Related papers: Nonlinear Wave Dynamics in Black Hole Spacetimes
The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and…
We study the dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of this paper is to establish Strichartz estimates for solutions of the aforementioned equation. As an application,…
The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with…
This work is an extensive literature review focusing on a few of the important topics in the large-scale structure of spacetime. The work is a Bachelor's thesis submitted at the Institute of Theoretical Physics, University of Leipzig. The…
We consider solutions to the linear wave equation on a suitable globally hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon.…
We present a new analytic approach for the study of late time evolution of linear test-fields, propagating on the exterior of black holes. This method provides a calculation scheme applicable to Kerr black holes (for which case no analytic…
The mode stability of the Kerr black hole in four dimensions was demonstrated by Whiting in 1989, by separating the Teukolsky equation that describes gravitational perturbations and then transforming the radial and angular equations in such…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
This doctoral thesis is organized into seven chapters. The first chapter introduces readers to the formation of black holes and naked singularities as an end state of continuous gravitational collapse. The physical and geometrical…
It has recently been demonstrated (Class. Quantum Grav. 31, 085010, 2014) that the conformally invariant wave equation on a Minkowski background can be solved with a fully pseudospectral numerical method. In particular, it is possible to…
We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005 (2017), to the…
We continue a study by Adler and Ramazano\uglu (AR) of "black" holes as modified by a scale invariant dark energy action. For the spherically symmetric Schwarzschild-like case, (AR) found that there is no event horizon; hence spacetime is…
Phase space method provides a novel way for deducing qualitative features of nonlinear differential equations without actually solving them. The method is applied here for analyzing stability of circular orbits of test particles in various…
We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since…
Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret…
We improve on recent results that establish the existence of solutions of certain semilinear wave equations possessing an interface that roughly sweeps out a timelike surface of vanishing mean curvature in Minkowski space. Compared to…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
In \cite{Luk}, Luk proved global existence for semilinear wave equations in Kerr spacetime with small angular momentum($a\ll M$) \[ \Box_{g_K}\phi=F(\partial \phi), \] when the quadratic nonlinear term satisfies the null condition. In this…
We prove a new type of finite time blow-up for a class of semilinear wave equations on extremal black holes. The initial data can be taken to be arbitrarily close to the trivial data. The first singularity occurs along the (degenerate)…