Related papers: Light Rays, Singularities, and All That
Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a…
These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as conserved quantities in theories of gravity; (2) Classical…
The nature of gravity is fundamental to understand the scaffolding of the Universe and its evolution. Einstein's general theory of relativity has been scrutinized for over ninety five years and shown to describe accurately all phenomena…
Assuming the Bousso bound, we prove a singularity theorem: if the light rays entering a hyperentropic region contract, then at least one light ray must be incomplete. "Hyperentropic" means that the entropy of the region exceeds the…
The problem of the event horizon in relativistic gravity is discussed. Singular solutions in general relativity are well known. The Schwarschild metric of a spherical mass is singular at zero ($r = 0$) and at the event horizon ($r = r_g$).…
The singularity theorems of Penrose, Hawking, and Geroch predict the existence of incomplete inextendible causal geodesics in a wide range of physically adequate spacetimes modeling the gravitational collapse of stars and the expanding…
In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like…
I discuss the idea of relativistic causality, i.e. the requirement that causal processes or signals can propagate only within the light-cone. After briefly locating this requirement in the philosophy of causation, my main aim is to draw…
We present here a spectrum of developments and predictions in gravitation theory in recent years which appear to be amongst some of the most exciting directions. These include the spacetime singularities, gravitational collapse final…
A brief discussion on the pseudo-complex General Relativity is presented. It is shown that this theory is a viable extension of GR, with deviations centered near to the event horizon. The theory introduces a dark energy accumulation, due to…
These lectures notes contain an introduction to General Relativity. They are addressed to a general mathematical audience with no specific background in physics. The goal is to motivate and explain Einstein's theory of gravity and discuss…
The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of these results under weakened hypotheses, by…
In 1945 Einstein concluded that [1]: 'The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality…
A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3+1)-space-time, based on the full classification of special transformations and the corresponding velocity addition…
This is a brief review article of a seminar given at the International Conference on Gravitation, Astrophysics and Cosmology 2024 (ICGAC-2024), Mathura, India. We begin with a historical survey of some singular solutions in the theory of…
The formulation of General Relativity presented in math-ph/0506077 and the Hamiltonian formulation of Gauge theories described in math-ph/0507001 are made to interact. The resulting scheme allows to see General Relativity as a constrained…
In this article we present a review of a geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with the causal structure related to special and general relativity. We describe…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
Recently, [3], it was shown that Special Relativity is in fact based on one single physical axiom which is that of Reciprocity. Originally, Einstein, [1], established Special Relativity on two physical axioms, namely, the Galilean…
We discuss some aspects of recent research as well as more general issues about motivation, useful methods and open problems in the field of cosmological singularities. In particular, we review some of the approaches to the general area and…