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Introduction to the mathematics of general relativity
About: Introduction to the mathematics of general relativity is a research topic. Over the lifetime, 2583 publications have been published within this topic receiving 73295 citations.
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TL;DR: Double Special Relativity (DSR) theories as discussed by the authors are the relativistic theories in which the transformations between inertial observers are characterized by two observer-independent scales of the light speed and the Planck length.
Abstract: Double Special Relativity theories are the relativistic theories in which the transformations between inertial observers are characterized by two observer-independent scales of the light speed and the Planck length. We study two main examples of these theories and want to show that these theories are not the new theories of relativity, but only are re-descriptions of Einstein's special relativity in the non-conventional coordinates.
11 citations
TL;DR: In this paper, a modification of general relativity is proposed to describe local space-time defects and solve the Friedmann equations, and it turns out that the defects' density dilutes quickly, somewhat faster than radiation.
Abstract: General relativity is incomplete because it cannot describe quantum effects of space-time. The complete theory of quantum gravity is not yet known and to date no observational evidence exists that space-time is quantized. However, in most approaches to quantum gravity the space-time manifold of general relativity is only an effective limit that, among other things like higher curvature terms, should receive corrections stemming from space-time defects. We here develop a modification of general relativity that describes local space-time defects and solve the Friedmann equations. From this, we obtain the time-dependence of the density of defects. It turns out that the defects' density dilutes quickly, somewhat faster even than radiation.
11 citations
TL;DR: In this paper, a new numerical technique for following the evolution of a self-gravitating collisionless system in general relativity is proposed, where matter is modeled as a scalar field obeying the coupled Klein-Gordon and Einstein equations.
Abstract: We propose a new numerical technique for following the evolution of a self-gravitating collisionless system in general relativity. Matter is modeled as a scalar field obeying the coupled Klein-Gordon and Einstein equations. A phase-space distribution function, constructed using covariant coherent states, obeys the relativistic Vlasov equation provided the de Broglie wavelength for the field is very much smaller than the scales of interest. We illustrate the method by solving for the evolution of a system of particles in a static, plane-symmetric, background spacetime.
11 citations
Book•
01 Jan 1964
11 citations