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.
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