Instability of the Kerr Cauchy horizon under linearised gravitational perturbations

Sbierski, Jan

doi:10.48550/arxiv.2201.12295

Cited by 3 publications

(7 citation statements)

References 54 publications

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“…Proof. (87) follows immediately from (86), (53) and the fact that B −1/2 is a bijection from H to D. As / D, D x and D ϕ commute with B, (88) follows from (87). To prove the two estimates in (89), we use (87) and (88) with the following two identities,…”

Section: The Comparison Operatormentioning

confidence: 93%

“…[11,16,28,46,56] for a general overview on the maximal analytic extensions. Also see [32,34,53] for brief descriptions of the constructions relevant to the interior of black holes.…”

Section: The Kerr-newman(-anti)-de Sitter Metricsmentioning

confidence: 99%

“…The same year, Sbierksi provided a mathematical proof of the blue-shift instability at the Cauchy horizon in a sub-extremal Kerr black hole Teukolsky equation of spin-2 fields, also using a scattering approach [53].…”

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confidence: 99%

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Conformal scattering and the Goursat problem for Dirac fields in the interior of charged spherically symmetric black holes

Mokdad

2022

Rev. Math. Phys.

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In this paper, we construct a conformal scattering theory for Dirac fields in the interior of a Reissner–Nordström-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.

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Section: The Comparison Operatormentioning

confidence: 93%

“…[11,16,28,46,56] for a general overview on the maximal analytic extensions. Also see [32,34,53] for brief descriptions of the constructions relevant to the interior of black holes.…”

Section: The Kerr-newman(-anti)-de Sitter Metricsmentioning

confidence: 99%

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Conformal scattering and the Goursat problem for Dirac fields in the interior of charged spherically symmetric black holes

Mokdad

2022

Rev. Math. Phys.

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“…For intrinsic definitions and properties of these spaces, see also the original work [NP66], or [DHR19a] or [Sbi22]. In large parts of the physics literature on spin s-weighted functions, readers will likely also encounter the eth operators (eth referring to the Old English letter ð):…”

Section: Computing a Few Higher-order Limitsmentioning

confidence: 99%

The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher $$\ell $$-Modes of Linear Waves on a Schwarzschild Background

Kehrberger

2022

Ann. PDE

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In this paper, we derive the early-time asymptotics for fixed-frequency solutions $$\phi _\ell $$ ϕ ℓ to the wave equation $$\Box _g \phi _\ell =0$$ □ g ϕ ℓ = 0 on a fixed Schwarzschild background ($$M>0$$ M > 0 ) arising from the no incoming radiation condition on $${\mathscr {I}}^-$$ I - and polynomially decaying data, $$r\phi _\ell \sim t^{-1}$$ r ϕ ℓ ∼ t - 1 as $$t\rightarrow -\infty $$ t → - ∞ , on either a timelike boundary of constant area radius $$r>2M$$ r > 2 M (I) or an ingoing null hypersurface (II). In case (I), we show that the asymptotic expansion of $$\partial _v(r\phi _\ell )$$ ∂ v ( r ϕ ℓ ) along outgoing null hypersurfaces near spacelike infinity $$i^0$$ i 0 contains logarithmic terms at order $$r^{-3-\ell }\log r$$ r - 3 - ℓ log r . In contrast, in case (II), we obtain that the asymptotic expansion of $$\partial _v(r\phi _\ell )$$ ∂ v ( r ϕ ℓ ) near spacelike infinity $$i^0$$ i 0 contains logarithmic terms already at order $$r^{-3}\log r$$ r - 3 log r (unless $$\ell =1$$ ℓ = 1 ). These results suggest an alternative approach to the study of late-time asymptotics near future timelike infinity $$i^+$$ i + that does not assume conformally smooth or compactly supported Cauchy data: In case (I), our results indicate a logarithmically modified Price’s law for each $$\ell $$ ℓ -mode. On the other hand, the data of case (II) lead to much stronger deviations from Price’s law. In particular, we conjecture that compactly supported scattering data on $${\mathscr {H}}^-$$ H - and $${\mathscr {I}}^-$$ I - lead to solutions that exhibit the same late-time asymptotics on $${\mathscr {I}}^+$$ I + for each $$\ell $$ ℓ : $$r\phi _\ell |_{{\mathscr {I}}^+}\sim u^{-2}$$ r ϕ ℓ | I + ∼ u - 2 as $$u\rightarrow \infty $$ u → ∞ .

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“…In these two H 1 loc -inextendibility results, they both rely on conservation laws associated to Killing vector fields to derive the lower bound for the energy flux on a hypersurface transversally asymptotic to the Cauchy horizon. Recently, Luk-Oh-Shlapentokh-Rothman [38] reproved the H 1 loc -inextendibility result of [35] in R-N spacetimes by analyzing the scattering map near 0 time-frequency, and Sbierski [58] adapted this approach to show the instability of the Kerr Cauchy horizon for the linearized gravity by assuming suitable integrated upper and lower bounds of decay on the event horizon 10 .…”

Section: Main Statement and Introductionmentioning

confidence: 99%

Precise late-time asymptotics of scalar field in the interior of a subextreme Kerr black hole and its application in Strong Cosmic Censorship conjecture

Ma¹,

Zhang²

2022

Preprint

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In this work, we compute the precise late-time asymptotics for the scalar field in the interior of a non-static subextreme Kerr black hole, based on recent progress on deriving its precise asymptotics in the Kerr exterior region. This provides a new proof of the generic H 1 locinextendibility of the Kerr Cauchy horizon against scalar perturbations that is first shown by . The analogous results in Reissner-Nordström spacetimes are also discussed.

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Instability of the Kerr Cauchy horizon under linearised gravitational perturbations

Cited by 3 publications

References 54 publications

Conformal scattering and the Goursat problem for Dirac fields in the interior of charged spherically symmetric black holes

Conformal scattering and the Goursat problem for Dirac fields in the interior of charged spherically symmetric black holes

The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher $$\ell $$-Modes of Linear Waves on a Schwarzschild Background

Precise late-time asymptotics of scalar field in the interior of a subextreme Kerr black hole and its application in Strong Cosmic Censorship conjecture

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