Related papers: The Similarity Hypothesis in General Relativity
A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which…
We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models,…
Consider an iterated function system consisting of similarities on the complex plane of the form $g_{i}(z) = \lambda_i z + t_i,\ \lambda_i, t_i \in \mathbb{C},\ |\lambda_i|<1, i=1,\ldots, k$. We prove that for almost every choice of…
The resolution of the problem of cosmological singularity in the framework of gauge theories of gravitation is discussed. Generalized cosmological Friedmann equations for homogeneous isotropic models filled by interacting scalar fields and…
In this paper we review two symmetry axioms of special relativity and their connections to each other together with their role in some famous predictions of relativity theory, such as time dilation, length contraction, and the twin paradox.…
The role of the Raychaudhuri equation in studying gravitational collapse is discussed. A self-similar distribution of a scalar field along with an imperfect fluid in a conformally flat spacetime is considered for the purpose. The general…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or…
According to this principle, the relativistic changes occurring to the bodies, after velocity changes, cannot be detected by observers moving with them because bodies and stationary radiations change in identical proportion after identical…
Spherically symmetric solutions in F(R) theories in astronomical systems with rising energy density are studied. The range of parameters is established for which the flat space-time approximation for the background metric is valid. For the…
Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include…
Gravitation is described in the context of a dilatonic theory that is conformally related to general relativity. All dimensionless ratios of fundamental dimensional quantities, e.g. particle masses and the Planck mass, as well as the…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak…
The notion of an existentially closed model is generalised to a property of geometric morphisms between toposes. We show that important properties of existentially closed models extend to existentially closed geometric morphisms, such as…
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
Basis and limitations of singularity theorems for Gravity are examined. As singularity is a critical situation in course of time, study of time paths, in full generality of Equivalence principle, provides two mechanisms to prevent…
The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in…