Numerical methods for finding stationary gravitational solutions

ÓJC Dias, JE Santos, B Way - Classical and Quantum Gravity, 2016 - iopscience.iop.org
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled
the search for new stationary solutions of the Einstein equation (possibly coupled to matter) …

Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov)

A Vasy - Inventiones mathematicae, 2013 - Springer
In this paper we develop a general, systematic, microlocal framework for the Fredholm
analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which …

A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds

M Dafermos, I Rodnianski - Inventiones mathematicae, 2011 - Springer
We consider Kerr spacetimes with parameters a and M such that| a|≪ M, Kerr-Newman
spacetimes with parameters| Q|≪ M,| a|≪ M, and more generally, stationary axisymmetric …

Decay Properties of Klein‐Gordon Fields on Kerr‐AdS Spacetimes

G Holzegel, J Smulevici - Communications on Pure and …, 2013 - Wiley Online Library
This paper investigates the decay properties of solutions to the massive linear wave
equation for g being the metric of a Kerr‐AdS spacetime satisfying satisfying the …

Recent progress on the fractional Laplacian in conformal geometry

M del Mar González - arxiv preprint arxiv:1609.08988, 2016 - degruyter.com
The aim of this paper is to report on recent development on the conformal fractional
Laplacian, both from the analytic and geometric points of view, but especially towards the …

A proof of the instability of AdS for the Einstein--massless Vlasov system

G Moschidis - arxiv preprint arxiv:1812.04268, 2018 - arxiv.org
In recent years, the AdS instability conjecture, put forward by Dafermos-Holzegel in 2006,
has attracted a substantial amount of numerical and heuristic studies. Following the …

Semilinear wave equations on asymptotically de Sitter, Kerr–de Sitter and Minkowski spacetimes

P Hintz, A Vasy - Analysis & PDE, 2015 - msp.org
We show the small data solvability of suitable semilinear wave and Klein–Gordon equations
on geometric classes of spaces, which include so-called asymptotically de Sitter and Kerr …

Hadamard states for a scalar field in anti–de Sitter spacetime with arbitrary boundary conditions

C Dappiaggi, HRC Ferreira - Physical Review D, 2016 - APS
We consider a real, massive scalar field on PAdS d+ 1, the Poincaré domain of the (d+ 1)-
dimensional anti–de Sitter (AdS) spacetime. We first determine all admissible boundary …

Quasimodes and a lower bound on the uniform energy decay rate for Kerr–AdS spacetimes

G Holzegel, J Smulevici - Analysis & PDE, 2014 - msp.org
We construct quasimodes for the Klein–Gordon equation on the black hole exterior of Kerr–
AdS (anti-de Sitter) spacetimes. Such quasimodes are associated with time-periodic …

The massive wave equation in asymptotically AdS spacetimes

CM Warnick - Communications in Mathematical Physics, 2013 - Springer
We consider the massive wave equation on asymptotically AdS spaces. We show that the
timelike F behaves like a finite timelike boundary, on which one may impose the equivalent …