Showing papers on "Introduction to the mathematics of general relativity published in 1993"
TL;DR: In this paper, the authors discuss the role of tensionors in the normalism of tensors and general relation in special and general relations, including black holes and grazitational waves.
Abstract: PART A: SPECIAL RELATIVITY PART B: THE FORMALISM OF TENSORS PART C: GENERAL RELATIVITY PART D: BLACK HOLES PART E: GRAVITATIONAL WAVES PART F: COSMOLOGY
295 citations
TL;DR: In this paper, the authors derive necessary and sufficient junction conditions for signature type change in general relativity and investigate the extent to which they are equivalent. But they only consider the case of smooth signature type changes.
Abstract: There are two proposals for the classical implementation of signature type change in general relativity. We derive necessary and sufficient junction conditions for both proposals and investigate the extent to which they are equivalent. In the case of discontinuous signature type change there does not exist a non-flat vacuum solution of the Einstein equation. However, we show that in the case of smooth signature type change such solutions exist.
65 citations
24 citations
01 Jan 1993
17 citations
TL;DR: The use of potentials describing perfect fluids illuminates the role of time in general relativity as discussed by the authors, and using Hamilton-Jacobi methods, one can find solutions for inhomogeneous situations of interest to cosmology without making an explicit time choice until the very end of the calculation.
Abstract: The use of potentials describing perfect fluids illuminates the role of time in general relativity. Using Hamilton-Jacobi methods, one can find solutions for inhomogeneous situations of interest to cosmology without making an explicit time choice until the very end of the calculation. We compute exact general solutions of long-wavelength matter and radiation interacting with gravity. Hamilton-Jacobi methods can describe adiabatic and isothermal fluctuations as well as the scalar, vector, and tensor modes.
16 citations
TL;DR: Canonical forms for the energy-momentum tensor of the scalar field in the framework of general relativity are derived and algebraically classified as mentioned in this paper, and four different types arise depending on the vectorial character of the gradient of the field.
Abstract: Canonical forms for the energy–momentum tensor of the scalar field in the framework of general relativity are derived and algebraically classified. Four different types arise depending on the vectorial character of the gradient of the scalar field. For each canonical form a solution of the Einstein‐massless scalar field equations is presented. There emerges from our investigation alternative physical interpretation for two known space–times.
15 citations
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TL;DR: In this paper, it was shown that in a curved space (or on a curved surface) in which the perimeter of concentric circles decreases with the increasing diameter, the local outward direction points towards the global center of the circles, and thus the centrifugal force attracts to the center.
Abstract: Much to everybody’s surprise, it was recently demonstrated that according to Einstein’s general theory of relativity, very close to a compact star or a black hole the centrifugal force may attract towards the center of a circular motion. We show here that Newtonian theory predicts exactly the same effect, and that the geometrical reason for it is identical in both theories. The centrifugal force always repels in the local outward direction. However, in a curved space (or on a curved surface) in which the perimeter of concentric circles decreases with the increasing diameter, the local outward direction points towards the global center of the circles, and thus the centrifugal force attracts to the center.
11 citations
TL;DR: It is found that such a generalized Einstein action must include at least one scalar field and one vector field as well as the quadratic term of the scalar curvature.
Abstract: We study a generalized Einstein theory with the following two criteria: (i) on the solar scale, it must be consistent with the classical tests of general relativity; (ii) on the galactic scale, the gravitational potential is a sum of Newtonian and Yukawa potentials so that it may explain the flat rotation curves of spiral galaxies. Under these criteria we find that such a generalized Einstein action must include at least one scalar field and one vector field as well as the quadratic term of the scalar curvature.
10 citations
TL;DR: In this paper, a new family of first order hyperbolic evolution systems for the vacuum Einstein field equations in the harmonic slicing gauge is presented, which can be used to scale the dynamical variables in future numerical applications.
Abstract: The construction of numerical solutions of Einstein's General Relativity equations is formulated as an initial-value problem. The space-plus-time (3 + 1) decomposition of the spacetime metric tensor is used to discuss the structure of the field equations. The resulting evolution system is shown to depend in a crucial way on the coordinate gauge. The mandatory use of singularity avoiding coordinate conditions (like maximal slicing or similar gauges) is explained. A brief historical review of Numerical Relativity is included, showing the enormous effort in constructing codes based in these gauges, which lead to non-hyperbolic evolution systems, using "ad hoc" numerical techniques. A new family of first order hyperbolic evolution systems for the vacuum Einstein field equations in the harmonic slicing gauge is presented. This family depends on a symmetric 3 × 3 array of parameters which can be used to scale the dynamical variables in future numerical applications.
10 citations
TL;DR: In this paper, it is shown that it is possible to formulate General Relativity in a phase space coordinatized by two SO(3) connections, and a suitable scalar constraint in this phase space is introduced.
Abstract: We show in this paper that it is possible to formulate General Relativity in a phase space coordinatized by two SO(3) connections. We analyze first the Husain-Kuchayr model and find a two connection description for it. Introducing a suitable scalar constraint in this phase space we get a Hamiltonian formulation of gravity that is close to the Ashtekar one, from which it is derived, but has some interesting features of its own. Among them a possible mechanism for dealing with the degenerate metrics and a neat way of writing the constraints of General Relativity.
9 citations
01 Jan 1993
TL;DR: In this article, the authors show that the canonical approach to general relativity in terms of reference systems leads to physically uninterpretable results and that the lack of quantum content of general relativity is reflected by Rosenfeld's uncertainty relations.
Abstract: The canonical approach to general relativity in terms of reference systems is discussed to show that Einstein's principles of equivalence and general relativity imply the physical insignificance of quantized general relativity. In particular it is demonstrated that even the (anholonomic) flat-space canonical formalism leads to physically uninterpretable results. This lack of quantum content of general relativity is reflected by Rosenfeld's uncertainty relations and can especially be removed by modifying general relativity in the spirit of classical Einstein-Cartan theory with teleparallelism.
TL;DR: In this article, a model of an expanding and rotating universe is constructed in the framework of general relativity, and the parameters of the model are compared with the fundamental observables and shown to be in good agreement.
Abstract: A model of an expanding and rotating universe is constructed in the framework of general relativity. The parameters of the model are compared with the fundamental observables and shown to be in good agreement.
01 Jan 1993
TL;DR: In this paper, a numerical code is presented which uses modern shock capturing methods to evolve spherically symmetric perfect fluid space-times, which is used to ensure singularity avoidance in strong field situations.
Abstract: A numerical code is presented which uses modern shock capturing methods to evolve spherically symmetric perfect fluid space-times. Harmonic slicing is used to ensure singularity avoidance, which is crucial in strong field situations. Some tests are presented, including an application to the stellar collapse problem.
01 Jan 1993
TL;DR: In this article, the equivalence between General Relativity and scalar-tensor theories is discussed and the vacuum solutions of the Brans-Dicke theory of gravity are shown to behave ambiguously whenever attempts are made to interpret them as Einstein's solutions generated by an effective energymomentum tensor.
Abstract: The equivalence between General Relativity and scalar-tensor theories is discussed. Vacuum solutions of the Brans-Dicke theory of gravity are shown to behave ambiguously whenever attempts are made to interpret them as Einstein's solutions generated by an ‘effective’ energymomentum tensor.
Book•
07 Jul 1993
TL;DR: In this article, a seminal idea -the principle of relativity toward an abstract view of nature -was introduced, from Galileo to Einstein relative time and the Mach Principle the curvature of space-time gravitation and crucial tests of general relativity.
Abstract: Introduction: a seminal idea - the principle of relativity toward an abstract view of nature Einstein's ideas of special relativity the principle of relativity - from Galileo to Einstein relative time and the twin paradox the Mach Principle the curvature of space-time gravitation and crucial tests of general relativity Faraday's unified field concept the night sky cosmology.
01 Jan 1993
TL;DR: In this paper, the Einstein-Maxwell equations in general relativity are modified in the light of the Maxwell macroscopic theory which deals with electromagnetic behaviour of ponderable matter and an axially symmetric solution of physical interest is obtained.
Abstract: Here the Einstein-Maxwell equations in general relativity are modified in the light of the Maxwell macroscopic theory which deals with electromagnetic behaviour of ponderable matter and an axially symmetric solution of physical interest is obtained.