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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: In this article, it was shown that a static, spherically symmetric gravitational field is given by the Schwarzschild metric, and that in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons.
Abstract: A gravitational theory is formulated on the Weitzenb\"ock space-time, characterized by the vanishing curvature tensor (absolute parallelism) and by the torsion tensor formed of four parallel vector fields. This theory is called new general relativity, since Einstein in 1928 first gave its original form. New general relativity has three parameters ${c}_{1}$, ${c}_{2}$, and $\ensuremath{\lambda}$, besides the Einstein constant $\ensuremath{\kappa}$. In this paper we choose ${c}_{1}=0={c}_{2}$, leaving open $\ensuremath{\lambda}$. We prove, among other things, that (i) a static, spherically symmetric gravitational field is given by the Schwarzschild metric, that (ii) in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons, and that (iii) new general relativity agrees with all the experiments so far carried out.
1,075 citations
TL;DR: In this article, a method for the derivation of the equations of motion of test particles in a given gravitational field is developed, where the transformation properties are discussed and the equation of motion is written in a covariant form.
Abstract: A method for the derivation of the equations of motion of test particles in a given gravitational field is developed. The equations of motion of spinning test particles are derived. The transformation properties are discussed and the equations of motion are written in a covariant form.
985 citations
TL;DR: In this paper, an extension of teleparallel, or torsion scalar T, gravity to f(T) theories is considered, where the field equations are naturally second order, avoiding pathologies.
Abstract: Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar R can be generalized to f(R) gravity, we consider extensions of teleparallel, or torsion scalar T, gravity to f(T) theories. The field equations are naturally second order, avoiding pathologies, and can give rise to cosmic acceleration with unique features.
982 citations
Book•
01 Jan 1924
TL;DR: In this article, the tensor calculus and the law of gravitation have been studied in a tensor tensor geometry setting, and the authors present a review of the literature.
Abstract: Introduction 1. Elementary principles 2. The tensor calculus 3. The law of gravitation 4. Relativity mechanics 5. Curvature of space and time 6. Electricity 7. World geometry Supplementary notes Bibliography Index.
917 citations
Book•
01 Jan 1985TL;DR: The second edition of this widely-used textbook as mentioned in this paper provides the first step into general relativity for undergraduate students with a minimal background in mathematics, and includes a revised chapter on relativistic stars, including new information on pulsars.
Abstract: Clarity, readability and rigor combine in the second edition of this widely-used textbook to provide the first step into general relativity for undergraduate students with a minimal background in mathematics. Topics within relativity that fascinate astrophysical researchers and students alike are covered with Schutz's characteristic ease and authority - from black holes to gravitational lenses, from pulsars to the study of the Universe as a whole. This edition now contains discoveries by astronomers that require general relativity for their explanation; a revised chapter on relativistic stars, including new information on pulsars; an entirely rewritten chapter on cosmology; and an extended, comprehensive treatment of modern detectors and expected sources. Over 300 exercises, many new to this edition, give students the confidence to work with general relativity and the necessary mathematics, whilst the informal writing style makes the subject matter easily accessible. Selected solutions for instructors are available under Resources.
847 citations