A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity
arXiv:2008.06733 · doi:10.1088/1402-4896/ac1cd1
Abstract
The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two third-order derivative terms generated by the action of the d'Alembertian operator and the exterior derivative upon a Killing vector. Then this higher-order corrected potential is extended to the Einstein gravity with a negative cosmological constant, yielding the potential that is the linear combination of the usual Komar one with it acted on by the d'Alembertian. The surface integral of the improved Komar potential can serve as a formula for conserved charges of asymptotically AdS spacetimes. Finally, we make use of such a formula to compute the mass and the angular momentum of Schwarzschild-AdS black holes, regular AdS black holes, asymptotically AdS Kerr-Sen black holes, Kerr-NUT-AdS black holes, and Kerr-AdS black holes in arbitrary dimensions. The results coincide with the ones in the literature.
arXiv comment27 pages, No figures, minor revision to V1
References in corpus (47)
- Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
- A Stress Tensor for Anti-de Sitter Gravity
- Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
- Enthalpy and the Mechanics of AdS Black Holes
- A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
- Rotation and the AdS/CFT correspondence
- Covariant theory of asymptotic symmetries, conservation laws and central charges
- The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes
- The General Kerr-de Sitter Metrics in All Dimensions
- Energy in Generic Higher Curvature Gravity Theories
- Construction of Regular Black Holes in General Relativity
- Asymptotically Anti-de Sitter Space-times: Conserved Quantities
- Rotating Black Holes in Higher Dimensions with a Cosmological Constant
- Gravitational Energy in Quadratic Curvature Gravities
- The Gravitational Action in Asymptotically AdS and Flat Spacetimes
- Surface charge algebra in gauge theories and thermodynamic integrability
- General Kerr-NUT-AdS Metrics in All Dimensions
- Conserved charges for gravity with locally AdS asymptotics
- Relativistic conservation laws and integral constraints for large cosmological perturbations
- Boundary charges in gauge theories: using Stokes theorem in the bulk
- Mass, Angular Momentum and Thermodynamics in Four-Dimensional Kerr-AdS Black Holes
- Conserved Charges for Even Dimensional Asymptotically AdS Gravity Theories
- Regularization of odd-dimensional AdS gravity: Kounterterms
- Quasi-Local Conserved Charges in Covariant Theory of Gravity
- Conserved Quantities in Kerr-anti-de Sitter Spacetimes in Various Dimensions
- Komar Integrals in Higher (and Lower) Derivative Gravity
- Generalized Smarr relation for Kerr AdS black holes from improved surface integrals
- Conserved Charges of Higher D Kerr-AdS Spacetimes
- On the mass of a Kerr-anti-de Sitter spacetime in D dimensions
- Are ultra-spinning Kerr-Sen-AdS black holes always super-entropic ?
- Radiation generated by accelerating and rotating charged black holes in (anti-)de Sitter space
- Regular black holes in an asymptotically de Sitter universe
- Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories
- Invariant conserved currents for gravity
- Energy in Higher-Derivative Gravity via Topological Regularization
- New approach to conserved charges of generic gravity in AdS
- Conserved charges in AdS: A new formula
- Invariant conserved currents in generalized gravity
- Topological invariants and the definition of energy in quadratic gravity theory
- Mass and angular momentum of black holes in low-energy heterotic string theory
- The Field-Theoretic Approach in General Relativity and Other Metric Theories. A Review
- Field-theoretical construction of currents and superpotentials in Lovelock gravity
- A new formula for conserved charges of Lovelock gravity in AdS spacetimes and its generalization
- A note on the mass of Kerr-AdS black holes in the off-shell generalized ADT formalism
- Constructing -forms from -forms via the Hodge star operator and the exterior derivative
- A note on the definition of gravitational energy for quadratic curvature gravity via topological regularization
- Generalized Komar currents for vector fields
Cited by in corpus (4)
- Dual Charges for AdS Spacetimes and the First Law of Black Hole Mechanics
- Thermodynamics of Black Holes with Rényi Entropy from Classical Gravity
- Slowly Rotating Black Holes in 4D Einstein Gauss-Bonnet Gravity
- Exact Taub-NUT-like Black Holes in Einstein-bumblebee gravity: their thermodynamics and thermodynamic topology