Energy in Higher-Derivative Gravity via Topological Regularization

Abstract

We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein equations. We focus on the theory in four dimensions, in presence of negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method differs qualitatively from other ones in the feature of being intrinsically non-linear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions, such as gravitational waves in AdS, for which we also find results in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory.

arXiv comment13 pages, no figures; In v2, a section (Logarithmic modes) and new references added

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Cited by in corpus (13)

• Topological Terms and the Misner String Entropy
• Mass in Lovelock Unique Vacuum gravity theories
• Higher-derivative harmonic oscillators: stability of classical dynamics and adiabatic invariants
• Dual Charges for AdS Spacetimes and the First Law of Black Hole Mechanics
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• Topological invariants and the definition of energy in quadratic gravity theory
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• CFT correlators from shape deformations in Cubic Curvature Gravity
• Universal renormalization procedure for higher curvature gravities in D$\le$5
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• Horizon thermodynamics in $f(R,R^{\mu \nu }{R}_{\mu \nu })$ theory
• A note on the definition of gravitational energy for quadratic curvature gravity via topological regularization