相关论文: Mode stability on the real axis

We prove boundedness and polynomial decay statements for solutions of the Teukolsky system for electromagnetic-gravitational perturbations of a Kerr-Newman exterior background, with parameters satisfying $|a|, |Q| \ll M$. The identification…

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized…

We compute the radiation emitted by a particle on the innermost stable circular orbit of a rapidly spinning black hole both (a) analytically, working to leading order in the deviation from extremality and (b) numerically, with a new…

A massive vector boson field in the vicinity of a rotating black hole is known to suffer an instability, due to the exponential amplification of (co-rotating, low-frequency) bound states by black hole superradiance. Here we calculate the…

It has been known classically that a star with an ergoregion but no event horizon is unstable to the emission of scalar, electromagnetic and gravitational waves. This classical ergoregion instability is characterized by complex frequency…

We examine the modes admitted by the Mestel disk, a disk with a globally flat rotation curve. In contrast to previous analyses of this problem by Zang (\cite{1976PhDT........26Z}) and Evans & Read (\cite{1998MNRAS.300...83E},…

Modifications to general relativity lead to effects in the spectrum of quasi-normal modes of black holes. In this paper, we develop a parametrized formalism to describe deviations from general relativity in the Teukolsky equation, which…

An existence and stability result for a class of purely radiative vacuum spacetimes arising from hyperboloidal data is given. This result generalises semiglobal existence results for Minkowski-like spacetimes to the case where the reference…

A Kerr-de Sitter black hole is a solution $(M,g_{\Lambda,\mathfrak{m},\mathfrak{a}})$ of the Einstein vacuum equations with cosmological constant $\Lambda>0$. It describes a black hole with mass $\mathfrak{m}>0$ and specific angular…

This paper proves the existence of a bounded energy and integrated energy decay for solutions of the massless Vlasov equation in the exterior of a very slowly rotating Kerr spacetime. This combines methods previously developed to prove…

This paper establishes the existence of quasinormal frequencies converging exponentially to the real axis for the Klein--Gordon equation on a Kerr-AdS spacetime when Dirichlet boundary conditions are imposed at the conformal boundary. The…

We prove that for axially symmetric linear gravitational perturbations of the extreme Kerr black hole there exists a positive definite and conserved energy. This provides a basic criteria for linear stability in axial symmetry. In the…

We prove the existence of instabilities for the geometric linear wave equation on extremal Kerr spacetime backgrounds, which describe stationary black holes rotating at their maximally allowed angular velocity. These instabilities can be…

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability as functions of the wave vector, the dissipation, and the density. In contrast…

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…

Motivated by recent results reporting the instability of horizonless objects with stable light rings, we revisit the linearized stability of such structures. In particular, we consider an exterior Kerr spacetime truncated at a surface where…

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kami\'nski [Gen Rel Grav 45 (2013)…

Black hole dynamical instabilities have been mostly studied in specific models. We here study the general properties of the complex-frequency modes responsible for such instabilities, guided by the example of a charged scalar field in an…

We present a novel theoretical framework for analysing the stability of rotating black hole spacetimes through the conformal properties of the Weyl tensor. By introducing a new conformal invariant constructed from the electric and magnetic…

The theory of polar forms of polynomials is used to provide for sharp bounds on the radius of the largest possible disc (absolute stability radius), and on the length of the largest possible real interval (parabolic stability radius), to be…