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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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Journal ArticleDOI
30 May 2016-Universe
TL;DR: An alternative approach to the theory of General Relativity (GR) is reviewed in this article, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T i k and unphysical solutions.
Abstract: An alternative approach to Einstein’s theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T i k and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to T i k . Supported by lots of evidence, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation R i k = 0 as the field equation of gravitation plus inertia in the very presence of matter.

51 citations

Journal ArticleDOI
TL;DR: In this article, a regularized expression of the gravitational energymomentum tensor of the teleparallel equivalent of general relativity (TEGR) is used to make the energies of the two tetrad fields equal.
Abstract: The energy–momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space-time their energies are different. Therefore, a regularized expression of the gravitational energy–momentum tensor of the teleparallel equivalent of general relativity (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy–momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space–times are calculated. In spite of using a static space–time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space–times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.

51 citations

Journal ArticleDOI
TL;DR: The field equations of general relativity are derived from a limit to force or to power in nature as mentioned in this paper, and the limits have the value of c4/4G and c5/ 4G.
Abstract: The field equations of general relativity are shown to derive from a limit to force or to power in nature. The limits have the value of c4/4G and c5/4G. The proof makes use of a result of Jacobson. All known experimental data are consistent with the limits. Applied to the universe, the limits predict its darkness at night and the observed scale factor. Other experimental tests of the limits are proposed. The main counterarguments and paradoxes are discussed, such as the transformation under boosts, the force felt at a black hole horizon, the mountain problem, and the contrast to scalar–tensor theories of gravitation. The resolution of the paradoxes also clarifies why the maximum force and the maximum power have remained hidden for so long. The derivation of the field equations shows that the maximum force or power plays the same role for general relativity as the maximum speed plays for special relativity.

51 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
20226
20191
20185
201734
201662