scholarly journals TACHYON CONDENSATION AND OFF-SHELL GRAVITY/GAUGE DUALITY

2007 ◽  
Vol 22 (01) ◽  
pp. 41-65 ◽  
Author(s):  
YUN SOO MYUNG
Keyword(s):  
Black Hole ◽  
Free Energy ◽  
Tachyon Condensation ◽  
Schwarzschild Black Hole ◽  
End Point ◽  
Verlinde Formula ◽  
Β Function ◽  
Canonical Ensembles

We investigate quasilocal tachyon condensation by using gravity/gauge duality. In order to cure the IR divergence due to a tachyon, we introduce two regularization schemes: AdS space and a d = 10 Schwarzschild black hole in a cavity. These provide stable canonical ensembles and thus are good candidates for the end point of tachyon condensation. Introducing the Cardy–Verlinde formula, we establish the on-shell gravity/gauge duality. We propose that the stringy geometry resulting from the off-shell tachyon dynamics matches onto the off-shell AdS black hole, where "off-shell" means nonequilibrium configuration. The instability induced by condensation of a tachyon behaves like an off-shell black hole and evolves toward a large stable black hole. The off-shell free energy and its derivative (β-function) are used to show the off-shell gravity/gauge duality for the process of tachyon condensation. Further, d = 10 Schwarzschild black hole in a cavity is considered for the Hagedorn transition as a possible explanation of the tachyon condensation.

scholarly journals Thermodynamic properties of Bardeen black holes in dRGT massive gravity

2021 ◽  
Author(s):  
R P Singh ◽  
B K Singh ◽  
B R K Gupta ◽  
S Sachan
Keyword(s):  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Black Hole Solution ◽  
Massive Gravity ◽  
Schwarzschild Black Hole ◽  
Regular Black Hole ◽  
Horizon Radius ◽  
Canonical Ensembles ◽  
Grand Canonical

The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is the modification of the Schwarzschild black hole. We present the Bardeen black hole solution in presence of the dRGT massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution interpolates with the Bardeen black hole in the absence of massive gravity parameter and the Schwarzschild black hole in the limit of magnetic charge g=0. We investigate the thermodynamical quantities viz. mass (M), temperature (T), entropy (S) and free energy (F) in terms of horizon radius for both canonical and grand canonical ensembles. We check the local and global stability of the obtained solution by studying the heat capacity and free energy. The heat capacity flips the sign at r = r<sub>c</sub>. The black hole is thermodynamically stable with positive heat capacity C>0 for i.e., globally preferred with negative free energy F < 0. In addition, we also study the phase structure of the obtained solution in both ensembles.

The Free Energy for Rotating and Charged Black Holes and Banados, Teitelboim and Zanelli Black Holes

2018 ◽  
Vol 73 (11) ◽  
pp. 1061-1073 ◽  
Author(s):  
N.A. Hussein ◽  
D.A. Eisa ◽  
T.A.S. Ibrahim
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Quantum Correction ◽  
Kerr Black Hole ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Charged Black Holes ◽  
Thermodynamic Variables

AbstractThis paper aims to obtain the thermodynamic variables (temperature, thermodynamic volume, angular velocity, electrostatic potential, and heat capacity) corresponding to the Schwarzschild black hole, Reissner-Nordstrom black hole, Kerr black hole and Kerr-Newman-Anti-de Sitter black hole. We also obtained the free energy for black holes by using three different methods. We obtained the equation of state for rotating Banados, Teitelboim and Zanelli black holes. Finally, we used the quantum correction of the partition function to obtain the heat capacity and entropy in the quantum sense.

scholarly journals HOLOGRAPHIC ENTROPY AND BRANE FRW DYNAMICS FROM AdS BLACK HOLE IN d5 HIGHER DERIVATIVE GRAVITY

2001 ◽  
Vol 16 (31) ◽  
pp. 5085-5099 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV ◽  
SACHIKO OGUSHI
Keyword(s):  
Black Hole ◽  
Gravitational Constant ◽  
Scale Parameter ◽  
Riemann Tensor ◽  
Schwarzschild Black Hole ◽  
Strongly Coupled ◽  
Verlinde Formula ◽  
Higher Derivative ◽  
Entropy Bounds ◽  
Tensor Square

Higher derivative bulk gravity (without Riemann tensor square term) admits AdS–Schwarzschild black hole as an exact solution. It is shown that induced brane geometry on such background is open, flat or closed FRW radiation dominated universe. Higher derivative terms contributions appear in the Hawking temperature, entropy and Hubble parameter via the redefinition of five-dimensional gravitational constant and AdS scale parameter. These higher derivative terms do not destroy the AdS-dual description of radiation represented by strongly-coupled CFT. The Cardy–Verlinde formula which expresses cosmological entropy as the square root from other parameters and entropies is derived in R2gravity. The corresponding cosmological entropy bounds are briefly discussed.

scholarly journals HOLOGRAPHIC ENTROPY ON THE BRANE IN de SITTER SCHWARZSCHILD SPACE

2002 ◽  
Vol 17 (01) ◽  
pp. 51-58 ◽  
Author(s):  
SACHIKO OGUSHI
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Black Hole Entropy ◽  
Brane Tension ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Verlinde Formula ◽  
The Relationship ◽  
Friedmann Robertson Walker ◽  
Schwarzschild Background

The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann–Robertson–Walker (FRW) equations and Cardy–Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both for time-like and space-like cases, the entropy of the CFT exactly agrees with the black hole entropy of five-dimensional dS background as it happens in the AdS/CFT correspondence.

scholarly journals Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
G. Abbas
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Conformal Field Theory ◽  
Total Energy ◽  
Arbitrary Dimension ◽  
Casimir Energy ◽  
Schwarzschild Black Hole ◽  
Conformal Field ◽  
Entropy Formula ◽  
Verlinde Formula

Few years ago, Setare (2006) has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.

Thermodynamic phase transition of quantum-corrected Schwarzschild black hole based on nonsingular temperature

2019 ◽  
Vol 34 (21) ◽  
pp. 1950161 ◽  
Author(s):  
Md. Shahjalal
Keyword(s):  
Phase Transition ◽  
Black Hole ◽  
Free Energy ◽  
Hole State ◽  
Thermodynamic Quantities ◽  
Schwarzschild Black Hole ◽  
Radiation Process ◽  
Spacetime Geometry ◽  
Large Black Hole ◽  
The Stability

Due to thermal radiation process, the temperature of the Schwarzschild black hole diverges at the time the black hole evaporates, while it is natural to expect a vanishing temperature, since the spacetime geometry becomes Minkowskian whose intrinsic temperature is identically zero. Recently, a nonsingular temperature has been proposed in this research line, which follows the Hawking temperature for the large black hole system, at the same time becomes null in the limiting case the black hole mass tends to zero. In this paper, the stability and the phase transition of the quantum-corrected Schwarzschild black hole are investigated based on this modified temperature. For that, the thermodynamic quantities like the local temperature, the heat capacity, and the off-shell free energy are calculated. The results show that the free energy of the black hole follows the characteristic swallow-tail behavior, implying the existence of an unstable intermediate black hole state quickly decaying into the stable small or large black hole.

The Schwarzschild black hole

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Equilibrium Configuration ◽  
Original Form ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

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