Boundedness of massless scalar waves on Kerr interior backgrounds | Paper Citation Record

Observation 7e87487a-69ca-403b-8f75-50f86b719e3f · outbound

This paper cites Therefore, we are interested in the error term EV (Yψ ) = 2g(Yψ )V (Yψ ), (E1) resulting from commutation with the vector ﬁeld Y as deﬁned in (94), according to (17).

Boundedness of massless scalar waves on Kerr interior backgrounds Therefore, we are interested in the error term EV (Yψ ) = 2g(Yψ )V (Yψ ), (E1) resulting from commutation with the vector ﬁeld Y as deﬁned in (94), according to (17)

Reference 1

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Observation 2171ca20-8b71-4655-b715-1f61082ae73f · outbound

This paper cites Appendix F: The wave equation and higher derivatives The wave on ﬁxed background is given by 2gψ = 1√−g ∂ ∂xµ ( gµν√−g ∂ψ ∂xν ) , (F1) where√−g = 2Ω2L sinθ.

Boundedness of massless scalar waves on Kerr interior backgrounds Appendix F: The wave equation and higher derivatives The wave on ﬁxed background is given by 2gψ = 1√−g ∂ ∂xµ ( gµν√−g ∂ψ ∂xν ) , (F1) where√−g = 2Ω2L sinθ

Reference 2

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Observation 22de2b65-9691-4a74-91bf-2755593f93c9 · outbound

This paper cites Stability and Instability of Extreme Reissner-Nordstr\"om Black Hole Spacetimes for Linear Scalar Perturbations I.

Boundedness of massless scalar waves on Kerr interior backgrounds Stability and Instability of Extreme Reissner-Nordstr\"om Black Hole Spacetimes for Linear Scalar Perturbations I

Reference 3

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Observation 16a5fa26-3512-40e2-8ecb-fe617f57560e · outbound

This paper cites Propagation through the redshift region R to r⋆ =r⋆ red The following proposition was shown in [23], see also [60] for a detailed proof.

Boundedness of massless scalar waves on Kerr interior backgrounds Propagation through the redshift region R to r⋆ =r⋆ red The following proposition was shown in [23], see also [60] for a detailed proof

Reference 4

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This paper cites Recall that the crux of our proof was to obtain estimates which actually reach up tov =∞, which we have shown in our analysis of the characteristic rectangle Ξ.

Boundedness of massless scalar waves on Kerr interior backgrounds Recall that the crux of our proof was to obtain estimates which actually reach up tov =∞, which we have shown in our analysis of the characteristic rectangle Ξ

Reference 5

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This paper cites poor man’s.

Boundedness of massless scalar waves on Kerr interior backgrounds poor man’s

Reference 6

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 7

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Observation e990f646-56e6-4c00-9400-88c74b03ef3d · outbound

This paper cites Hidden symmetries and decay for the wave equation on the Kerr spacetime.

Boundedness of massless scalar waves on Kerr interior backgrounds Hidden symmetries and decay for the wave equation on the Kerr spacetime

Reference 8

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Observation 6df2a518-008e-418f-998a-33b92b91a55e · outbound

This paper cites The Formation of Black Holes in General Relativity.

Boundedness of massless scalar waves on Kerr interior backgrounds The Formation of Black Holes in General Relativity

Reference 9

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Observation 699705e3-8512-4cfe-8ef0-dd5cbe8c5a19 · outbound

This paper cites Stability and Instability of Extreme Reissner-Nordstr\"om Black Hole Spacetimes for Linear Scalar Perturbations II.

Boundedness of massless scalar waves on Kerr interior backgrounds Stability and Instability of Extreme Reissner-Nordstr\"om Black Hole Spacetimes for Linear Scalar Perturbations II

Reference 10

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Observation 858da620-8510-4fab-a9ed-66da1b57dd5e · outbound

This paper cites Decay of Axisymmetric Solutions of the Wave Equation on Extreme Kerr Backgrounds.

Boundedness of massless scalar waves on Kerr interior backgrounds Decay of Axisymmetric Solutions of the Wave Equation on Extreme Kerr Backgrounds

Reference 11

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Observation bd9e0fe1-c4b4-4c0d-83c8-b09473110fc2 · outbound

This paper cites Note that n depends only on the smallness condition on ϵ from Proposition 4.20, since n ≲ u⋄−u ϵ.

Boundedness of massless scalar waves on Kerr interior backgrounds Note that n depends only on the smallness condition on ϵ from Proposition 4.20, since n ≲ u⋄−u ϵ

Reference 12

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 13

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 14

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 15

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Observation 1892c08a-78f2-4b7d-8136-7f0d605a8415 · outbound

This paper cites Bounded energy waves on the black hole interior of Reissner-Nordstr\"om-de Sitter.

Boundedness of massless scalar waves on Kerr interior backgrounds Bounded energy waves on the black hole interior of Reissner-Nordstr\"om-de Sitter

Reference 16

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Observation 6633da9b-d426-4a00-a6c0-750dd81e05cd · outbound

This paper cites On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions.

Boundedness of massless scalar waves on Kerr interior backgrounds On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 3: Mass inflation and extendibility of the solutions

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:43:46.512448Z

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Observation 7a2714c4-fa6d-4222-a44b-e7b846cd2efe · outbound

This paper cites On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon.

Boundedness of massless scalar waves on Kerr interior backgrounds On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 2: Structure of the solutions and stability of the Cauchy horizon

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:43:46.496640Z

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Observation b060e3fe-5581-44c9-85d7-e51e8cbb0978 · outbound

This paper cites On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion.

Boundedness of massless scalar waves on Kerr interior backgrounds On the global uniqueness for the Einstein-Maxwell-scalar field system with a cosmological constant. Part 1: Well posedness and breakdown criterion

Reference 19

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Observation 2453cf4d-3af0-40e4-bbdf-5b08d563ed9e · outbound

This paper cites On the occurrence of mass inflation for the Einstein-Maxwell-scalar field system with a cosmological constant and an exponential Price law.

Boundedness of massless scalar waves on Kerr interior backgrounds On the occurrence of mass inflation for the Einstein-Maxwell-scalar field system with a cosmological constant and an exponential Price law

Reference 20

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.888322Z

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.876743Z

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Observation 8170f78f-4ed2-49b2-93fe-bf85f206b03c · outbound

This paper cites Black holes without spacelike singularities.

Boundedness of massless scalar waves on Kerr interior backgrounds Black holes without spacelike singularities

Reference 23

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 24

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Observation 973d1d81-03f7-4646-8178-9d3dfe4538ee · outbound

This paper cites and Luk, J.

Boundedness of massless scalar waves on Kerr interior backgrounds and Luk, J

Reference 25

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Observation 8868ed04-d7f3-4d58-b56d-a439b7c06f70 · outbound

This paper cites and Rodnianski, I.

Boundedness of massless scalar waves on Kerr interior backgrounds and Rodnianski, I

Reference 26

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Observation 76c62d2e-b4bf-4473-a4b2-f429edb6f2b2 · outbound

This paper cites Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: The cases |a| << M or axisymmetry.

Boundedness of massless scalar waves on Kerr interior backgrounds Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: The cases |a| << M or axisymmetry

Reference 27

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Observation 57f56865-6923-4a9d-a058-2a2471d883d5 · outbound

This paper cites A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds.

Boundedness of massless scalar waves on Kerr interior backgrounds A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds

Reference 28

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Observation 341aeb04-10e0-4832-ad4c-2be876270161 · outbound

This paper cites Lectures on black holes and linear waves.

Boundedness of massless scalar waves on Kerr interior backgrounds Lectures on black holes and linear waves

Reference 29

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Observation 4f32c1db-4d82-490d-aa44-e17775cf00d8 · outbound

This paper cites Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes.

Boundedness of massless scalar waves on Kerr interior backgrounds Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes

Reference 30

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Observation 9bfa9dbb-2ab6-47c4-aa7c-c9f08806d490 · outbound

This paper cites and Rodninanski, I.

Boundedness of massless scalar waves on Kerr interior backgrounds and Rodninanski, I

Reference 31

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This paper cites The linear stability of the Schwarzschild solution to gravitational perturbations.

Boundedness of massless scalar waves on Kerr interior backgrounds The linear stability of the Schwarzschild solution to gravitational perturbations

Reference 32

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This paper cites Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M.

Boundedness of massless scalar waves on Kerr interior backgrounds Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M

Reference 33

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 34

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 35

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Observation 57d4d384-4610-439f-bf1b-16b8b4662805 · outbound

This paper cites Boundedness of massless scalar waves on Reissner-Nordstr\"om interior backgrounds.

Boundedness of massless scalar waves on Kerr interior backgrounds Boundedness of massless scalar waves on Reissner-Nordstr\"om interior backgrounds

Reference 36

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 37

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Observation 6c4c472a-8211-415b-9ae7-528db77c8382 · outbound

This paper cites Linear waves in the interior of extremal black holes I.

Boundedness of massless scalar waves on Kerr interior backgrounds Linear waves in the interior of extremal black holes I

Reference 38

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This paper cites Linear waves in the interior of extremal black holes II.

Boundedness of massless scalar waves on Kerr interior backgrounds Linear waves in the interior of extremal black holes II

Reference 39

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 40

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 41

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Observation 2ba8cad3-0a15-43a4-a9ff-c875e0e8e229 · outbound

This paper cites Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime.

Boundedness of massless scalar waves on Kerr interior backgrounds Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime

Reference 42

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Observation e6dde223-45fa-4f1a-9202-fbe217d04d10 · outbound

This paper cites Analysis of linear waves near the Cauchy horizon of cosmological black holes.

Boundedness of massless scalar waves on Kerr interior backgrounds Analysis of linear waves near the Cauchy horizon of cosmological black holes

Reference 43

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This paper cites The global non-linear stability of the Kerr-de Sitter family of black holes.

Boundedness of massless scalar waves on Kerr interior backgrounds The global non-linear stability of the Kerr-de Sitter family of black holes

Reference 44

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 45

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 46

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 47

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Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 48

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Observation 228d9ffc-bf5f-4b67-9203-74c010fea9ec · outbound

This paper cites Weak null singularities in general relativity.

Boundedness of massless scalar waves on Kerr interior backgrounds Weak null singularities in general relativity

Reference 49

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This paper cites Proof of linear instability of the Reissner-Nordstr\"om Cauchy horizon under scalar perturbations.

Boundedness of massless scalar waves on Kerr interior backgrounds Proof of linear instability of the Reissner-Nordstr\"om Cauchy horizon under scalar perturbations

Reference 50

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Observation e7818085-d5f1-400c-8b56-f6b61de2ce19 · outbound

This paper cites Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data I. The interior of the black hole region.

Boundedness of massless scalar waves on Kerr interior backgrounds Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data I. The interior of the black hole region

Reference 51

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This paper cites Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II. The exterior of the black hole region.

Boundedness of massless scalar waves on Kerr interior backgrounds Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II. The exterior of the black hole region

Reference 52

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Observation 49f52fad-63f1-417b-9b1f-93f2a21e6845 · outbound

This paper cites and Sbierski, J.

Boundedness of massless scalar waves on Kerr interior backgrounds and Sbierski, J

Reference 53

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Observation 3b1b4fd3-ac5c-4bc6-a01d-9d24961d56ef · outbound

This paper cites and Tohaneanu, M.

Boundedness of massless scalar waves on Kerr interior backgrounds and Tohaneanu, M

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:43:46.741748Z

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 3bf1f812-a1db-4935-9370-009cd58c320b · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.730217Z

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 12506309-2ce3-4965-9c05-2f75a0f9e09b · outbound

This paper cites Conformal scattering on the Schwarzschild metric.

Boundedness of massless scalar waves on Kerr interior backgrounds Conformal scattering on the Schwarzschild metric

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-14T10:43:45.817261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e5563d4-8a58-4b34-ae80-4424858ac92e · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.718539Z

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 70d29e0a-59a7-4c70-abef-07be94c601bd · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.706666Z

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 e2914a82-c06b-4f3f-a82f-d8878fed6e91 · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.695278Z

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 a00c4ecb-81c3-4bd0-b853-2e8348ead93a · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 60

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.684382Z

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 9285c61d-1dcf-44c7-abc7-4f0868730d35 · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 61

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.673909Z

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 c398de88-638e-4074-9f73-c4f4a21864ba · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 62

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.663200Z

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 c77c24e9-89de-42e4-923a-feedfac1583e · outbound

This paper cites and Walker, M.

Boundedness of massless scalar waves on Kerr interior backgrounds and Walker, M

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:43:46.652317Z

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 84d9d6de-596c-4a61-b734-86272d63f730 · outbound

This paper cites and Israel, W.

Boundedness of massless scalar waves on Kerr interior backgrounds and Israel, W

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:43:46.640965Z

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 01b6ac56-4dae-4712-b9eb-880534c16ca8 · outbound

This paper cites Quasi-Spherical Light Cones of the Kerr Geometry.

Boundedness of massless scalar waves on Kerr interior backgrounds Quasi-Spherical Light Cones of the Kerr Geometry

Reference 65

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:43:45.945042Z

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 5fe3b33f-7bb4-4a51-9128-f9153739a636 · outbound

This paper cites Decay of linear waves on higher dimensional Schwarzschild black holes.

Boundedness of massless scalar waves on Kerr interior backgrounds Decay of linear waves on higher dimensional Schwarzschild black holes

Reference 66

Resolution: verified exact; local_arxiv, observed 2026-08-14T10:43:45.927858Z

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 d6a6eab7-a86e-4889-9643-57361d22eda3 · outbound

This paper cites Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime.

Boundedness of massless scalar waves on Kerr interior backgrounds Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-14T10:43:45.857296Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dde01d13-4ea7-4666-b6df-c9cd518dbd53 · outbound

This paper cites and Penrose, R.

Boundedness of massless scalar waves on Kerr interior backgrounds and Penrose, R

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:43:46.628509Z

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 a07d673a-f952-4778-8f1b-d08bf3b11d0a · outbound

This paper cites and Tohaneanu, M.

Boundedness of massless scalar waves on Kerr interior backgrounds and Tohaneanu, M

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:43:46.616939Z

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 71d616b0-7751-4f84-a4b6-2f0a94eea525 · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 70

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.605518Z

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 b369f39a-771f-49b3-9b46-4c5deb3bc735 · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 71

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.594384Z

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 49f3121b-3e64-41de-b8a9-0790ee1512d6 · outbound

This paper cites an unresolved cited work.

Boundedness of massless scalar waves on Kerr interior backgrounds Unresolved cited work

Reference 72

Resolution: unresolved; raw_fallback, observed 2026-08-14T10:43:46.582956Z

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.

Coverage vector

Reference resolution

Outbound references

Pith citing papers