Related papers: Light Rays, Singularities, and All That
Earlier, we had presented \cite{heuristic} heuristic arguments to show that a {\em natural unification} of the ideas of the quantum theory and those underlying the general principle of relativity is achievable by way of the measure theory…
The strong proper time dilation and radial contraction in the gravitational field of compact sources leads to a frozen state of matter. It is shown that the falling particles and photons can not cross the gravitational radius due to the…
Based on several recent developments in relativistic astrophysics and observational cosmology, this article discusses prospects of (1) theoretical structure of General Relativity (GR) in the new era and (2) submission of GR to new and…
General Relativity allows for a unique black hole solution, characterized by its mass M, angular momentum J, and electric charge Q. Black holes in General Relativity are thus said to have no hair, that is, no other independent physical…
An alternative approach towards quantum theory is described, and tentative attempts to connect his approach to special and general relativity are discussed. Important concepts are gauge groups and information/entropy connected to some…
We extend both the Hawking-Penrose Theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity $C^1$. For metrics of such low regularity, two main obstacles have to be addressed. On the one hand, the…
Boundary conditions defining a generic isolated horizon are introduced. They generalize the notion available in the existing literature by allowing the horizon to have distortion and angular momentum. Space-times containing a black hole,…
Some relevant aspects of a new form of generalized entropic cosmology, recently introduced by Nojiri, Odintsov and Faraoni, are considered. The setup is a logarithmic equation of state for a viscous dark fluid coupled with dark matter, in…
Infinite Derivative Gravity is able to resolve the Big Bang curvature singularity present in general relativity by using a simplifying ansatz. We show that it can also avoid the Hawking- Penrose singularity, by allowing defocusing of null…
The present work deals with the Raychaudhuri equation (RE) to examine the space-time singularity both from classical and quantum point of view. The RE has been looked upon in terms of a classical linear Harmonic oscillator and Focusing…
We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie…
The 2017 Nobel Prize in physics awarded to Rainer Weiss, Barry C. Barish and Kip S. Thorne has generated unprecedented interest in gravitational waves (GWs). These notes are based on my lectures on various occasions - in the University of…
We describe how causality and energy-momentum conservation constrain the superhorizon behaviour of perturbation variables in a general FRW spacetime. The effect of intrinsic curvature upon the horizon scale is discussed and `white noise'…
We analyse conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through…
We give a pedagogical introduction of the essential features of General Theory of Relativity (GTR) in the format of an undergraduate (UG) project. A set of simple MATHEMATICA code is developed which enables the UG students to calculate the…
We reexamine the focusing effect crucial to the theorems that predict the emergence of spacetime singularities and various results in the general theory of black holes in general relativity. Our investigation incorporates the fully…
The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all…
Exploring the characterization of singular black hole spacetimes, we study the relation between energy density, curvature invariants, and geodesic completeness using a quadratic $f(R)$ gravity theory coupled to an anisotropic fluid. Working…
A major issue in general relativity and blackhole physics today is to determine the conditions when the spacetime singularities forming as end-states of gravitational collapse are visible to external observers, and when these are hidden…
General Relativity can be reformulated as a diffeomorphism invariant SU(2) gauge theory. A new action principle for this "pure connection" formulation of GR is described.