Related papers: The wave equation on Schwarzschild-de Sitter space…
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…
Here we prove a global existence theorem for the solutions of the semi-linear wave equation with critical non-linearity admitting a positive definite Hamiltonian. Formulating a parametrix for the wave equation in a globally hyperbolic…
The quasinormal-mode spectrum of the Schwarzschild-de Sitter black hole is studied in the limit of near-equal black-hole and cosmological radii. It is found that the mode_frequencies_ agree with the P"oschl-Teller approximation to one more…
This paper investigates the decay properties of solutions to the massive linear wave equation $\Box_g \psi + \frac{{\alpha}}{l^2} \psi =0$ for $g$ the metric of a Kerr-AdS spacetime satisfying $|a|l<r_+^2$ and $\alpha<9/4$ satisfying the…
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak…
We use a novel physical space method to prove relatively non-degenerate integrated energy estimates for the wave equation on subextremal Schwarzschild-de Sitter spacetimes with parameters $(M,\Lambda)$. These are integrated decay statements…
We investigate static spherically symmetric solutions within the framework of the local limit of nonlocal gravity. This theory departs from Einstein's general relativity (GR) through the introduction of a scalar gravitational susceptibility…
We investigate the quantum evolution of large black holes that nucleate spontaneously in de Sitter space. By numerical computation in the s-wave and one-loop approximations, we verify claims that such black holes can initially…
We prove the non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region: general vacuum initial data, with no symmetry assumed, sufficiently close to…
We prove global existence and decay for small-data solutions to a class of quasilinear wave equations on a wide variety of asymptotically flat spacetime backgrounds, allowing in particular for the presence of horizons, ergoregions and…
The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m>0 which is characterized by the condition that 9 Lambda m^2=1. The global…
We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both…
Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity.…
It has recently been demonstrated (Class. Quantum Grav. 31, 085010, 2014) that the conformally invariant wave equation on a Minkowski background can be solved with a fully pseudospectral numerical method. In particular, it is possible to…
We consider solutions of the massless scalar wave equation $\Box_g\psi=0$ on a fixed Rindler background and show polynomial decay of the energy flux related to the Rindler observers near null infinity and to local observers near the Rindler…
Recently, Hawking radiation has been treated, by Robinson and Wilczek, as a compensating flux of the energy momentum tensor required to cancel gavitational anomaly at the event horizon(EH) of a Schwarzschild-type black hole. In this paper,…
In this last part of the series we prove that the slow (inverse logarithmic) decay in time of solutions to the linearised Einstein equations on Schwarzschild-Anti-de Sitter backgrounds obtained in~\cite{Gra.Hol24,Gra.Hol24a} is in fact…
We give a short introduction to the formalism of noncommutative (twisted) differential geometry that is used to derive the equations of motion for the gravitational perturbation of the Schwarzschild black hole in quantized spacetime.…
We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes. Specifically, we derive a new hierarchy of higher-order weighted energy estimates by…
In general relativity, nonsingular black holes contain (at least) a Cauchy horizon, a null hypersurface beyond which determinism breaks down. Even though the strong cosmic censorship conjecture establishes the impossibility of extending…