The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity

Author:

Capozziello Salvatore1,Capriolo Maurizio2

Affiliation:

1. Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Complesso Universitario di Monte S. Angelo, Edificio G, Napoli, Italy + Scuola Superiore Meridionale, Napoli, Italy + Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Edificio G, Napoli, Italy

2. Dipartimento di Fisica “E. R. Caianiello”, Università degli Studi di Salerno, Fisciano, Italy + Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Edificio G, Napoli, Italy

Abstract

The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pseudo-tensor. Therefore we propose a possible prescription of gravitational energy and momentum density for ?k gravity governed by the gravitational Lagrangian L1 = (R + a0R2 + Pp k=1 akR?kR) ??g and generally for n-order gravity described by the gravitational Lagrangian L = L (g??, g??,i1, 1??,i1i2, g??,i1i2i3 ,..., g??,i1i2i3...in). The extended pseudo-tensor reduces to the one introduced by Einstein in the limit of general relativity where corrections vanish. Then, we explicitly show a useful calculation, i.e., the power per unit solid angle ? emitted by a massive system and carried by a gravitational wave in the direction ? x for a fixed wave number k. We fix a suitable gauge, by means of the average value of the pseudo-tensor over a spacetime domain and we verify that the local pseudo-tensor conservation holds. The gravitational energy-momentum pseudo-tensor may be a useful tool to search for possible further gravitational modes beyond the two standard ones of general relativity. Their finding could be a possible observable signatures for alternative theories of gravity.

Publisher

National Library of Serbia

Reference44 articles.

1. L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, Pergamon Press, Oxford, 1971.

2. A. Einstein, Zur Allgemeinen Relativitätstheorie, Sitzungsber. Preus. Akad. Wiss. Berlin (Math. Phys.) 47(1915) 778-779.

3. D. Hestenes, Energy-Momentum Complex in General Relativity and Gauge Theory, Adv. Appl. Clifford Algebra 31(2021), 51.

4. J. N. Goldberg, Conservation Laws in General Relativity, Phys. Rev. 111(1958) 315.

5. B. Dongsu, D. Cangemi, R. Jackiw, Energy-momentum conservation in gravity theories, Phys. Rev. D 49(1994) 5173.

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