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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 paper, the authors describe a theory of gravity in (1 + 1) dimensions that can be thought of as a toy model of general relativity, and derive the theory from fundamental physical principles using two different methods.
Abstract: We describe a theory of gravity in (1 + 1) dimensions that can be thought of as a toy model of general relativity. The theory should be a useful pedagogical tool, because it is mathematically much simpler than general relativity but shares much of the same conceptual structure; in particular, it gives a simple illustration of how gravity arises from spacetime curvature. We derive the theory from fundamental physical principles using two different methods, one based on extrapolating from Newtonian gravity and one based on the equivalence principle, and present several exact solutions.
16 citations
TL;DR: In this paper, a set of first principles is proposed to obtain general relativity in the canonical Hamiltonian framework without presupposing space-time in any way, and the ADM Hamiltonian can be obtained in CMC gauge with arbitrary (finite, nonzero) speed of light and an extra term linear in York time.
16 citations
TL;DR: In this paper, the authors discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves, and they show that classical and quantum gravitation have the same physical meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies.
Abstract: We discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a “quantization of geometry.” However, classical and quantum gravitation have the same physical meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies.
16 citations
TL;DR: It is desirable to investigate the proper method of extending the ordinary principles of thermodynamics so as to make them hold for considerations in curved space-time where the methods of general relativity must be employed.
Abstract: Introduction. The recent interesting article of Lenz(1) on the equilibrium between radiation and matter in Einstein's closed universe makes it desirable to investigate the proper method of extending the ordinary principles of thermodynamics so as to make them hold for considerations in curved space-time where the methods of general relativity must be employed.
16 citations
01 Jan 2005
TL;DR: The authors conjecture that a second hitherto unrecognized error also defeated Einstein's efforts, which was the assumption that weak, static gravitational fields must be spatially flat and a corresponding assumption about general covariant field equations.
Abstract: Two fundamental errors led Einstein to reject generally covariant gravitational field equations for over two years as he was developing his general theory of relativity. The first is well known in the literature. It was the presumption that weak, static gravitational fields must be spatially flat and a corresponding assumption about his
weak field equations. I conjecture that a second hitherto unrecognized error also defeated Einstein's efforts. The same error, months later, allowed the hole argument to convince Einstein that all generally covariant gravitational field equations would be physically uninteresting.
16 citations