Author
A. Held
Bio: A. Held is an academic researcher from University of Bern. The author has contributed to research in topics: GHP formalism. The author has an hindex of 1, co-authored 1 publications receiving 52 citations.
Topics: GHP formalism
Papers
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TL;DR: In this paper, a new formalism is proposed for the investigation of algebraically special metrics and the essential calculations are co-ordinate free and the equations are gauge invariant, hence easy to work with and the approach is rich in possibilities not explored by previous techniques.
Abstract: A new formalism is proposed for the investigation of algebraically special metrics. Among its advantages are that the essential calculations are co-ordinate free and the equations are gauge invariant. The derived equations are simple in form hence easy to work with and the approach is rich in possibilities not explored by previous techniques.
53 citations
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01 Dec 1982
1,915 citations
TL;DR: In this article, the concept of space-times in general relativity was introduced, and a definition of perturbations of space times was proposed, leading in a natural way to a concept of gauge invariance, and to an extension of a lemma of Sachs (i964).
Abstract: A definition of perturbations of space-times in general relativity is proposed. The definition leads in a natural way to a concept of gauge invariance, and to an extension of a lemma of Sachs (i964). Coupled equations governing linearized perturbations of certain tetrad components of scalar, electromagnetic, and gravitational fields are derived by the use of Geroch, Held & Penrose's (I 973) version of the tetrad formalism of Newman & Penrose (i 962). It is shown that these perturbations are gauge invariant if and only if the unperturbed space-time is vacuum of algebraic type {22} or, equivalently, if and only if the perturbation equations decouple. Finally the maximal subclass of type {22} space-times for which the decoupled perturbation equations can be solved by separation of variables is found. This class comprises all the nonaccelerating type {22} space-times, including that of Kerr, thus elucidating earlier results of Bardeen & Press
385 citations
TL;DR: In this paper, the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives is used to find locally rotationally symmetric (LRS) perfect-fluid solutions to Einstein's equations.
Abstract: We use the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives in order to find locally rotationally symmetric (LRS) perfect-fluid solutions to Einstein's equations. A new method is introduced, which makes it possible to choose the coordinates at any stage of the calculations. Three classes are examined, one with fluid rotation (LRS class I), one with twist in the preferred spacelike direction (LRS class III), and the spacetime homogeneous models. It is also shown that there are no LRS spacetimes with dependence on one null coordinate. Using an extension of the method, we find the full metric in terms of curvature quantities for LRS class I and LRS class III.
37 citations
TL;DR: The general nature of computer algebra is discussed, along with some aspects of CA system design; features particular to GR’s requirements are considered; information on packages for CA in GR is provided, both for those packages currently available and for their predecessors.
Abstract: The complicated nature of calculations in general relativity was one of the driving forces in the early development of computer algebra (CA). CA has become widely used in gravity research (GR) and its use can be expected to grow further. Here the general nature of computer algebra is discussed, along with some aspects of CA system design; features particular to GR’s requirements are considered; information on packages for CA in GR is provided, both for those packages currently available and for their predecessors; and applications of CA in GR are outlined.
36 citations
TL;DR: In this paper, it is shown that in Held's integration method in the GHP formalism, it is usually sufficient and sufficient to apply GHP commutator equations to two complex, zero-weighted quantities which consist of four real, functionally independent scalars.
Abstract: The NP and GHP formalisms are reviewed in order to understand and demonstrate the important role played by the commutator equations in the structure of the system of equations in each formalism, and also in the associated integration procedures. Particular attention is focused on how the commutator equations are to be satisfied (or checked for consistency) in each of the formalisms. In particular, it is shown that in Held's integration method in the GHP formalism, it is usually sufficient—alongside the GHP Ricci and Bianchi equations—to apply the GHP commutator equations to two complex, zero-weighted quantities which consist of four real, functionally independent scalars. This result is used, first of all, to suggest an additional step in Held's method, which ensures that there is no possibility of ambiguity in the procedure; secondly a restatement/ modification of Held's integration method is suggested, which enables the integration procedure to be completely self-contained and fully co-ordinate- and gauge-independent. An example of its use for a subclass of Petrov type D vacuum spaces is given.
34 citations