A note on the definition of gravitational energy for quadratic curvature gravity via topological regularization

doi:10.1088/1674-1056/abb3e0

Abstract Within the framework of four-dimensional quadratic curvature gravities in the appearance of a negative cosmological constant, a definition for the gravitational energy of solutions with anti-de Sitter (AdS) asymptotics was put forward by Giribet et al. [Phys. Rev. D 98 044046 (2018)]. This was achieved by adding proper topological invariant terms to the gravity action to render the variation problem well-posed. We prove that the definition via the procedure of topological regularization can be covered by our previous work [Int. J. Mod. Phys. A 35 2050102 (2020)] in four dimensions. Motivated by this, we further generalize the results to generic diffeomorphism invariant theories of gravity in arbitrary even dimensions.

Keywords: gravitational energy higher-derivative gravity asymptotically AdS gravity

Received: 23 April 2020
Revised: 23 April 2020
Accepted manuscript online: 01 September 2020

PACS:	04.50.Kd	(Modified theories of gravity)
	04.50.-h	(Higher-dimensional gravity and other theories of gravity)
	04.70.-s	(Physics of black holes)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11865006 and 11847152).

Corresponding Authors: ^†Corresponding author. E-mail: mengliang.wang@mail.gufe.edu.cn ^‡Corresponding author. E-mail: pengjjph@163.com

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Meng-Liang Wang(王梦亮) and Jun-Jin Peng(彭俊金) A note on the definition of gravitational energy for quadratic curvature gravity via topological regularization 2020 Chin. Phys. B 29 120401

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