Related papers: Decay estimates for the one-dimensional wave equat…
We consider the total energy decay of the Cauchy problem for wave equations with a potential and an effective damping. We treat it in the whole one-dimensional Euclidean space. Fast energy decay is established with the help of potential.…
We derive the metric for a Schwarzschild black hole with global monopole charge by relaxing asymptotic flatness of the Schwarzschild field. We then study the effect of global monopole charge on particle orbits and the Hawking radiation. It…
We compute the low energy decay rates of near-extremal three(four) charge black holes in five(four) dimensional N=4 string theory to sub-leading order in the large charge approximation. This involves studying stringy corrections to…
We investigate the black hole thermodynamics in a "deformed" relativity framework where the energy-momentum dispersion law is Lorentz-violating and the Schwarzchild-like metric is momentum-dependent with a Planckian cut-off. We obtain net…
Solutions to the wave equation on de Sitter-Schwarzschild space with smooth initial data on a Cauchy surface are shown to decay exponentially to a constant at temporal infinity, with corresponding uniform decay on the appropriately…
We establish an exponential decay estimate for linear waves on the Kerr-de Sitter slowly rotating black hole. Combining the cutoff resolvent estimate of arXiv:1003.6128 with the red-shift effect and a parametrix near the event horizons, we…
We consider the Cauchy problem for systems of semilinear wave equations in two space dimensions. We present a structural condition on the nonlinearity under which the energy decreases to zero as time tends to infinity if the Cauchy data are…
We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole…
The optimality of decay properties of the one-dimensional damped wave equations with potentials belonging to a certain class is discussed. The typical ingredient is a variant of Nash inequality which involves an invariant measure for the…
We derive the large time asymptotics of initially regular and localized solutions of the Teukolsky equation on the exterior of a subextremal Kerr black hole for any half integer spin. More precisely, we obtain the leading order term…
We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical…
We consider the initial-value problem for a one-dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we…
In this paper we study spectral properties associated to Schrodinger operator with potential that is an exponential decaying function. As applications we prove local energy decay for solutions to the perturbed wave equation and lack of…
A deformation of the wave equation on a two-dimensional black hole is considered as a toy-model for possible gravitational or stringy nonlocal effects. The deformed wave-equation allows for an initial-value problem despite being nonlocal.…
It is known that for some time periodic potentials $q(t, x) \geq 0$ having compact support with respect to $x$ some solutions of the Cauchy problem for the wave equation $\partial_t^2 u - \Delta_x u + q(t,x)u = 0$ have exponentially…
We use a novel physical space method to prove relatively non-degenerate integrated energy estimates for the wave equation on subextremal Schwarzschild-de Sitter spacetimes with parameters $(M,\Lambda)$. These are integrated decay statements…
In this paper, we construct a new class of solutions for five dimensional third order quasi-topological black holes coupled to a power-law Maxwell nonlinear electrodynamics. To have real solutions, we should establish condition…
We study black hole radiation of a Reissner-Nordstrom black hole with an electric charge in the framework of quantum gravity. Based on a canonical quantization for a spherically symmetric geometry, under physically plausible assumptions, we…
We study the asymptotics of the Schr\"odinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as $|x| \to \infty$, we prove that the solution can be written as the sum of a…
Scalar field self-force effects on a scalar charge orbiting a Reissner-Nordstr\"om black hole are investigated. The scalar wave equation is solved analytically in a post-Newtonian framework, and the solution is used to compute the…