Non-uniform black strings and the critical dimension in the $1/D$ expansion

Abstract

Non-uniform black strings (NUBS) are studied by the large $D$ effective theory approach. By solving the near-horizon geometry in the $1/D$ expansion, we obtain the effective equation for the deformed horizon up to the next-to-next-to-leading order (NNLO) in $1/D$. We also solve the far-zone geometry by the Newtonian approximation. Matching the near and far zones, the thermodynamic variables are computed in the $1/D$ expansion. As the result, the large $D$ analysis gives a critical dimension $D_{\ast }\simeq 13.5$ at which the translation-symmetry-breaking phase transition changes between first and second order. This value of $D_{\ast }$ agrees perfectly, within the precision of the $1/D$ expansion, with the result previously obtained by E. Sorkin through the numerical resolution. We also compare our NNLO results for the thermodynamics of NUBS to earlier numerical calculations, and find good agreement within the expected precision.

33 pages, 8 figures, Ancillary Mathematica notebook contains details of NNLO results; v2: Published version

References in corpus (12)

• Black Strings, Low Viscosity Fluids, and Violation of Cosmic Censorship
• Classical Effective Field Theory and Caged Black Holes
• Effective theory of Black Holes in the 1/D expansion
• A membrane paradigm at large D
• High and Low Dimensions in The Black Hole Negative Mode
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• New nonuniform black string solutions
• Nonuniform black strings in various dimensions
• Stable non-uniform black strings below the critical dimension
• Lumpy AdS${}_5\times$ S${}^5$ Black Holes and Black Belts
• Bumpy black holes
• Stationary black holes: Large $D$ analysis

Cited by in corpus (39)

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• Currents and Radiation from the large $D$ Black Hole Membrane
• Phases and Stability of Non-Uniform Black Strings
• Instability of de Sitter Reissner-Nordstrom black hole in the 1/D expansion
• Black rings at large D
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Unstable `black branes' from scaled membranes at large $D$
• Rotating black holes and black bars at large D
• On Brane Instabilities in the Large $D$ Limit
• 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
• Charged Black Rings at large D
• The large D black hole dynamics in AdS/dS backgrounds
• Black holes in presence of cosmological constant: Second order in 1/D
• 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
• Holographic Turbulence in Einstein-Gauss-Bonnet Gravity at Large $D$
• Elastic instability of black rings at large D
• Stationary black holes: Large $D$ analysis
• Black Ripples, Flowers and Dumbbells at large $D$
• Non-spherically symmetric black string perturbations in the large D limit
• The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity
• The Fate of Instability of de Sitter Black Holes at Large $D$
• The large D effective theory of black strings in AdS
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• Black hole interactions at large $D$: brane blobology
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• Phase and stability of black strings in Einstein-Gauss-Bonnet theory at large D
• Lattice Black Branes at Large $D$
• Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit
• Stress Tensor for Large-$D$ membrane at subleading orders
• Squashed black holes at large $D$