Related papers: The formation of a weak null singularity in the in…
We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere. The metric of these spacetimes extends…
These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and…
It is widely expected that generic black holes have a non-empty but weakly singular Cauchy horizon, due to mass inflation. Indeed this has been proven by the author in the spherical collapse of a charged scalar field, under decay…
We prove the precise asymptotics of the spin $-2$ Teukolsky field in the interior and along the Cauchy horizon of a subextremal Kerr black hole. Together with the oscillatory blow-up asymptotics of the spin $+2$ Teukolsky field proven in…
We consider solutions of the Einstein vacuum equations which arise from smooth initial data on a hypersurface slightly inside a dynamical black hole settling down to a subextremal Kerr black hole, and satisfying a precise non-linear Price's…
Extreme black holes have been argued to be unstable, in the sense that under linearized gravitational perturbations of the extreme Kerr spacetime the Weyl scalar $\psi_4$ blows up along their event horizons at very late advanced times. We…
This paper establishes a mathematical proof of the blue-shift instability at the sub-extremal Kerr Cauchy horizon for the linearised vacuum Einstein equations. More precisely, we exhibit conditions on the $s=+2$ Teukolsky field, consisting…
In this paper we prove integrated energy and pointwise decay estimates for solutions of the vacuum linearized Einstein equation on the domain of outer communication of the Kerr black hole spacetime. The estimates are valid for the full…
We study the behavior of a self-gravitating perfect relativistic fluid satisfying the Einstein-Euler system in the presence of a weak null terminal spacetime singularity. This type of singularities is expected in the interior of generic…
It was long believed that the singularity inside a realistic, rotating black hole must be spacelike. However, studies of the internal geometry of black holes indicate a more complicated structure is typical. While it seems likely that an…
We examine whether the Schwarzschild black hole can emerge as the continuous end state of gravitational collapse from a non-singular configuration. Employing a time dependent extension of the regular Schwarzschild metric, we track the…
We begin a program of work aimed at examining the interior of a rotating black hole with a non--zero cosmological constant. The generalisation of Teukolsky's equation for the radial mode functions is presented. It is shown that the energy…
The initial idea underlying the Weak Gravity Conjecture is that extremal black holes must always be "unstable", in the sense that they should slowly decay by emitting either particles or smaller black holes. Here we show that, when this…
We prove the $C^{0,1}_{\mathrm{loc}}$-inextendibility of weak null singularities without any symmetry assumptions. The proof introduces a new strategy to infer $C^{0,1}_{\mathrm{loc}}$-inextendibility from the blow-up of curvature. The…
We analytically study the linear response of a near-extremal Kerr black hole to external scalar, electromagnetic, and gravitational field perturbations. We show that the energy density, electromagnetic field strength, and tidal force…
It is proven that for smooth initial data with compact support outside the event horizon, the solution of every azimuthal mode of the Teukolsky equation for general spin decays pointwise in time.
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations…
We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of…
It is shown that for small, spherically symmetric perturbations of asymptotically flat two-ended Reissner-Nordstr\"om data for the Einstein-Maxwell-real scalar field system, the boundary of the dynamic spacetime which evolves is globally…
We study gravitational perturbations on the near-horizon region of extremal and near-extremal rotating black holes in a general higher-derivative extension of Einstein gravity. We find a decoupled modified Teukolsky equation that rules the…