Topic
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.
Papers published on a yearly basis
Papers
More filters
Posted Content•
09 Jul 2003
TL;DR: In this paper, it was shown that the existence of an invariant cosmic length-scale LU = 2.85 ± 0.25 Mpc has been proved in the case of the Pioneer 10/11 and the Galileo spacecrafts.
Abstract: An anomalous constant acceleration of (8.7 ± 1.3) × 10 −8 cm.s −2 directed toward the Sun has been discovered by Anderson et al. in the motion of the Pioneer 10/11 and Galileo spacecrafts. In parallel, the WMAP results have definitively established the existence of a cosmological constant � = 1/L 2 , and therefore of an invariant cosmic length-scale LU = 2.85 ± 0.25 Mpc. We show that the existence of this invariant scale definitively implements Mach’s principle in Einstein’s theory of general relativity. Then we demonstrate, in the framework of an exact cosmological solution of Einstein’s field equations which is valid both locally and globally, that the definition of inertial systems ultimately depends on this length-scale. As a consequence, usual local coordinates are not inertial, so that the motion of a free body is expected to contain an additional constant acceleration aP = c 2 / p 3 LU = (5.9±0.5)×10 −8 cm.s −2 . Such an effect represents a major contribution to the Pioneer acceleration. The recent definitive proof of the existence, in Einstein’s general relativity equations, of a cosmological constant term � = 0.73 ± 0.05 [1] (or of an equivalent contribution coming e.g. from vacuum energy) can be considered as a corner stone in the history of cosmology. We shall in this paper investigate one of its possible consequences: namely, its very existence allows the full theory of general relativity to come under Mach’s principle, as was initially required by Einstein in its construction.
15 citations
TL;DR: In this paper, the covariant and contravariant components of the metric tensor and its determinant have been derived based on the sequential approximation in Einstein's General Relativity (GR).
Abstract: The main aim of this paper is to develop a mathematical tool for General Relativity (GR). For this purpose useful tensor expressions have been worked out, which considerably ease various calculations using the sequential approximation in Einstein's GR. Based upon these expressions, compact and explicit formulae have been worked out for the covariant and contravariant components of the metric tensor and its determinant.
15 citations
TL;DR: The principle of equivalence special relativity inertial observers in a curved spacetime spacetime near a massive sphere parallel transport and the Riemann tensor but what exactly is a curvature as mentioned in this paper.
Abstract: The principle of equivalence special relativity inertial observers in a curved spacetime spacetime near a massive sphere parallel transport and the principle of equivalence the Riemann tensor but what exactly is a curvature? the field equations for the curvature of empty spacetime black holes the matter tensor cosmology the interior equations for a spherically symmetric star weak gravity and gravity waves retrospect.
15 citations
TL;DR: In this paper, an exact solution of the vacuum gravitational field equation in new general relativity was given, which gives the Kerr metric and the parallel vector fields are axially symmetric.
Abstract: We give an exact solution of the vacuum gravitational field equation in new general relativity. The solution gives the Kerr metric and the parallel vector fields are axially symmetric. A parameter h in the expression of the metric is related to the angular momentum of the rotating source, when the spin density S,f of the gravitational source satisfies the condition a~Si/=O. In the Kerr metric space· time, we cannot discriminate new general relativity from general relativity, so far as scalar, the Dirac and the Yang-Mills fields and macroscopic bodies ·are used as probes. The space-time given by the solution does not have singularities at all, although it has an "effective singularity". Two kinds of Schwarzschild metric solutions, one is our solution with h=O and the other is a solution given by Hayashi and Shirafuji, are physically equivalent with each other. Nevertheless, these are markedly different from each other with regard to the asymptotic behavior of the torsion tensor for r-->OO and the space-time singularities.
15 citations
TL;DR: In this article, it was shown that the spontaneous scalarization phenomenon is linked to another strong-field effect: a spontaneous violation of the weak energy condition, which causes the scalar field inside a neutron star to rapidly become inhomogeneous once the star's mass increases above some critical value.
Abstract: A decade ago, it was shown that a wide class of scalar-tensor theories can pass very restrictive weak-field tests of gravity and yet exhibit nonperturbative strong-field deviations away from general relativity. This phenomenon, called "spontaneous scalarization," causes the (Einstein frame) scalar field inside a neutron star to rapidly become inhomogeneous once the star's mass increases above some critical value. For a star whose mass is below the threshold, the field is instead nearly uniform (a state that minimizes the star's energy) and the configuration is similar to the general relativity one. Here we show that the spontaneous scalarization phenomenon is linked to another strong-field effect: a spontaneous violation of the weak energy condition.
15 citations