Related papers: Structural stability of spherical horizons
A spherical dust cloud which is initially at rest and which has a monotonously decaying density profile collapses and forms a shell-focussing singularity. Provided the density profile is not too flat, meaning that its second radial…
We study some features of static and spherically symmetric solutions (SSS) with a horizon in $f(R)$ theories of gravitation by means of a near-horizon analysis. A necessary condition for an $f(R)$ theory to have this type of solution is…
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…
For the Schr\"odinger equation with a cubic-quintic, focusing-defocusing nonlinearity in one space dimension, we prove the asymptotic stability of solitary waves for a large range of admissible frequencies. For this model, the linearized…
We study static, spherically symmetric black hole solutions of the Einstein equations with a positive cosmological constant and a conformally coupled self interacting scalar field. Exact solutions for this model found by Mart{\'\i}nez,…
Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they…
We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [Walkington 2014],…
Several properties of canonical quantum gravity modify space-time structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then…
Black hole apparent horizons possess a natural notion of stability, whose spectral characterization can be related to the problem of the stationary quantum charged particle. Such mathematical relation leads to an "analyticity conjecture" on…
We examine the robustness of black hole ringdown to stochastic horizon-scale structure within an effective field framework. Consistent with the understanding that the spectral instability of quasinormal modes does not necessarily imply…
We consider stability properties of spherically symmetric spacetimes of stars in metric f(R) gravity. We stress that these not only depend on the particular model, but also on the specific physical configuration. Typically configurations…
A class of exact solutions of the field equations with higher derivative terms is presented when the matter field is a pressureless null fluid plus a Maxwellian static electric component. It is found that the stable solutions are black…
Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered, with the Maxwell…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
For arbitrary static space-times, it is shown that an equilibrium between a Killing horizon and matter is only possible for some discrete values of the parameter $w = p_1/\rho$, where $\rho$ is the density and $p_1$ is pressure in the…
In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the…
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…
We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the phase space and the Hamiltonian of general…
The presence and evolution of apparent horizons in a two-parameter family of spherically symmetric, time-dependent solutions of Brans-Dicke gravity are analyzed. These solutions were introduced to model space- and time-varying gravitational…
We revisit the stability analysis of cylindrical thin shell wormholes which have been studied in literature so far. Our approach is more systematic and in parallel to the method which is used in spherically symmetric thin shell wormholes.…