相关论文: Small-amplitude nonlinear waves on a black hole ba…

We study scattering solutions $\phi$ of the linear wave equation on extremal Reissner-Nordstr\"{o}m spacetimes, satisfying the following properties: i) $\phi$ attains a prescribed radiation field $\psi_{\mathcal{I}}$ through future null…

We consider solutions to the linear wave equation in the interior region of extremal Reissner-Nordstr\"om black holes. We show that, under suitable assumptions on the initial data, the solutions can be extended continuously beyond the…

In this article we study the blow-up phenomena for the solutions of the semilinear Klein-Gordon equation $\Box_g \phi-m^2 \phi = -|\phi |^p $ with the small mass $m \le n/2$ in de Sitter space-time with the metric $g$. We prove that for…

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically…

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are…

We study both of the scattering and Cauchy problems for the semilinear wave equation with null quadratic form on the Schwarzschild background. Prescribing the scattering data that are given by the short pulse data on the future null…

An axisymmetric collapse of non-rotating gravitational waves is numerically investigated in the subcritical regime where no black holes form but where curvature attains a maximum and decreases, following the dispersion of the initial wave…

In this paper, the real scalar field equation in Schwarzschild-de Sitter spacetime is solved numerically with high precision. A method called polynomial approximation is introduced to derive the relation between the tortoise coordinate x…

Spherically symmetric solutions in Brans-Dicke theory of relativity with zero coupling constant, $\omega=0$, are derived in the Schwarzschild line-element. The solutions are obtained from a cubic transition equation with one small…

We consider the global regularity problem for nonlinear wave systems $$ \Box u = f(u) $$ on Minkowski spacetime ${\bf R}^{1+d}$ with d'Alambertian $\Box := -\partial_t^2 + \sum_{i=1}^d \partial_{x_i}^2$, where the field $u \colon {\bf…

Static spherically symmetric black holes and particle like solutions with self interacting minimally coupled scalar field {\phi} are analyzed. They are asymptotically flat or anti-de Sitter (AdS). We express them in terms of a single…

The stability of naked singularities in self-similar collapse is probed using scalar waves. It is shown that the multipoles of a minimally coupled massless scalar field propagating on a spherically symmetric self-similar background…

Following an earlier suggestion of the authors(gr-qc/9607030), we use some basic properties of Euclidean black hole thermodynamics and the quantum mechanics of systems with periodic phase space coordinate to derive the discrete…

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…

We show that linear scalar waves are bounded and continuous up to the Cauchy horizon of Reissner-Nordstr\"om-de Sitter and Kerr-de Sitter spacetimes, and in fact decay exponentially fast to a constant along the Cauchy horizon. We obtain our…

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and…

It is shown that the axial and polar perturbations of the spherically symmetric black hole can be described in a gauge-invariant way. The reduced phase space describing gravitational waves outside of the horizon is described by the…

We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…

We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation…

We study the structure and stability of the recently discussed spherically symmetric Brans-Dicke black-hole type solutions with an infinite horizon area and zero Hawking temperature, existing for negative values of the coupling constant…