Related papers: Strichartz estimates on Schwarzschild black hole b…
The scalar scattering cross section is computed for Schwarzschild-Tangherlini black holes on the brane. The cross sections are computed numerically via the partial-wave method. The phase shifts are found numerically and also via the Born…
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…
In this paper, we prove energy and Morawetz estimates for solutions to the scalar wave equation in spacetimes with metrics that are perturbations, compatible with nonlinear applications, of Kerr metrics in the full subextremal range.…
It is known how to choose initial data for Einstein's equations describing an arbitrary number of black holes at a moment of time symmetry. This idea has been used to give insight into the cosmological averaging problem. We study the local…
We study the thermodynamics of a moving Schwarzschild black hole, identifying the temperature and entropy in a relativistic scenario. Furthermore, we set arguments in a framework relating invariant geometrical quantities under global…
We present an exhaustive analysis of scalar, electromagnetic and gravitational perturbations in the background of a Schwarzchild-de Sitter spacetime. The field propagation is considered by means of a semi-analytical (WKB) approach and two…
We analyze the scalar radiation emitted by a source in a circular geodesic orbit around a spherically symmetric black hole. The black hole spacetime considered is quite general, in the sense that it encompasses the solutions of…
Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein…
We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon…
We propose a simple procedure for evaluating the main thermodynamical attributes of a Schwarzschild's black hole: Bekenstein-Hawking entropy, Hawking's temperature and Bekenstein's quantization of the surface area. We make use of the…
The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid onto black holes are solved in Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary…
We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein…
We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.
The success of the moving puncture method for the numerical simulation of black hole systems can be partially explained by the properties of stationary solutions of the 1+log coordinate condition. We compute stationary 1+log slices of the…
We describe the gravitational degrees of freedom of the Schwarzschild black hole by one free variable. We introduce an equation which we suggest to be the Schroedinger equation of the Schwarzschild black hole corresponding to this model. We…
Motivated by the recent work about a new physical interpretation of quasinormal modes by Maggiore, we investigate the quantization of near-extremal Schwarzschild-de Sitter black holes in the four dimensional spacetime. Following…
In this contribution, we investigate the scattering and absorption sections of the improved Schwarzschild black hole. The differential scattering section is analysed using three complementary approaches: the classical approximation, the…
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…
The purpose of this note is to present an alternative proof of a result by H. Smith and C. Sogge showing that in odd dimension of space, local (in time) Strichartz estimates and exponential decay of the local energy for solutions to wave…
In this article we consider variable coefficient, time-dependent wave equations. Using phase space methods we construct outgoing parametrices and prove Strichartz-type estimates globally in time. This is done in the context of C^2 metrics…