Related papers: A physical application of Kerr-Schild groups
We investigate the motion of spinning test bodies in General Relativity. By means of a multipolar approximation method for extended test bodies we derive the equations of motion, and classify the orbital motion of pole-dipole test bodies in…
The Kerr spacetime is one of the most widely known solutions to Einstein's vacuum field equations and is commonly used to describe a black hole with mass $m$ and spin $a$. Astrophysical observations in the electromagnetic spectrum as well…
In this work, we study linearised gravitational fields on the entire Minkowski space-time including space-like infinity. The generalised conformal field equations linearised about a Minkowski background are utilised for this purpose. In…
The Zak transform on $\mathbb{R}^d$ is an important tool in condensed matter physics, signal processing, time-frequency analysis, and harmonic analysis in general. This article introduces a generalization of the Zak transform to a class of…
The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.
We investigate the geometry of median metric spaces. The group-theoretic applications are towards Kazhdan's property (T) and Haagerup's property.
We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
The Kerr spacetime is perhaps the most astrophysically important of the currently known exact solutions to the Einstein field equations. Whenever spacetimes can be put in unit-lapse form it becomes possible to identify some very…
In the present paper we discuss about a set of geometric and physical properties of hyper-generalised quasi-Einstein spacetime. At the beginning we discuss about pseudosymmetry over a hyper-generalised quasi-Einstein spacetime. Here we…
We derive the Kerr solution in a pedagogically transparent way, using physical symmetry and gauge arguments to reduce the candidate metric to just two unknowns. The resulting field equations are then easy to obtain, and solve. Separately,…
It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors $\gamma >5\times 10^{10} ,$ indicated by the situation which has developed in the physics of ultra-high energy cosmic rays (the absence…
In this study, we review some current studies on Gravitational Lensing for black holes, mainly in the context of general relativity. We mainly focus on the analytical studies related to lensing with references to observational results. We…
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
It has been shown that generalized Einstein-Aether theories may lead to significant modifications to the non-relativistic limit of the Einstein equations. In this paper we study the effect of a general class of such theories on the Solar…
Deformed generalized gauge groups, whch were created from physical considerations and made it possible to clarify some long-standing problems in physics, such as the problem of motion and the problem of the energy of the gravitational…
Dynamical realizations of the Lifshitz group are studied within the group-theoretic framework. A generalization of the 1d conformal mechanics is constructed, which involves an arbitrary dynamical exponent z. A similar generalization of the…
Grids - the collection of heterogeneous computers spread across the globe - present a new paradigm for the large scale problems in variety of fields. We discuss two representative cases in the area of condensed matter physics outlining the…
We consider the spherically reduced Einstein-Hilbert action, Einstein field equations and Schwarzschild spacetime modified by a renormalization-group (RG) scale-dependent gravitational Newton coupling, and present a systematic and…