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A simple, though rarely considered, thought experiment on relativistic rotation is described in which internal inconsistencies in the theory of relativity seem to arise. These apparent inconsistencies are resolved by appropriate insight…
The present work deals with the classical and quantum aspects of the Raychaudhuri equation in the framework of f(T)-gravity theory. In the background of homogeneous and isotropic Friedmann Lemaitre Robertson Walker space time, the…
Suppose we assume that in gently curved spacetime (a) causality is not violated to leading order (b) the Birkoff theorem holds to leading order and (c) CPT invariance holds. Then we argue that the `mostly empty' universe we observe around…
The theory of Space rotations is introduced. The relativity principle is generalized to satisfy to reference frames rotating in 3D space. It is shown that the most postulates and limitations of quantum theories are consequences of this…
Recently, a singularity theorem for full SD-brane spacetimes was given in hep-th/0305055. We comment on the relation between this and previous work as well as provide a more geometric formulation interpreted as a no-go theorem. We then…
There have been of late renewed debates on the role of inhomogeneities to explain the observed late acceleration of the universe. We have looked into the problem analytically with the help of the well known spherically symmetric but…
It has recently been suggested that observed galaxy rotation curves can be accounted for by general relativity without recourse to dark-matter halos. Good fits have been produced to observed galatic rotation curves using this model. We show…
The paper establishes the result that solutions of the type described in the title of the article are only those that have been already presented in the literature. The procedure adopted in the paper is somewhat novel - while the usual…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
We provide mathematicaly rigorous justification of using term "probability" in connection to the so called non-signalling theories,known also as Popescu's and Rohrlich's box worlds. No only do we prove correctness of these models (in the…
A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach…
We consider the possibility to produce a bouncing universe in the framework of scalar-tensor gravity when the scalar field has a nonconformal coupling to the Ricci scalar. We prove that bouncing universes regular in the future with…
We propose a set of equations as a simple model for non singular evolutions of a $10 + 1$ dimensional M theory universe. Our model uses ideas from Loop Quantum Cosmology and offers a solution to the important problem of singularity…
We reconstruct an $f(R)$ gravity model that gives rise to the particular $\Lambda$CDM background evolution of the universe. We find well-defined, real-valued analytical forms for the $f(R)$ model to describe the universe both in the early…
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…
A unified theory of all forces should be nonsingular. In such a unified theory, Einstein's general relativity will be a very low curvature effective theory. At larger curvatures, new terms will become important. The question then arises as…
We describe the non-minimal Standard Model, consisting of minimalistic extensions of the Standard Model, which for all we know is the theory of the universe, able to describe all of the universe from the beginning of time. Extensions…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…