201072483
Corrections to the Bekenstein-Hawking entropy in the brick wall approach
The brick wall model is a semi-classical approach to underst and he microscopic origin of black hole entropy. In this approach, the entropy of the black hole arises due to the canonical entropy of matter fields outside the black hole event horizon, evaluate d the Hawking temperature. Usually, in the brick wall model, the density of states and the resulti ng canonical entropy of the matter fields are calculated at the leading order (in terms of h̄) in the WKB approximation. We extend this approach and compute the brick wall entropy of a quantum scalar field around static and spherically symmetric black holes at the higher orders in th e WKB approximation. We find that the brick wall model generally predicts corrections to the B kenstein-Hawking entropy in all spacetime dimensions. We compare our results with the sub-l eading contributions to the black hole entropy that has been obtained from various other appro ches.
120714502
The Membrane Paradigm for Gauss-Bonnet gravity
We construct the membrane paradigm for black objects in Einstein-Gauss-Bonnet gravity in spacetime dimensions $ \ge 5$. As in the case of general relativity, for the observers outside the horizon the dynamics of the perturbations of the horizon can be modelled as a membrane endowed with fluid-like properties. We derive the stress-tensor for this membrane fluid and study the perturbation around static backgrounds with constant curvature horizon cross-section to express the stress tensor in the form of a Newtonian viscous fluid with pressure, shear viscosity and bulk viscosity. The ratio of the shear viscosity and the entropy density is shown to generically violate the bound suggested by Policastro, Son and Starinets. We evaluate the transport coefficients for some static geometries. For the black brane geometry our results match with those available in the literature. For the spherically symmetric AdS black hole our results can be interpreted as a holographic prediction for the transport coefficients and viscosity to the entropy density ratio for the dual conformal field theory living on the boundary, $S^3 \times R$.
28943117
Physical process first law and increase of horizon entropy for black holes in Einstein-Gauss-Bonnet gravity.
We establish the physical process version of the first law by studying small perturbations of a stationary black hole with a regular bifurcation surface in Einstein-Gauss-Bonnet gravity. Our result shows that when the stationary black hole is perturbed by a matter stress energy tensor and finally settles down to a new stationary state, the Wald entropy increases as long as the matter satisfies the null energy condition.
44195025
Subleading contributions to the black hole entropy in the brick wall approach
The brick wall model is a semiclassical approach to understand the microscopic origin of black hole entropy. In this approach, the black hole geometry is assumed to be a fixed classical background on which matter fields propagate, and the entropy of black holes supposedly arises due to the canonical entropy of matter fields outside the black hole event horizon, evaluated at the Hawking temperature. Apart from certain lower dimensional cases, the density of states of the matter fields around black holes cannot be evaluated exactly. As a result, often, in the brick wall model, the density of states and the resulting canonical entropy of the matter fields are evaluated at the leading order (in terms of ({Dirac_h}/2{pi})) in the WKB approximation. The success of the approach is reflected by the fact that the Bekenstein-Hawking area law - viz. that the entropy of black holes is equal to one-quarter the area of their event horizon, say, A{sub H} - has been recovered using this model in a variety of black hole spacetimes. In this work, we compute the canonical entropy of a quantum scalar field around static and spherically symmetric black holes through the brick wall approach at the higher ordersmore » (in fact, up to the sixth order in ({Dirac_h}/2{pi})) in the WKB approximation. We explicitly show that the brick wall model generally predicts corrections to the Bekenstein-Hawking entropy in all spacetime dimensions. In four dimensions, we find that the corrections to the Bekenstein-Hawking entropy are of the form [A{sub H}{sup n}logA{sub H}], while, in six dimensions, the corrections behave as [A{sub H}{sup m}+A{sub H}{sup n}logA{sub H}], where (m,n)<1. We compare our results with the corrections to the Bekenstein-Hawking entropy that have been obtained through the other approaches in the literature, and discuss the implications.« less
199678166
Horizon entropy and higher curvature equations of state
The Clausius relation between entropy change and heat flux has previously been used to derive Einstein's field equations as an equation of state. We examine here whether a similar derivation can be given for extensions beyond Einstein gravity to include higher derivative and higher curvature terms.
119281634
Second Law Violations in Lovelock Gravity for Black Hole Mergers
We study the classical second law of black hole thermodynamics, for Lovelock theories (other than general relativity), in arbitrary dimensions. Using the standard formula for black hole entropy, we construct scenarios involving the merger of two black holes in which the entropy instantaneously decreases. Our construction involves a Kaluza-Klein compactification down to a dimension in which one of the Lovelock terms is topological. We discuss some open issues in the definition of the second law which might be used to remove this entropy decrease.
15573377
A Note on matrix model with IR cutoff and AdS/CFT
We study effective gauge theory at finite temperature on a three-sphere in the presence of an IR cutoff using AdS/CFT. Comparing with the thermodynamic behavior of its gravity dual, we analyze a phenomenological matrix model which describes the gauge theory in the strongly coupled regime. Subsequently, we study the behavior of the model as a function of the IR cutoff. We further argue that a similar matrix model represents the effective gauge theory on R3 with an IR-cutoff and analyze the model numerically.
118722812
Quantum phase diagram of a spin-1/2 antiferromagnetic chain with magnetic impurity
Abstract We present the renormalization group (RG) flow diagram of a spin-half antiferromagnetic chain with magnetic impurity and one altered link. In this two parameters (competing interactions) model, one can find the complex phase diagram with many interesting fixed points. There is no evidence of intermediate stable fixed point in weak coupling phase. It may arise at the strong coupling phase. Depending on the strength of couplings the phases correspond either to a decoupled spin with Curie law behavior or a logarithmically diverging impurity susceptibility as in the two channel Kondo problem.
119340528
Aspects of open-closed duality in a background B-field
We study closed string exchanges in background B-field. By analysing the two point one loop amplitude in bosonic string theory, we show that tree-level exchange of lowest lying, tachyonic and massless closed string modes, have IR singularities similar to those of the nonplanar sector in noncommutative gauge theories. We further isolate the contributions from each of the massless modes. We interpret these results as the manifestation of open/closed string duality, where the IR behaviour of the boundary noncommutative gauge theory is reconstructed from the bulk theory of closed strings.
122369912
Interacting holographic dark energy with variable deceleration parameter and accreting black holes in Bianchi type-V universe
In this paper, we have considered the spatially homogeneous and anisotropic Bianchi type-V space time filled with two interacting fluids; dark matter and a hypothetical isotropic fluid as the holographic dark energy components. To obtain an exact solution of the Einstein’s field equations, we used the assumption of time dependent deceleration parameter. We have investigated geometric and kinematic properties of the model. It is observed that the anisotropy parameter of the universe approaches to zero and the universe achieve flatness for large cosmic time. We have shown that this expanding solution is stable against the perturbation with respect to anisotropic spatial directions. We have also studied the evolution of the mass of a black hole embedded in a universe which interacts with a combination of dark matter and dark energy, considering that in the vicinity of the black hole the metric is of Schwarzschild type. We found that the black hole mass increases with the evolution of the universe, and on later epochs the increase in mass stops as dark energy accretion takes over. The results are found to be consistent with recent cosmological observations.
624279
Phase Transitions in Higher Derivative Gravity
This paper deals with black holes, bubbles and orbifolds in Gauss–Bonnet theory in five dimensional anti de Sitter space. In particular, we study stable, unstable and metastable phases of black holes from thermodynamical perspective. By comparing bubble and orbifold geometries, we analyse associated instabilities. Assuming AdS/CFT correspondence, we discuss the effects of this higher derivative bulk coupling on a specific matrix model near the critical points of the boundary gauge theory at finite temperature. Finally, we propose another phenomenological model on the boundary which mimics various phases of the bulk space-time.