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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, a unified description of singular hypersurfaces in general relativity is proposed, and a relation between the singular part of the stress energy tensor and the discontinuities of fundamental forms associated with the hypersurface is established.
Abstract: The author proposes a unified description of arbitrary singular hypersurfaces in general relativity. The author obtains a relation, valid for any hypersurface (spacelike, timelike or null), between the singular part of the stress-energy tensor and the discontinuities of fundamental forms associated with the hypersurface.
26 citations
TL;DR: In this article, a new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source, and certain physical and geometric properties of the models are also discussed.
Abstract: A new class of solutions of Einstein field equations has been investigated for inhomogeneous cylindrically symmetric space-time with string source. To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ
1 1 of the shear tensor σ
i
j
. Certain physical and geometric properties of the models are also discussed.
25 citations
01 Jan 1973
TL;DR: The nature and role of the various relativity principles has been correspondingly unclear as discussed by the authors, and exactly how they are associated with given physical theories, has been far from clear, as well as the nature of the role of these principles.
Abstract: Traditionally, certain physical theories have been thought to have relativity principles associated with them. Associated with Newtonian mechanics is the principle of Galilean relativity, associated with special relativity is the special or restricted principle of relativity, associated with general relativity is the general principle of relativity, etc. Such relativity principles are often expressed in terms of groups of transformations. The principle of Galilean relativity is expressed by the ‘invariance’ of Newtonian mechanics under the Galilean group, that of special relativity by the ‘invariance’ of special relativity under the Lorentz group, and that of general relativity by the ‘invariance’ (or ‘covariance’) of general relativity under the group of all 1–1 transformations with non-vanishing Jacobian. Unfortunately, just what these various groups are groups of, and exactly how they are associated with given physical theories, has been far from clear. Similarly, the nature and role of the various relativity principles has been correspondingly unclear.
25 citations
TL;DR: In this article, it was shown that in general, finite perturbations in the gravitational field travel no faster than light, and that it is impossible to construct a warp drive as considered by Alcubierre (1994 The warp drive: hyper-fast travel within general relativity Class. 11 L73-7) in the absence of exotic matter.
Abstract: Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994 The warp drive: hyper-fast travel within general relativity Class. Quantum Grav. 11 L73-7) in the absence of exotic matter.
25 citations
25 citations