Conservation Laws and Symmetry Properties of a Class of Higher Order Theories of Gravity

Details Conservation Laws and Symmetry Properties of a Class of Higher Order Theories of Gravity Conservation Laws and Symmetry Properties of a Class of Higher Order Theories of Gravity

Apr 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998gregr..30..629b&link_type=abstract

General Relativity and Gravitation, Volume 30, Issue 4, pp.629-642

Mathematics

Logic

1

Higher Order Gravity, Conservation Laws

Scientific paper

We consider a class of fourth order theories of gravity with arbitrary matter fields arising from a diffeomorphism invariant Lagrangian density mathcal{L}_T = mathcal{L}_G + mathcal{L}_M, with mathcal{L}_G = sqrt { - g} left[ {R + hleft( R right)} right]and mathcal{L}_Mthe phenomenological representation of the nongravitational fields. We derive first the generalization of the Einstein pseudotensor and the von Freud superpotential. We then show, using the arbitrariness that is always present in the choice of pseudotensor and superpotential, that we can choose these superpotentials to have the same form as those for the Hilbert Lagrangian of general relativity (GR). In particular we may introduce the Moller superpotential of GR as associated with a double-index differential conservation law. Similarly, using the Moller superpotential we prove that we can choose the Komar vector of GR to construct a conserved quantity for isolated asymptotically flat systems. For the example R + R2theory we prove then, that the active mass is equal to the total energy (or inertial mass) of the system.

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