Topic

# GHP formalism

About: GHP formalism is a(n) research topic. Over the lifetime, 41 publication(s) have been published within this topic receiving 1138 citation(s).

##### Papers

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TL;DR: In this paper, a spin and boost-weighted quantity is defined and modified differentiation operators are introduced, one of which represents a natural extension of the definition of the operator, which had been introduced earlier by Newman and Penrose.

Abstract: A formalism is presented for the treatment of space‐times, which is intermediate between a fully covariant approach and the spin‐coefficient method of Newman and Penrose. With the present formalism, a pair of null directions only, rather than an entire null tetrad, is singled out at each point. The concept of a spin‐ and boost‐weighted quantity is defined, the formalism operating entirely with such quantities. This entails the introduction of modified differentiation operators, one of which represents a natural extension of the definition of the operator ð which had been introduced earlier by Newman and Penrose. For suitable problems, the present formalism should lead to considerable simplifications over that achieved by the standard spin‐coefficient method.

423 citations

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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

363 citations

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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.

52 citations

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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

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TL;DR: In this paper, the authors show that the conformally flat, pure radiation metrics which are not plane waves are a larger class than Wils has obtained, and they show that such a metric is the only metric which admits no Killing vectors.

Abstract: Held has proposed an integration procedure within the GHP formalism built around four real, functionally independent, zero-weighted scalars. He suggests that such a procedure would be particularly simple for the `optimal situation', when the formalism directly supplies the full quota of four scalars of this type; a spacetime without any Killing vectors would be such a situation. Wils has recently obtained a metric which he claims is the only conformally flat, pure radiation metric which is not a plane wave; this metric has been shown by Koutras to admit no Killing vectors, in general. Therefore, as a simple illustration of the GHP integration procedure, we obtain systematically the complete class of conformally flat, pure radiation metrics. Our result shows that the conformally flat, pure radiation metrics, which are not plane waves, are a larger class than Wils has obtained.

26 citations