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Four-force

About: Four-force is a research topic. Over the lifetime, 3459 publications have been published within this topic receiving 87308 citations.


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Book
01 May 2004
TL;DR: In this article, the authors provide practical tools for the computation of many physically interesting quantities in general relativity, including congruencies of timelike and null geodesics, embedding of spacelike hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity.
Abstract: This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.

912 citations

Book
01 Jan 1985
TL;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

Journal ArticleDOI
TL;DR: In this paper, the field equations of general relativity are applied to pressure-free spherically symmetrical systemsof particles and the equations of motion are determined without the use of approximations and are compared with the Newtonian equations.
Abstract: The field equations of general relativity areapplied to pressure-free spherically symmetrical systemsof particles. The equations of motion are determinedwithout the use of approximations and are compared with the Newtonian equations. The total energyis found to be an important parameter, determining thegeometry of 3-space and the ratio of effectivegravitating to invariant mass. The Doppler shift isdiscussed and is found to contain both the velocity shiftand the Einstein shift combined in a rather complexexpression.

811 citations

Journal ArticleDOI
Arthur Komar1
TL;DR: In this paper, a set of covariant conservation laws is constructed in the general theory of relativity, and their relationship to the generators of infinitesimal coordinate transformations is indicated.
Abstract: A set of covariant conservation laws is constructed in the general theory of relativity. Their relationship to the generators of infinitesimal coordinate transformations is indicated. In a given coordinate system certain of these quantities may be naturally identified as energy and momentum. We can continue to recognize these conserved quantities in all coordinate systems due to the covariant character of the expressions.

793 citations

Journal ArticleDOI
TL;DR: In this paper, a modification of the equation that must be satisfied by a Hamiltonian is proposed, which is applicable to a very general class of asymptotic conditions in arbitrary diffeomorphism covariant theories of gravity derivable from a Lagrangian.
Abstract: In general relativity, the notion of mass and other conserved quantities at spatial infinity can be defined in a natural way via the Hamiltonian framework: Each conserved quantity is associated with an asymptotic symmetry and the value of the conserved quantity is defined to be the value of the Hamiltonian which generates the canonical transformation on phase space corresponding to this symmetry. However, such an approach cannot be employed to define ``conserved quantities'' in a situation where symplectic current can be radiated away (such as occurs at null infinity in general relativity) because there does not, in general, exist a Hamiltonian which generates the given asymptotic symmetry. (This fact is closely related to the fact that the desired ``conserved quantities'' are not, in general, conserved.) In this paper we give a prescription for defining ``conserved quantities'' by proposing a modification of the equation that must be satisfied by a Hamiltonian. Our prescription is a very general one, and is applicable to a very general class of asymptotic conditions in arbitrary diffeomorphism covariant theories of gravity derivable from a Lagrangian, although we have not investigated existence and uniqueness issues in the most general contexts. In the case of general relativity with the standard asymptotic conditions at null infinity, our prescription agrees with the one proposed by Dray and Streubel from entirely different considerations.

703 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20239
202211
20208
20193
20185
201756