相关论文: Numerical Approaches to Spacetime Singularities

We study analytically the spacelike singularity inside a spherically-symmetric, charged black hole coupled to a self-gravitating spherical massless scalar field. We assume spatial homogeneity, and find a generic solution in terms of a…

Progress in numerical relativity has been hindered for 30 years because of the difficulties of avoiding spacetime singularities in numerical evolution. We propose a scheme which excises a region inside an apparent horizon containing the…

We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity…

I review four decades of numerical simulations of galaxy clusters focussing on the attempts to resolve their internal structure. Overmerging describes the numerical or physical disruption of dark matter halos within dense environments. This…

The purpose of these lectures is to give a short introduction into a very vast field of numerical simulations for cosmological applications. I focus on major features of the simulations: the equations, main numerical techniques, effects of…

We investigate the dynamical features of a large family of running vacuum cosmologies for which $\Lambda$ evolves as a polynomial in the Hubble parameter. Specifically, using the critical point analysis we study the existence and the…

The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…

My research work can be classified into two parts namely, (i) Cosmological phenomena with varying speed of light and (ii) Gravitational collapse and black holes. We have investigated several cosmological phenomena when velocity of light…

Studies of galaxy clusters have proved crucial in helping to establish the standard model of cosmology, with a universe dominated by dark matter and dark energy. A theoretical basis that describes clusters as massive, multi-component,…

We consider a heat equation and a wave equation in a spatial interval over a time interval. This article deals with inverse problems of determining sizes of spatial intervals by extra boundary data of solutions of the governing equations.…

In this contribution, we study spacetimes of cosmological interest, without making any symmetry assumptions. We prove a rigid Hawking singularity theorem for positive cosmological constant, which sharpens known results. In particular, it…

This thesis is concerned with global properties of those cosmological solutions of Einstein's field equations which obey accelerated expansion into the future driven by a non-vanishing cosmological constant, as suggested by current…

Very compact objects probe extreme gravitational fields and may be the key to understand outstanding puzzles in fundamental physics. These include the nature of dark matter, the fate of spacetime singularities, or the loss of unitarity in…

Clusters of galaxies are studied from a theoretical point of view, comparing with observational results whenever possible. The problem is approached both analytically as well as by means of high-resoultion numerical simulations. The dark…

We review the properties of naked time-like singularities in the General Relativity and quantum effects in their vicinity. We demonstrate that only line-like singularities can be formed by a collapse and are the only candidates to break the…

In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…

We consider Gaussian multiplicative chaos measures defined in a general setting of metric measure spaces. Uniqueness results are obtained, verifying that different sequences of approximating Gaussian fields lead to the same chaos measure.…

Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the most promising sources of gravitational radiation for future…

A naked singularity occurs in the generic collapse of an inhomogeneous dust ball. We study the even-parity mode of gravitational waves from a naked singularity of the Lema\^{\i}tre-Tolman-Bondi spacetime. The wave equations for…

We investigate the occurrence and nature of naked singularities in the gravitational collapse of an adiabatic perfect fluid in self-similar higher dimensional space-times. It is shown that strong curvature naked singularities could occur if…