Fake Supersymmetry and Extremal Black Holes

Abstract

We derive the BPS type of first order differential equations for the rotating black hole solutions in the three-dimensional Einstein gravity coupled minimally with a self-interacting scalar field, using fake supersymmetry formalism. It turns out that the formalism is not complete and should be augmented by an additional equation to imply the full equations of motion. We identify this additional equation as a constraint by using an effective action method. By computing the renormalized boundary stress tensor, we obtain the mass and angular momentum of the black hole solutions of these first order equations and confirm that they saturate the BPS bound.

1+18 pages, no figure v2: references added, typos fixed

References in corpus (6)

• Thermodynamics of the Maxwell-Gauss-Bonnet anti-de Sitter Black Hole with Higher Derivative Gauge Corrections
• The CFT-interpolating Black Hole in Three Dimensions
• Mass and Angular momentum of Black Holes in New Massive Gravity
• Mass and Thermodynamics of Kaluza-Klein Black Holes with Squashed Horizons
• Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity
• Extremal Black Holes and Holographic C-Theorem

Cited by in corpus (26)

• The Weak Gravity Conjecture in three dimensions
• Quantum Extremal Islands Made Easy, Part IV: Massive Black Holes on the Brane
• A unified phase transition picture of the charged topological black hole in Horava-Lifshitz gravity
• Thermodynamical topology of quantum BTZ black hole
• The kinetics and its turnover of Hawking-Page phase transition under the black hole evaporation
• AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity
• Critical behavior of AdS Gauss-Bonnet massive black holes in the presence of external string cloud
• (2+1)-dimensional solutions in $F(R)$ gravity
• Hawking--Page phase transitions of the black holes in a cavity
• Kinetics of Hawking-Page phase transition with the non-Markovian effects
• Thermal fluctuations of black holes with non-linear electrodynamics and charged Renyi entropy
• Fubini instantons in Dilatonic Einstein-Gauss-Bonnet theory of gravitation
• A unified thermodynamic picture of Hořava-Lifshitz black hole in arbitrary space time
• Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics
• Thermodynamic phase transition based on the non-singular temperature
• Thermodynamics and phase transition of BTZ black hole in a cavity
• On the dual relation in the Hawking--Page phase transition of the black holes in a cavity
• Stability and topological nature of charged Gauss-Bonnet AdS black holes in five dimensions
• Calculating the Hawking Temperatures of Conventional Black Holes in the f(R) Gravity Models with the RVB Method
• Hawking radiation and entropy of a BTZ black hole with minimum length
• Topological Entanglement Entropy in Euclidean AdS3 via Surgery
• Validity of black hole complementarity in the BTZ black hole
• Phase transition of black holes in Brans--Dicke Born--Infeld gravity through geometrical thermodynamics
• Phase transition in black holes
• Thermodynamic geometric analysis of RN black holes under f(R) gravity
• Topological entanglement entropy of the BTZ black hole