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Luk, Jonathan; Oh, Sung-Jin; Shlapentokh-Rothman, Yakov

A scattering theory approach to Cauchy horizon instability and applications to mass inflation. (English) Zbl 1521.83136

Ann. Henri Poincaré 24, No. 2, 363-411 (2023).
Summary: Motivated by the strong cosmic censorship conjecture, we study the linear scalar wave equation in the interior of subextremal strictly charged Reissner-Nordström black holes by analyzing a suitably defined “scattering map” at 0 frequency. The method can already be demonstrated in the case of spherically symmetric scalar waves on Reissner-Nordström: we show that assuming suitable \((L^2\)-averaged) upper and lower bounds on the event horizon, one can prove \((L^2\)-averaged) polynomial lower bound for the solution
(1)
on any radial null hypersurface transversally intersecting the Cauchy horizon, and
(2)
along the Cauchy horizon toward timelike infinity.
Taken together with known results regarding solutions to the wave equation in the exterior, (1) above in particular provides yet another proof of the linear instability of the Reissner-Nordström Cauchy horizon. As an application of (2) above, we prove a conditional mass inflation result for a nonlinear system, namely the Einstein-Maxwell-(real)-scalar field system in spherical symmetry. For this model, it is known that for a generic class of Cauchy data \(\mathcal{G}\), the maximal globally hyperbolic future developments are \(C^2\)-future-inextendible. We prove that if a (conjectural) improved decay result holds in the exterior region, then for the maximal globally hyperbolic developments arising from initial data in \(\mathcal{G}\), the Hawking mass blows up identically on the Cauchy horizon.

Cited in 2 Documents

MSC:

83C57 Black holes
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
83E05 Geometrodynamics and the holographic principle
81V22 Unified quantum theories
32S25 Complex surface and hypersurface singularities
83C22 Einstein-Maxwell equations
81U90 Particle decays
58J47 Propagation of singularities; initial value problems on manifolds
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References:

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