相关论文: Global results for linear waves on expanding Kerr …

We examine the solutions of the semilinear wave equation, and, in particular, of the $\varphi ^p$ model of quantum field theory in the curved space-time. More exactly, for $1< p<4$ we prove that solution of the massless self-interacting…

This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…

In the first part of this work we show a uniqueness result for globally hyperbolic spacetimes with a spacelike conformal boundary satisfying the vacuum Einstein equations with positive cosmological constant. Then we present applications of…

We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…

We present short proofs of integrated local energy decay estimates on Schwarzschild, extremal Reissner-Nordstr\"om, and Schwarzschild-de Sitter spacetimes. The proofs employ novel global physical space multipliers, which, besides their…

We study the long time existence of solutions to nonlinear wave equations with power-type nonlinearity (of order $p$) and small data, on a large class of $(1+n)$-dimensional nonstationary asymptotically flat backgrounds, which include the…

This is the main paper of a series establishing the linear stability of Schwarzschild-Anti-de Sitter (AdS) black holes to gravitational perturbations. Specifically, we prove that solutions to the linearisation of the Einstein equations…

We study the solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a massive conformally coupled scalar field. In particular, we show that it is possible to give initial conditions at finite time to get…

It is already known that a simple nonlocal de Sitter gravity model, which we denote as $\sqrt{dS}$ gravity, contains an exact vacuum cosmological solution which mimics dark energy and dark matter and is in very good agreement with the…

We study spherically symmetric solutions of semilinear wave equations in the case where the nonlinearity satisfies the null condition on extremal Reissner--Nordstrom black hole spacetimes. We show that solutions which arise from…

We study the future stability of cosmological fluids, in spacetimes with an accelerated expansion, which exhibit extreme tilt behavior, ie. their fluid velocity becoming asymptotically null at timelike infinity. It has been predicted in the…

In this short paper, we prove a well-posedness theorem for the massive wave equation (with the mass satisfying the Breitenlohner-Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed as a limit of solutions to…

In hep-th/0506040 we discussed a classically constrained model of gravity. This theory contains known solutions of General Relativity (GR), and admits solutions that are absent in GR. Here we study cosmological implications of some of these…

Recent observations in cosmology indicate an accelerating expansion of the universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic…

We propose a new cosmological scenario which resolves the conventional initial singularity problem. The space-time geometry has an unconventional time-like singularity on a lower dimensional hypersurface, with localized energy density. The…

We prove a unique continuation from infinity theorem for regular waves of the form $[ \Box + \mathcal{V} (t, x) ]\phi=0$. Under the assumption of no incoming and no outgoing radiation on specific halves of past and future null infinities,…

We investigate static spherically symmetric solutions within the framework of the local limit of nonlocal gravity. This theory departs from Einstein's general relativity (GR) through the introduction of a scalar gravitational susceptibility…

A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This…

We describe an expansion of the solution of the wave equation in the De Sitter - Schwarzschild metric in terms of resonances. The main term in the expansion is due to a zero resonance. The error term decays polynomially if we permit a…

The massive wave equation $\Box_g \psi - \alpha\frac{\Lambda}{3} \psi = 0$ is studied on a fixed Kerr-anti de Sitter background $(\mathcal{M},g_{M,a,\Lambda})$. We first prove that in the Schwarzschild case (a=0), $\psi$ remains uniformly…