Riemannian-Maxwellian invertible structures in general relativity

Debever, Robert; McLenaghan, Raymond R.G.; Tariq, N.

doi:10.1007/bf00756664

Cited by 29 publications

(22 citation statements)

References 25 publications

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“…We can write the conservation equation (18) in terms of the canonical energetic variables (U, φ). Indeed, from (14) and expression (6) it follows that (18) is equivalent to the first Maxwell-Rainich equation (10):…”

Section: Maxwell Equations For the Energy Tensormentioning

confidence: 99%

A Rainich-Like Approach to the Killing-Yano Tensors

Ferrando

Sáez

2003

General Relativity and Gravitation

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The Rainich problem for Killing-Yano tensors posed by Collinson [1] is solved. In intermediate steps, we first obtain the necessary and sufficient conditions for a 2+2 almost-product structure to determine the principal 2-planes of a skew-symmetric Killing-Yano tensor and then we give the additional conditions on a symmetric Killing tensor for it to be the square of a Killing-Yano tensor. We also analyze a similar problem for the conformal Killing-Yano and the conformal Killing tensors. Our results show that, in both cases, the principal 2-planes define a maxwellian structure. The associated Maxwell fields are obtained and we outline how this approach is of interest in studying the spacetimes that admit these kind of first integrals of the geodesic equation.

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Section: Maxwell Equations For the Energy Tensormentioning

confidence: 99%

A Rainich-Like Approach to the Killing-Yano Tensors

Ferrando

Sáez

2003

General Relativity and Gravitation

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“…Debever-McLenaghan-Tariq metric in general form [15]. Output in normal form (does not simplify further).…”

Section: Dmt2mentioning

confidence: 99%

“…Spacetime: Debever-McLenaghan-Tariq (modified) (DMT2) [15] Input file Contravariant tetrad npupdmt.mpl l a = 1 2…”

Section: Input File Covariant Tetradmentioning

confidence: 99%

Algorithms for computer algebra calculations in spacetime: I. The calculation of curvature

Pollney¹,

Musgrave²,

Santosuosso³

et al. 1996

Class. Quantum Grav.

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We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of spacetimes, and distinct coordinates and tetrads for a given spacetime.Within the system GRTensorII, we find that there is no single preferred approach on the basis of speed. Rather, we find that the fastest algorithm is the one that minimizes the amount of time spent on simplification. This means that arguments concerning the theoretical superiority of an algorithm need not translate into superior performance when applied to a specific spacetime calculation. In all cases it is the global simplification strategy which is of paramount importance. An appropriate simplification strategy can change an untractable problem into one which can be solved essentially instantaneously. *

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“…In section 2 we present a brief review of the Newman-Penrose (NP) formalism in the complex vectorial rep-resentation of Cahen, Debever, Defrise [13], [14], [15] …”

Section: Introductionmentioning

confidence: 99%