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 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.

The Wheeler–Dewitt Equation for the Superstring World Sheet

1997 ◽  
Vol 06 (01) ◽  
pp. 91-105 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Black Hole ◽  
Ground State ◽  
Total Mass ◽  
Equation Of Motion ◽  
Schwarzschild Black Hole ◽  
World Sheet ◽  
Integral Expression ◽  
Higher Derivative ◽  
The World ◽  
The Universe

The Wheeler–DeWitt equation for the wave function ψ is obtained from the two-dimensional world-sheet action for the bosonic string and the superstring, including higher-derivative terms, as the Schrödinger equation i ∂ ψ/ ∂τ = V(τ)ψ. The potential is given by the rate at which the world-sheet area is swept out, V(τ) = dA(τ)/dτ, and is positive semi-definite, allowing the existence of a ground state, corresponding to the absence of the string, with a non-vanishing probability density ψ ψ*. Integration of this equation yields the solution [Formula: see text], where [Formula: see text] is the action, minus the higher-derivative terms [Formula: see text] (and terms involving ∊ab in the case of the superstring), which, however, are constrained to vanish semi-classically, being constructed from the square of the equation of motion for the bosonic coordinates XA derived from [Formula: see text] alone. This path-integral expression for ψ is consistent with the operator replacements for the canonical momenta used in its derivation, and forms the basis of the approach due to Polyakov of summing over random surfaces. Comparison is made with the Schrödinger equations derived previously from the reduced, four-dimensional effective action for the heterotic superstring, and for the Schwarzschild black hole (by Tomimatsu), where the potential is also positive semi-definite, being (twice) the total mass of the Universe and the mass of the black hole, respectively, showing the unity of the method.

On the internal state of the Schwarzschild black hole

2017 ◽  
Vol 26 (09) ◽  
pp. 1750088
Author(s):  
M. D. Pollock
Keyword(s):  
Black Hole ◽  
Internal State ◽  
Energy Condition ◽  
Momentum Tensor ◽  
Schwarzschild Black Hole ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Central Singularity ◽  
Symmetric Line ◽  
Tensor Formula

If the classical gravitational Lagrangian contains higher-derivative terms [Formula: see text], where [Formula: see text], then vacuum solutions of the Einstein–Hilbert theory [Formula: see text] are subject to modification at sufficiently large spacetime curvatures. Previously, we have calculated the effective energy–momentum tensor [Formula: see text] due to the quartic gravitational terms [Formula: see text] of the heterotic superstring theory in the four-dimensional background spacetime of the Schwarzschild black hole, obtaining an expression which satisfies the strong energy condition, and thereby suggests that the [Formula: see text] might not remove the central singularity. This conjecture was put forward from a different viewpoint by Horowitz and Myers, who argued that a non-singular black-hole interior resulting from the [Formula: see text] would be unstable, necessitating reappraisal of the notion of a singular interior spacetime. Here, we show that the chief features of the solution can be simulated by a Bardeen-type ansatz, assuming the spherically symmetric line element [Formula: see text], where [Formula: see text], which, when [Formula: see text], can explain heuristically why [Formula: see text] in the shell region [Formula: see text] of a macroscopic black hole for which [Formula: see text], while [Formula: see text] remains finite at [Formula: see text].

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.

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.

scholarly journals Black hole S-matrix for a scalar field

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Panos Betzios ◽  
Nava Gaddam ◽  
Olga Papadoulaki
Keyword(s):  
Black Hole ◽  
Normal Modes ◽  
Massless Scalar ◽  
Scattering Process ◽  
Schwarzschild Black Hole ◽  
Asymptotically Flat ◽  
Scalar Particles ◽  
Black Hole Background ◽  
S Matrix ◽  
Do So

Abstract We describe a unitary scattering process, as observed from spatial infinity, of massless scalar particles on an asymptotically flat Schwarzschild black hole background. In order to do so, we split the problem in two different regimes governing the dynamics of the scattering process. The first describes the evolution of the modes in the region away from the horizon and can be analysed in terms of the effective Regge-Wheeler potential. In the near horizon region, where the Regge-Wheeler potential becomes insignificant, the WKB geometric optics approximation of Hawking’s is replaced by the near-horizon gravitational scattering matrix that captures non-perturbative soft graviton exchanges near the horizon. We perform an appropriate matching for the scattering solutions of these two dynamical problems and compute the resulting Bogoliubov relations, that combines both dynamics. This allows us to formulate an S-matrix for the scattering process that is manifestly unitary. We discuss the analogue of the (quasi)-normal modes in this setup and the emergence of gravitational echoes that follow an original burst of radiation as the excited black hole relaxes to equilibrium.

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