GHP formalism

About: GHP formalism is a research topic. Over the lifetime, 41 publications have been published within this topic receiving 1138 citations.

A space‐time calculus based on pairs of null directions

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.

Perturbations of space--times in general relativity

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

A formalism for the investigation of algebraically special metrics. II

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.

Integration methods within existing tetrad formalisms in general relativity

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.

Integration in the GHP formalism IV : A new Lie derivative operator leading to an efficient treatment of killing vectors

Abstract: In order to achieve efficient calculations and easy interpretations of symmetries, a strategy for investigations in tetrad formalisms is outlined: work in an intrinsic tetrad using intrinsic coordi ...