Related papers: Singularity Theorems in General Relativity: Achiev…
Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity, QG), but also to characterise this new theory and shape expectations of what it is…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of material systems,…
In this article we show that some recent results on the existence of best proximity points can be obtained from the same result in fixed point theory.
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
Our assumption that spacetime is a continuum leads to many challenges in mathematical physics. Singularities, divergent integrals and the like threaten many of our favorite theories, from Newtonian gravity to classical electrodynamics,…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze…
In this presentation, I review physical principles behind a recently proposed \cite{smw-utr} Universal Theory of Relativity and speculate on the mathematical requirements implied by these physical principles. Some unresolved issues will…
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…
This is a review of some of the concepts and results of the effective field theory treatment of quantum general relativity. Included are lessons of low energy quantum gravity, and a discussion of the limits of effective field theory…
We present some gauge conditions to eliminate all second time derivative terms in the vierbein forms of the ten Einstein equations of general relativity; at the same time, we present the corresponding Lagrangian in which there is not any…
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…
One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are…
The analysis of certain singularities in scalar-tensor gravity contained in a recent paper is completed, and situations are pointed out in which these singularities cannot occur.
A century ago, Einstein formulated his elegant and elaborate theory of General Relativity, which has so far withstood a multitude of empirical tests with remarkable success. Notwithstanding the triumphs of Einstein's theory, the tenacious…
The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
Einstein's theory of General Relativity is the benchmark example for empirical success and mathematical elegance in theoretical physics. However, in spite of being the most successfully tested theory in physics, there are strong theoretical…