The gravitational energy‐momentum pseudo‐tensor of higher‐order theories of gravity |
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| Authors: | Salvatore Capozziello Maurizio Capriolo Maria Transirico |
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| Institution: | 1. Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, Napoli, Italy;2. INFN Sezione di Napoli, Compl. Univ. di Monte S. Angelo, Napoli, Italy;3. Gran Sasso Science Institute, L'Aquila, Italy;4. Tomsk State Pedagogical University, Russia;5. Dipartimento di Matematica Università di Salerno, Fisciano, SA, Italy |
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| Abstract: | We derive the gravitational energy momentum tensor  for a general Lagrangian of any order  and in particular for a Lagrangian such as  . We prove that this tensor, in general, is not covariant but only affine, then it is a pseudo‐tensor. Furthermore, the pseudo‐tensor  is calculated in the weak field limit up to a first non‐vanishing term of order h2 where h is the metric perturbation. The average value of the pseudo‐tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle Ω carried by a gravitational wave in a direction  for a fixed wave number  under a suitable gauge. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with nonlocal theories of gravity where terms involving  are present. The general aim of the approach is to deal with theories of any order under the same standard of Landau pseudo‐tensor. |
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| Keywords: | general relativity alternative theories of gravity affine transformations gravitational waves |
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for a general Lagrangian of any order 
and in particular for a Lagrangian such as 
. We prove that this tensor, in general, is not covariant but only affine, then it is a pseudo‐tensor. Furthermore, the pseudo‐tensor 
is calculated in the weak field limit up to a first non‐vanishing term of order h2 where h is the metric perturbation. The average value of the pseudo‐tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle Ω carried by a gravitational wave in a direction 
for a fixed wave number 
under a suitable gauge. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with nonlocal theories of gravity where terms involving 
are present. The general aim of the approach is to deal with theories of any order under the same standard of Landau pseudo‐tensor.