相关论文: An Invitation to Lorentzian Geometry

One of the central difficulties of settling the $L^2$-bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to…

The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…

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…

Existence of global CMC foliations of constant curvature 3-dimensional maximal globally hyperbolic Lorentzian manifolds, containing a constant mean curvature hypersurface with $\genus(\Sigma) > 1$ is proved. Constant curvature 3-dimensional…

We prove that if in a spacetime endowed with a merely continuous metric, a complete partial Cauchy hypersurface has nonempty Cauchy horizon, then the horizon is caused by the presence of almost closed causal curves behind it or by the…

This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…

The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon…

We consider gravitational field equations which are Einstein equations written in terms of embedding coordinates in some higher dimensional Minkowski space. Our main focus is to address some tricky issues relating to the Cauchy problem and…

We survey our recent results on classifying complete constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space with low total curvature. There are two natural notions of "total curvature"-- one is the total absolute curvature which…

The paper is concerned with regularity properties of boundaries of causal pasts of points in a 3+1-dimensional Einstein-vacuum spacetime. In a Lorentzian manifold such boundaries play crucial role in propagation of linear and nonlinear…

The causal boundary construction of Geroch, Kronheimer, and Penrose has some universal properties of importance for general studies of spacetimes, particularly when equipped with a topology derived from the causal structure. Properties of…

In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is…

Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are…

We overview main topics and ideas in spaces with their scalar curvatures bounded from below, and present a more detailed exposition of several known and some new geometric constraints on Riemannian spaces implied by the lower bounds on…

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities…

Problem of cosmological singularity of general relativity theory is discussed. The possible resolution of this problem in the framework of inflationary cosmology is proposed. Physical conditions leading to bouncing inflationary solutions in…

This talk describes some recent results [16] regarding the problem of uniqueness in the large (also known as strong cosmic censorship) for the initial value problem in general relativity. In order to isolate the essential analytic features…

In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of…

This article discusses methods of geometric analysis in general relativity, with special focus on the role of "critical surfaces" such as minimal surfaces, marginal surface, maximal surfaces and null surfaces.

General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily…