Related papers: The wave equation on Schwarzschild-de Sitter space…
We solve Wheeler-De Witt (WDW) metric probability wave equation on the apparent horizon hypersurface of the Schwarzschild de Sitter (SdS) black hole. To do so we choose radial dependent mass function $M(r)$ for its internal regions in the…
We prove sharp pointwise $t^{-3}$ decay for scalar linear perturbations of a Schwarzschild black hole without symmetry assumptions on the data. We also consider electromagnetic and gravitational perturbations for which we obtain decay rates…
In canonical quantum gravity, the wave function for a hypersurface inside a Schwarzschild black hole can be obtained by solving the Wheeler-DeWitt equation. What is of prime importance is the behavior of the wave function for the future…
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…
We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation on a suitable globally hyperbolic subset of such a…
We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in a slow-roll inflationary cosmology. We show that the metric evolves quasi-statically through a sequence of…
In this work, we prove that the classical Schwarzschild-de Sitter spacetime is an exact solution of a class of weakly non-local, UV finite conformal quantum gravity theories, without the necessity of including a cosmological constant term…
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant…
We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro-)vacuum exact solutions of Einstein's equations, we first…
We solve analytically the low-frequency s-wave dynamics of a massless scalar field propagating on a Schwarzschild-de Sitter black hole background. A rigorous application of the method of matched asymptotic expansions allows us to connect…
We review our recent work on linear stability for scalar perturbations of Kerr spacetimes, that is to say, boundedness and decay properties for solutions of the scalar wave equation \Box_g{\psi} = 0 on Kerr exterior backgrounds. We begin…
A rigidity theorem that applies to smooth electrovac spacetimes which represent either (A) an asymptotically flat stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics was given…
We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In particular, we prove results corresponding to "existence and uniqueness of…
The Schwarzschild solution is generalized for the case of n internal Ricci-flat spaces. It is shown that in the four-dimensional section of the metric a horizon exists only when the internal space scale factors are constant. The…
We construct one-parameter families of static spherically symmetric asymptotically anti-de Sitter black hole solutions $(\mathcal{M},g_{\epsilon},\phi_{\epsilon})$ to the Einstein-Maxwell-(charged) Klein-Gordon equations. Each family…
A regular solution of the system of coupled equations of the nonlinear electrodynamics and gravity describing static and spherically-symmetric black holes in an asymptotically de Sitter universe is constructed and analyzed. Special emphasis…
In the context of $f(R)$ theories of gravity, we address the problem of finding static and spherically symmetric black hole solutions. Several aspects of constant curvature solutions with and without electric charge are discussed. We also…
In this paper, we establish a conformal scattering theory for defocusing semilinear wave equations on Schwarzschild spacetime. We combine the energy and pointwise decay results for solutions obtained in \cite{Yang} with a Sobolev embedding…
We study the thermodynamic properties associated with black hole horizon and cosmological horizon for the Gauss-Bonnet solution in de Sitter space. When the Gauss-Bonnet coefficient is positive, a locally stable small black hole appears in…
The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual…