Related papers: Singularity Theorems in General Relativity: Achiev…
I give a brief review of the search for a proper definition of energy in General Relativity (GR), a far from trivial quest, which was only completed after four and a half decades. The equally (or perhaps more) difficult task of establishing…
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…
The most simple observed cases of gravitational lensing of distant quasars and galaxies by galaxies and clusters of galaxies are used to test Einstein's theory of General Relativity and Newtonian Gravity over galactic and intergalactic…
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…
General relativity, despite its profound successes, fails as a complete theory due to presence of singularities. While it is widely believed that quantum gravity has the potential to be a complete theory, in which spacetime consistently…
This thesis focuses on modifications on Einstein's theory of General Relativity, which could explain the current problems in gravitation and cosmology. More specifically, modifications of the affine structure of the spacetime, which is the…
To date, both quantum theory, and Einstein's theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be…
In this survey article we introduce the notion of frontals, which provides a class of generalised submanifolds with singularities but with well-defined tangent spaces. We present a review of basic theory and known studies on frontals in…
I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality.…
We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum…
This is a summary of how the definition of quantum singularity is extended from static space-times to conformally static space-times. Examples are given.
We review uniqueness theorems as well as other general results about higher dimensional black hole spacetimes. This includes in particular theorems about the topology of higher dimensional spacetimes, theorems about their symmetries…
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…
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 give an overview of literature related to J\"urgen Ehlers' pioneering 1981 paper on Frame theory--a theoretical framework for the unification of General Relativity and the equations of classical Newtonian gravitation. This unification…
General Relativity is today the best theory of gravity addressing a wide range of phenomena. Our understanding of physical laws, from cosmology to local scales, cannot be properly formulated without taking into account it. It is based on…
The present status of Unified Theories is summarized with special emphasis on their possible experimental tests. Outline: i) Unification of couplings; ii) Where can a positive signal come from? iii) HERA anomaly and Unification; iv) Recent…
In this article, we argue that the theory of special relativity, as formulated by Einstein, is a philosophical rather than a scientific theory. What is scientific and experimentally supported is the formalism of the relativistic mechanics…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
The missing of a Keplerian fall-off in the observed galaxy rotation curves represents classical evidence for the existence of dark matter on galactic scales. There has been some recent activity concerning the potential of modelling galactic…