Related papers: The singularity theorems of General Relativity and…
We review recent results on the Cauchy-Kowalevsky structure of theories with higher derivatives in vacuum. We prove genericity of regularity of solutions under the assumption of analyticity. Our approach is framed in the general context of…
We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress-energy averages inspired by the Quantum Energy Inequalities satisfied by…
We explore the consequences of requiring that quantum theories of gravity be unitary, mostly focusing on simple cosmological models to illustrate the main points. We show that unitarity for a clock that encounters a classical singularity at…
In this article, we will review Noether's Theorems and their application in General Relativity. We will present Noether's Theorems in their original form and restate them as they are usually applied to physics. Some basic equations of…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
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…
In General Relativity the metric can be recovered from the structure of the lightcones and a measure giving the volume element. Since the causal structure seems to be simpler than the Lorentzian manifold structure, this suggests that it is…
Special relativity is no longer a new revolutionary theory but a firmly established cornerstone of modern physics. The teaching of special relativity, however, still follows its presentation as it unfolded historically, trying to convince…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a…
After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on…
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
We study the notion of regular singularities for parameterized complex ordinary linear differential systems, prove an analogue of the Schlesinger theorem for systems with regular singularities and solve both a parameterized version of the…
We prove that the "generic condition" used in singularity theorems of general relativity is generic in the space of Lorentzian metrics on a given manifold, in the sense that it is satisfied for all metrics in a residual set in the Whitney…
In this paper we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular,…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
There is rich literature on regular black holes from loop quantum gravity (LQG), where quantum geometry effects resolve the singularity, leading to a quantum extension of the classical space-time. As we will see, the mechanism that resolves…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
It is well-known that global hyperbolicity implies that the Lorentzian distance is finite and continuous. By carefully analysing the causes of discontinuity of the Lorentzian distance, we show that in most other respects the finiteness and…