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
TL;DR: In this article, the authors discuss the failure of general relativity to provide a proper Newtonian limit when the spacetime dimensionality is reduced to 2+1 and try to bypass this difficulty by assuming alternative equations for the gravitational field.
Abstract: We discuss the failure of general relativity to provide a proper Newtonian limit when the spacetime dimensionality is reduced to 2+1 and try to bypass this difficulty by assuming alternative equations for the gravitational field. We investigate the properties of spacetimes generated by circularly symmetric matter distributions in two cases: weakening Einstein equations, and by considering the Brans-Dicke theory of gravity. A comparison with the corresponding Newtonian picture is made.
13 citations
TL;DR: A close study of all known solutions in general relativity which can be written in terms of Painleve transcendental functions reveals that they can all be derived from a solution found by Leaute and Marcilhacy in 1984 as mentioned in this paper.
Abstract: A close study of all known solutions in general relativity which can be written in terms of Painleve transcendental functions reveals that they can all be derived from a solution found by Leaute and Marcilhacy in 1984. In the course of this analysis a new solution of the Einstein-Maxwell equations was found, generalising some well known metrics. Also the complex transformations relating cylindrically symmetric and stationary axisymmetric solutions were fully exploited to derive previously unidentified metrics.
13 citations
Book•
01 Dec 2008
TL;DR: The Tully-Fisher law is obtained directly from the theory, and thus it is found that there is no necessity to assume the existence of dark matter in the halo of galaxies, nor in galaxy clusters as mentioned in this paper.
Abstract: This book describes Carmeli's cosmological general and special relativity theory, along with Einstein's general and special relativity. These theories are discussed in the context of Moshe Carmeli's original research, in which velocity is introduced as an additional independent dimension. Four- and five-dimensional spaces are considered, and the five-dimensional braneworld theory is presented. The Tully–Fisher law is obtained directly from the theory, and thus it is found that there is no necessity to assume the existence of dark matter in the halo of galaxies, nor in galaxy clusters.The book gives the derivation of the Lorentz transformation, which is used in both Einstein's special relativity and Carmeli's cosmological special relativity theory. The text also provides the mathematical theory of curved spacetime geometry, which is necessary to describe both Einstein's general relativity and Carmeli's cosmological general relativity. A comparison between the dynamical and kinematic aspects of the expansion of the universe is made. Comparison is also made between the Friedmann–Robertson–Walker theory and the Carmeli theory. And neither is it necessary to assume the existence of dark matter to correctly describe the expansion of the cosmos.
13 citations
13 citations
TL;DR: In this paper, the authors showed that the first-order formula for travel time in the circular-orbit model is strictly independent of the nonlinear term in the theory of general relativity.
Abstract: Using a model of circular coplanar orbits and an analysis accurate to first order in the sun's gravitational radius, Ross and Schiff discussed the recent proposal to test general relativity by measuring round-trip travel times of radar pulses transmitted from the earth towards an inner planet. Their main conclusion, that such measurements would be sensitive to a nonlinear term in Einstein's theory, we find to be invalid. Since first-order differences between Newtonian and Einsteinian orbits are well known to depend on a nonlinear term in the metric, one might expect the round-trip travel times also to depend in first order on such a term. Curiously, this expectation is not realized for circular orbits. When expressed as a function solely of clock readings, the first-order formula for travel time in the circular-orbit model is strictly independent of the nonlinear term. Even were the combined use of radar-pulse travel times and the results of "exact" optical measurements envisioned, their sensitivity to this nonlinear term would be masked almost completely by unavoidable uncertainties in the estimates of other unknown parameters such as the mass of the sun. For noncircular orbits, however, the travel-time measurements will be noticeably sensitive to this nonlinear term through its effect on the advance of the perihelion. In addition to re-examining the circular-orbit model, we describe the operational procedures that we have developed for testing general relativity with data obtained from actual planetary observations. These data cannot be expected in the near future to provide a significant test of more than the first-order influence of solar gravity on radar-pulse travel times and the non-Newtonian advance of Mercury's perihelion, as we previously pointed out.
13 citations