A tale of two horizons

2015 ◽  
Vol 93 (9) ◽  
pp. 995-998 ◽  
Author(s):  
Sean Stotyn
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Space Time ◽  
Extremal Black Hole ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Event Horizons ◽  
Extremal Limit ◽  
Horizon Geometry ◽  
Killing Horizons

I revisit the fate of coinciding horizons and the volume between them in the extremal limit of spherically symmetric black holes in four space–time dimensions, focusing on the Schwarzschild – de Sitter black hole for concreteness. The two Killing horizons in the limit space–time that are traditionally identified with the limiting event horizons of the non-extremal black hole are shown to instead be generated by an enhanced symmetry of the near horizon geometry (NHG). This dismantles the interpretation of the four-volume between the horizons remaining finite in the extremal limit. The NHG is reinterpreted as a tangent space–time to the degenerate black hole horizon, and geometrical objects, such as Killing vectors and Killing horizons, are carefully mapped between the bulk and the NHG. The implications for extremal black hole entropy are then discussed.

scholarly journals REGULAR BLACK HOLES IN AN ASYMPTOTICALLY DE SITTER UNIVERSE

2008 ◽  
Vol 23 (40) ◽  
pp. 3377-3392 ◽  
Author(s):  
JERZY MATYJASEK ◽  
DARIUSZ TRYNIECKI ◽  
MARIUSZ KLIMEK
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Nonlinear Electrodynamics ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Coupled Equations ◽  
Sitter Universe ◽  
De Sitter Universe ◽  
Horizon Geometry ◽  
Interesting Solution

A regular solution of the system of coupled equations of the nonlinear electrodynamics and gravity describing static and spherically-symmetric black holes in an asymptotically de Sitter universe is constructed and analyzed. Special emphasis is put on the degenerate configurations (when at least two horizons coincide) and their near horizon geometry. It is explicitly demonstrated that approximating the metric potentials in the region between the horizons by simple functions and making use of a limiting procedure one obtains the solutions constructed from maximally symmetric subspaces with different absolute values of radii. Topologically they are AdS2×S2 for the cold black hole, dS2×S2 when the event and cosmological horizon coincide, and the Plebański–Hacyan solution for the ultraextremal black hole. A physically interesting solution describing the lukewarm black holes is briefly analyzed.

scholarly journals Extremal charged Vaidya and its near horizon geometry

2017 ◽  
Vol 26 (04) ◽  
pp. 1750036
Author(s):  
S. Sadeghian ◽  
A. Shafiekhani
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Black Hole Solution ◽  
Spherically Symmetric ◽  
Nonstationary Solution ◽  
Vaidya Black Hole ◽  
Extremal Limit ◽  
Horizon Geometry ◽  
Extremal Black Holes

Recently [Formula: see text]-dimensional spherically symmetric charged Vaidya black hole solution has been constructed. We observe that this nonstationary solution admits extremal limit and study its near horizon geometry. We show that the symmetry of the near horizon geometry is [Formula: see text]. Our analysis shows that the theorems for the near horizon geometry of stationary extremal black holes, may be extended to nonstationary cases.

scholarly journals QUANTUM ENTROPY FUNCTION FROM AdS2/CFT1 CORRESPONDENCE

2009 ◽  
Vol 24 (23) ◽  
pp. 4225-4244 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Black Hole ◽  
Partition Function ◽  
Classical Limit ◽  
Black Hole Entropy ◽  
Entropy Function ◽  
Quantum Entropy ◽  
Extremal Black Hole ◽  
Statistical Entropy ◽  
Specific Relation ◽  
Horizon Geometry

We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS 2/ CFT 1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry — named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical entropy and Wald entropy.

scholarly journals SPHERICALLY SYMMETRIC SPACE–TIME WITH REGULAR DE SITTER CENTER

2003 ◽  
Vol 12 (06) ◽  
pp. 1015-1034 ◽  
Author(s):  
IRINA DYMNIKOVA
Keyword(s):  
Black Hole ◽  
Energy Condition ◽  
Space Time ◽  
Cosmological Term ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Sitter Group ◽  
Class Invariant ◽  
Time Symmetry ◽  
De Sitter Vacuum

We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center. The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure [Formula: see text] associated with an r-dependent cosmological term [Formula: see text], whose asymptotic at the origin, dictated by the weak energy condition, is the Einstein cosmological term Λgμν, while asymptotic at infinity is de Sitter vacuum with λ < Λ or Minkowski vacuum. For this class of metrics the mass m defined by the standard ADM formula is related to both the de Sitter vacuum trapped at the origin and the breaking of space–time symmetry. In the case of the flat asymptotic, space–time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through radial boosts in between. Geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild at large r. In the range of masses m ≥ m crit , the de Sitter–Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < m crit it describes G-lump — a vacuum selfgravitating particle-like structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild–de Sitter at large r. Λμν geometry describes, dependently on parameters m and [Formula: see text] and choice of coordinates, a vacuum nonsingular cosmological black hole, self-gravitating particle-like structure at the de Sitter background λgμν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.

NUMERICAL SOLUTIONS OF IDEAL TWO-FLUID TRANSVERSE EQUATIONS VERY CLOSED TO THE EVENT HORIZON OF REISSNER–NORDSTRÖM–ANTI-DE SITTER BLACK HOLE

2013 ◽  
Vol 22 (09) ◽  
pp. 1350063
Author(s):  
M. ATIQUR RAHMAN
Keyword(s):  
Black Hole ◽  
Electromagnetic Waves ◽  
Numerical Solutions ◽  
Linear Equations ◽  
Wave Number ◽  
Extremal Black Hole ◽  
De Sitter ◽  
Simultaneous Linear Equations ◽  
Horizon Geometry ◽  
Two Fluid

The Alfvén and high frequency electromagnetic waves propagating in a relativistic two-fluid plasma influenced by the gravitational field of the Reissner–Nordström–anti-de Sitter (RNAdS) black hole have been investigated applying 3+1 split of spacetime. The extremal cases also discussed here based on the simple observation that the near-horizon geometry of a static extremal black hole contains two-dimensional anti-de Sitter factor even in the presence of positive cosmological constant. We reformulate the relativistic two-fluid equations with the set of simultaneous linear equations for the perturbations. We derive the dispersion relation for these waves and solve numerically for the wave number k.

scholarly journals Driven black holes: from Kolmogorov scaling to turbulent wakes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Tomas Andrade ◽  
Christiana Pantelidou ◽  
Julian Sonner ◽  
Benjamin Withers
Keyword(s):  
Nonlinear Dynamics ◽  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Strong Field ◽  
De Sitter ◽  
Event Horizons ◽  
Binary Mergers ◽  
Tidal Deformations ◽  
Proof Of Principle

Abstract General relativity governs the nonlinear dynamics of spacetime, including black holes and their event horizons. We demonstrate that forced black hole horizons exhibit statistically steady turbulent spacetime dynamics consistent with Kolmogorov’s theory of 1941. As a proof of principle we focus on black holes in asymptotically anti-de Sitter spacetimes in a large number of dimensions, where greater analytic control is gained. We focus on cases where the effective horizon dynamics is restricted to 2+1 dimensions. We also demonstrate that tidal deformations of the horizon induce turbulent dynamics. When set in motion relative to the horizon a deformation develops a turbulent spacetime wake, indicating that turbulent spacetime dynamics may play a role in binary mergers and other strong-field phenomena.

scholarly journals Uptunneling to de Sitter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Mehrdad Mirbabayi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
False Vacuum ◽  
De Sitter ◽  
Dimensional Theory ◽  
Hole Geometry ◽  
Horizon Geometry ◽  
Two Sides ◽  
Extremal Black Holes

Abstract We propose a Euclidean preparation of an asymptotically AdS2 spacetime that contains an inflating dS2 bubble. The setup can be embedded in a four dimensional theory with a Minkowski vacuum and a false vacuum. AdS2 approximates the near horizon geometry of a two-sided near-extremal Reissner-Nordström black hole, and the two sides can connect to the same Minkowski asymptotics to form a topologically nontrivial worm- hole geometry. Likewise, in the false vacuum the near-horizon geometry of near-extremal black holes is approximately dS2 times 2-sphere. We interpret the Euclidean solution as describing the decay of an excitation inside the wormhole to a false vacuum bubble. The result is an inflating region inside a non-traversable asymptotically Minkowski wormhole.

ISOMETRY HORIZONS IN SPHERICALLY SYMMETRIC SPACE–TIMES

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1263-1271
Author(s):  
J. SZENTHE
Keyword(s):  
Symmetric Space ◽  
Spherically Symmetric ◽  
Isometric Action ◽  
Event Horizons ◽  
Killing Horizons

Some event horizons in space–times that are invariant under an isometric action, considered first by Carter, are called isometry horizons, especially Killing horizons. In this paper, isometry horizons in spherically symmetric space–times are considered. It is shown that these isometry horizons are all Killing horizons.

scholarly journals Near extremal black hole entropy as entanglement entropy viaAdS2/CFT1

2008 ◽  
Vol 77 (6) ◽  
Author(s):  
Tatsuo Azeyanagi ◽  
Tatsuma Nishioka ◽  
Tadashi Takayanagi
Keyword(s):  
Black Hole ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Extremal Black Hole
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