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9c3f7bfd-5f5c-43a3-8b96-8f273a8b945e · outbound

This paper cites Static Black Holes With Back Reaction From Vacuum Energy.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Static Black Holes With Back Reaction From Vacuum Energy

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.218354Z

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Unavailable: canonical work link unavailable.

Observation d4b56d76-785d-4bb8-89c3-188d6f633f29 · outbound

This paper cites The quantum fate of black hole horizons.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass The quantum fate of black hole horizons

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.224424Z

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Unavailable: canonical work link unavailable.

Observation aff40319-04e1-4739-a845-61237bf0abd5 · outbound

This paper cites On the Near-Horizon Geometry of an Evaporating Black Hole.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass On the Near-Horizon Geometry of an Evaporating Black Hole

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.230682Z

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Unavailable: canonical work link unavailable.

Observation cb66f9dd-47e8-4f27-a147-48e1dc610153 · outbound

This paper cites Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.237234Z

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Unavailable: canonical work link unavailable.

Observation 3b7ceec2-c224-4bc7-aa57-8aad8f3b6738 · outbound

This paper cites Schwarzschild geometry counterpart in semiclassical gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Schwarzschild geometry counterpart in semiclassical gravity

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.242378Z

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Observation 9d5104a6-503c-41e1-a49b-05f351523ddc · outbound

This paper cites Reissner-Nordstr\"om geometry counterpart in semiclassical gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Reissner-Nordstr\"om geometry counterpart in semiclassical gravity

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.246828Z

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Observation 1b40bb5b-c235-4bba-a66d-1e43d626d1c9 · outbound

This paper cites Asymptotically flat vacuum solutions in order-reduced semiclassical gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Asymptotically flat vacuum solutions in order-reduced semiclassical gravity

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.251064Z

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Unavailable: canonical work link unavailable.

Observation dbbe5a8d-dd0a-4e34-af1a-7f2c87331b7b · outbound

This paper cites Quantum corrections to the Schwarzschild metric from vacuum polarization.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Quantum corrections to the Schwarzschild metric from vacuum polarization

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.257089Z

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Observation fb648379-121b-450f-94d3-94010a6467fd · outbound

This paper cites Quantum corrected Einstein-Yang-Mills black holes in semiclassical gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Quantum corrected Einstein-Yang-Mills black holes in semiclassical gravity

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.265317Z

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Observation c6693b00-8732-40f7-b894-90705af63953 · outbound

This paper cites Dynamical evolution and stability of quantum corrected Schwarzschild black holes in semiclassical gravity.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Dynamical evolution and stability of quantum corrected Schwarzschild black holes in semiclassical gravity

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:00:06.639311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d7a93042-4e17-47d0-93d8-9c0cec3f7922 · outbound

This paper cites Quantum Field Theory in Schwarzschild and Rindler Spaces,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Quantum Field Theory in Schwarzschild and Rindler Spaces,

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.275130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 324ec8bb-1f27-4724-9f91-98ba36be71fc · outbound

This paper cites Hawking Radiation and Thin Shells,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Hawking Radiation and Thin Shells,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:00:07.146469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ad1ea195-51b3-4930-87e0-936ba740a387 · outbound

This paper cites Vacuum polarization in Schwarzschild spacetime,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Vacuum polarization in Schwarzschild spacetime,

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:00:07.281250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 30c27a06-c0e1-48a5-9478-9810308937bc · outbound

This paper cites Stress-energy tensor of quantized scalar fields in static spherically symmetric space-times,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Stress-energy tensor of quantized scalar fields in static spherically symmetric space-times,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:00:07.120164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 265d332c-68f5-4de6-b909-e1ced1844bd5 · outbound

This paper cites Macroscopic Effects of the Quantum Trace Anomaly.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Macroscopic Effects of the Quantum Trace Anomaly

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.292906Z

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Observation ddc874be-84f4-410c-b0e4-11573da319b7 · outbound

This paper cites The renormalized stress-energy tensor for scalar fields in the Boulware state with applications to extremal black holes.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass The renormalized stress-energy tensor for scalar fields in the Boulware state with applications to extremal black holes

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.297054Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aac30d06-6454-429b-a7b1-36b2134b2a61 · outbound

This paper cites Black holes, brick walls and the Boulware state.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Black holes, brick walls and the Boulware state

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.301479Z

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Unavailable: canonical work link unavailable.

Observation 98492b78-97a3-4366-9dbc-a382cc1028bb · outbound

This paper cites Two formalisms, one renormalized stress-energy tensor.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Two formalisms, one renormalized stress-energy tensor

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.309571Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6154f074-2abb-4fe5-b46f-77f72f460a38 · outbound

This paper cites Master field equations for spherically symmetric gravitational fields beyond general relativity,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Master field equations for spherically symmetric gravitational fields beyond general relativity,

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.315461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32c5f1b3-24c6-4e81-ab48-9c7c1487af19 · outbound

This paper cites Dynamical theory for spherical black holes in modified gravity,.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Dynamical theory for spherical black holes in modified gravity,

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.322581Z

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Unavailable: canonical work link unavailable.

Observation 131f0532-51ed-4107-a0fd-2e1ad39e5320 · outbound

This paper cites Novel black-bounce spacetimes: wormholes, regularity, energy conditions, and causal structure.

Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass Novel black-bounce spacetimes: wormholes, regularity, energy conditions, and causal structure

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-15T16:00:06.329833Z

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Pith citing papers

Observation 6b5c139b-76e0-47ad-8777-60255f5d6227 · inbound

Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds cites this paper.

Macroscopic backreaction of the trace anomaly on classical vacuum backgrounds Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-03T17:09:57.756756Z

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Observation 8147207c-7e44-4882-944d-a59702c51df5 · inbound

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics cites this paper.

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass

Reference 80

Resolution: verified exact; arxiv_id, observed 2026-06-09T03:07:03.975668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a32b5cfe-74bf-4554-ab4d-996e8fb75b31 · inbound

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics cites this paper.

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass

Reference 84

Resolution: verified exact; arxiv_id, observed 2026-06-09T03:07:03.975668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b65882c4-9ad8-45ff-af66-e020a26dd2a9 · inbound

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics cites this paper.

Photon Spheres and Shadows of Black Holes with Modified Entropy-Inspired Metrics Imprints of quantum vacuum fluctuations on the gravitational field of a spherical mass

Reference 84

Resolution: verified exact; arxiv_id, observed 2026-06-09T03:07:03.975668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.