Characterization of the Lovelock gravity by Bianchi derivative

Abstract

We prove the theorem: The second order quasi-linear differential operator as a second rank divergence free tensor in the equation of motion for gravitation could always be derived from the trace of the Bianchi derivative of the fourth rank tensor, which is a homogeneous polynomial in curvatures. The existence of such a tensor for each term in the polynomial Lagrangian is a new characterization of the Lovelock gravity.

Agrees with the published version

References in corpus (2)

• Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
• Formation of a black hole from an AdS spacetime

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