Paper Citation Record · LEDGER

Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

As of 16 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 31 inbound Pith citation observations for arXiv:hep-th/0412320.

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

pith.paper-citation-record.v1
hep-th/0412320 v2

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measured 0 of 0 reference resolution

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measured 31 of 31 standing notices

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

measured 31 of 31 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:51:11.456912Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T21:56:38.303284Z

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External citation measurements

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Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation bdabb9ec-29c6-4ba7-99c6-d0ca62867df1 · inbound

Stationary scalar clouds around a rotating BTZ-like black hole in the Einstein-bumblebee gravity cites this paper.

Stationary scalar clouds around a rotating BTZ-like black hole in the Einstein-bumblebee gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-10T14:06:42.872143Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 569197dc-468e-40d6-b808-ce0ea440736a · inbound

Taub-NUT-like Black Holes in Einstein-Bumblebee Gravity cites this paper.

Taub-NUT-like Black Holes in Einstein-Bumblebee Gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T13:07:49.621324Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9324bc2f-5ce9-437c-8812-b78ef2aa4813 · inbound

Gravitational-wave generation in the presence of Lorentz invariance violation cites this paper.

Gravitational-wave generation in the presence of Lorentz invariance violation Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 57

Resolution: unresolved; no resolver link, observed 2026-08-07T05:05:36.279782Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e08ffe91-404d-4524-a049-ff04497c7c92 · inbound

Spherical photon orbits around the Kerr-like black hole in Einstein-Bumblebee gravity cites this paper.

Spherical photon orbits around the Kerr-like black hole in Einstein-Bumblebee gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-06T20:10:46.023370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80c58bb8-b37b-4846-a136-f5873ad3ff1e · inbound

Gravitational Memory in Generalized Proca Gravity cites this paper.

Gravitational Memory in Generalized Proca Gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-15T16:50:11.102243Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a66b55a-e3f2-434c-9414-4f6559cfa446 · inbound

Probing Lorentz Symmetry Violation through Lensing Observables of Rotating Black Holes cites this paper.

Probing Lorentz Symmetry Violation through Lensing Observables of Rotating Black Holes Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 110

Resolution: unresolved; no resolver link, observed 2026-08-15T16:51:11.456912Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d457604-9f02-4752-9335-90e8534a8741 · inbound

Full Classification of Static Spherical Vacuum Solutions to Bumblebee Gravity with General VEVs cites this paper.

Full Classification of Static Spherical Vacuum Solutions to Bumblebee Gravity with General VEVs Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-05-18T01:50:38.497432Z

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 b778bc7d-20ba-47e8-ab13-bd9480c1e060 · inbound

Cosmological implications of Bumblebee theory on an FLRW background cites this paper.

Cosmological implications of Bumblebee theory on an FLRW background Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-05-17T02:38:54.239015Z

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 288b5fbf-1034-460d-aece-da97223f4a7d · inbound

Higgs-like inflation in scalar-torsion $f(T,\phi)$ gravity in light of ACT-SPT-DESI constraints cites this paper.

Higgs-like inflation in scalar-torsion $f(T,\phi)$ gravity in light of ACT-SPT-DESI constraints Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 95

Resolution: unresolved; no resolver link, observed 2026-08-03T13:26:42.013887Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8521926b-3065-4cf9-8059-7654391fe233 · inbound

Lorentz violating quadratic gravity cites this paper.

Lorentz violating quadratic gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T19:19:29.888029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 098486e4-69d9-4b98-9881-d71438bb1524 · inbound

Complex bumblebee model cites this paper.

Complex bumblebee model Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-05-14T22:19:31.575374Z

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 9c917979-bd37-452a-8ef3-6307dcd79fa2 · inbound

Probing Lorentz-violating effects via precession and accretion disk images of a rotating bumblebee black hole cites this paper.

Probing Lorentz-violating effects via precession and accretion disk images of a rotating bumblebee black hole Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-13T15:01:53.533153Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36bdc0ac-48e3-4704-a717-9ac49100e00f · inbound

Probing Kalb-Ramond gravity with charged rotating black holes: constraints from EHT observations cites this paper.

Probing Kalb-Ramond gravity with charged rotating black holes: constraints from EHT observations Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 126

Resolution: verified exact; arxiv_id, observed 2026-05-10T13:15:26.351611Z

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 7c4a8630-9b89-4d6a-b6b4-55921bfd16af · inbound

Macroscopic Optical Nonreciprocity: A Black Hole as an Optical Diode cites this paper.

Macroscopic Optical Nonreciprocity: A Black Hole as an Optical Diode Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-11T12:06:03.040595Z

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 70fa56a6-9c81-4c02-a1b2-377c7e9b9c39 · inbound

Gravitational-Bumblebee perturbations: Exact decoupling and isospectrality cites this paper.

Gravitational-Bumblebee perturbations: Exact decoupling and isospectrality Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-09T06:40:39.036886Z

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 ca826ade-1d04-45b2-aaa1-65545324a816 · inbound

Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals cites this paper.

Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-05-11T18:21:07.576933Z

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 b4d0ff8b-4288-492a-8b19-875d915ea8c0 · inbound

Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals cites this paper.

Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-05-11T04:36:00.641787Z

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 488501f7-2748-4d66-b9d4-2e67219bef7c · inbound

Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals cites this paper.

Constraining Lorentz symmetry breaking in bumblebee gravity with extreme mass-ratio inspirals Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 59

Resolution: verified exact; local_arxiv, observed 2026-07-01T13:25:45.728323Z

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 da8872d8-5b21-4cf9-8faa-a0809174e5c8 · inbound

When Bumblebee Meets NLED: Lorentz-Violating Black Holes and Regular Spacetimes cites this paper.

When Bumblebee Meets NLED: Lorentz-Violating Black Holes and Regular Spacetimes Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-05-15T02:43:32.720298Z

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 9db0965b-37ef-4af9-bb51-5993b7df0714 · inbound

Constitutive Origin of Hamiltonian Degeneracy in Nonlinear Electrodynamics with Spontaneous Lorentz Symmetry Breaking cites this paper.

Constitutive Origin of Hamiltonian Degeneracy in Nonlinear Electrodynamics with Spontaneous Lorentz Symmetry Breaking Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-05-15T01:49:38.245367Z

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 bfdf20c8-794c-4b41-8ce1-d8af7c0216be · inbound

Scattering, absorption and greybody factor of scalar particles by Lorentz-violating charged black holes cites this paper.

Scattering, absorption and greybody factor of scalar particles by Lorentz-violating charged black holes Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-05-19T22:52:50.663990Z

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 29569288-d0cb-4a89-aaa8-eaadf5d0ae10 · inbound

Black Hole Entropy Beyond the Wald Term in Nonminimally Coupled Gravity: A Covariant Phase Space Decomposition cites this paper.

Black Hole Entropy Beyond the Wald Term in Nonminimally Coupled Gravity: A Covariant Phase Space Decomposition Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-05-22T05:21:07.373672Z

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 6b8fabc2-31d8-4f4b-9774-9dde848b359b · inbound

ModMax black hole surrounded by perfect-fluid dark matter in Lorentz-violating Kalb-Ramond gravity cites this paper.

ModMax black hole surrounded by perfect-fluid dark matter in Lorentz-violating Kalb-Ramond gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-06-30T17:24:56.896136Z

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 b5cdbb7f-01ca-456b-bcaf-0fc5dbb6233f · inbound

Lorentz-Violating (Regular) Black Holes in Einstein Gravity cites this paper.

Lorentz-Violating (Regular) Black Holes in Einstein Gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-06-29T15:23:32.514532Z

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 6070eb85-c387-42b7-811a-a4ecec8193c5 · 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 Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-07-01T17:35:51.419581Z

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 db032ca7-0706-4360-acfb-a09b4b181948 · inbound

Reference Frames and Gravitational-Wave Polarizations: Symmetry Classification and Preferred-Frame Phenomenology cites this paper.

Reference Frames and Gravitational-Wave Polarizations: Symmetry Classification and Preferred-Frame Phenomenology Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-07-02T09:26:50.426062Z

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 50b094cc-c4b1-4419-9692-0ac0ed2e6b21 · inbound

Primordial black hole in Lorentz-violating theories: Insights from Bumblebee gravity cites this paper.

Primordial black hole in Lorentz-violating theories: Insights from Bumblebee gravity Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 61

Resolution: verified exact; local_arxiv, observed 2026-07-09T21:56:38.304514Z

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 7a5e4a45-4aeb-4f93-b003-b662242b3d7a · inbound

Axial Obstructions to Rotating Bumblebee Vacuum Solutions cites this paper.

Axial Obstructions to Rotating Bumblebee Vacuum Solutions Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T18:47:16.831197Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3fe289e1-662d-45b2-9846-b68810a0d391 · inbound

Axial Obstructions to Rotating Bumblebee Vacuum Solutions cites this paper.

Axial Obstructions to Rotating Bumblebee Vacuum Solutions Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T04:21:21.204310Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3644599-f83c-486c-aacc-9168f68dc094 · inbound

New constraints on modified gravity with dimension-six operators from gravitational waves cites this paper.

New constraints on modified gravity with dimension-six operators from gravitational waves Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T15:20:18.946446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28d0ec8d-8937-46b4-845e-f7438c9148d5 · inbound

Overlapping resonance branches of a gauge-invariant Lorentz-violating massive vector cites this paper.

Overlapping resonance branches of a gauge-invariant Lorentz-violating massive vector Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Gravity

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T15:34:25.877511Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.