Stationary Solutions from the Large D Membrane Paradigm

Abstract

It has recently been shown that the dynamics of black holes in large number of dimensions D can be recast as the dynamics of a probe membrane propagating in the background spacetime which solves Einstein equations without matter. The equations of motion of this membrane are simply the statement of conservation of the stress tensor and charge current defined on this membrane. In this paper we obtain the effective equations of motion for stationary membranes in any empty background both in presence and absence of charge. It turns out that the thermodynamic quantities associated with the stationary membranes that satisfy these effective equations also satisfy the first law of black hole thermodynamics. These stationary membrane equations have some interesting solutions such as charged rotating black holes in flat and AdS backgrounds as well as black ring solutions in large D.

arXiv comment48 pages(9 pages appendix), 5 figures, 2 tables, includes additional references

References in corpus (38)

• Instability of Ultra-Spinning Black Holes
• The large D limit of General Relativity
• An instability of higher-dimensional rotating black holes
• Large D gravity and low D strings
• Effective theory of Black Holes in the 1/D expansion
• Black Holes as Lumps of Fluid
• Decoupling and non-decoupling dynamics of large D black holes
• A membrane paradigm at large D
• Universal quasinormal modes of large D black holes
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• Hydro-elastic Complementarity in Black Branes at large D
• Instability of rotating black holes: large D analysis
• The holographic dual of a Riemann problem in a large number of dimensions
• The large D black hole Membrane Paradigm at first subleading order
• Currents and Radiation from the large $D$ Black Hole Membrane
• Phases and Stability of Non-Uniform Black Strings
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Unstable `black branes' from scaled membranes at large $D$
• Holographic superconductivity in the large D expansion
• On Brane Instabilities in the Large $D$ Limit
• Holographic Turbulence in a Large Number of Dimensions
• An Action for and Hydrodynamics from the improved Large D membrane
• Static Gauss-Bonnet Black Holes at Large $D$
• A Charged Membrane Paradigm at Large D
• Constraints on the effective fluid theory of stationary branes
• Charged Black Rings at large D
• The large D black hole dynamics in AdS/dS backgrounds
• Charged rotating black holes at large D
• Black Holes and Biophysical (Mem)-branes
• The Large Dimension Limit of a Small Black Hole Instability in Anti-de Sitter Space
• Einstein-Gauss-Bonnet Black Rings at Large $D$
• Large D holography with metric deformations
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Gravitational Tension, Spacetime Pressure and Black Hole Volume
• Elastic instability of black rings at large D
• Instability of Charged Gauss-Bonnet Black Hole in de Sitter Spacetime at Large $D$
• Non-spherically symmetric black string perturbations in the large D limit
• Horizon Tunneling Revisited: The Case of Higher Dimensional Black Holes

Cited by in corpus (13)

• The Large D Limit of Einstein's Equations
• Charged rotating black holes in higher dimensions
• Large D gravity and charged membrane dynamics with nonzero cosmological constant
• Black Ripples, Flowers and Dumbbells at large $D$
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity
• Fluid-gravity and membrane-gravity dualities - Comparison at subleading orders
• Hidden Conformal Symmetries from Killing Towers with an Application to Large-D/CFT
• Black hole interactions at large $D$: brane blobology
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Rotating black holes at large $D$ in Einstein-Gauss-Bonnet theory
• Black hole one-loop determinants in the large dimension limit
• Squashed black holes at large $D$