119290419
Hawking radiation as tunneling for spherically symmetric black holes: A generalized treatment
Abstract We present a derivation of Hawking radiation through tunneling mechanism for a general class of asymptotically flat, spherically symmetric spacetimes. The tunneling rate Γ ∼ exp ( Δ S ) arises as a consequence of the first law of thermodynamics, T d S = d E + P d V . Therefore, this approach demonstrates how tunneling is intimately connected with the first law of thermodynamics through the principle of conservation of energy. The analysis is also generally applicable to any reasonable theory of gravity so long as the first law of thermodynamics for horizons holds in the form, T d S = d E + P d V .
118627890
Beyond the Einstein Equation of State: Wald Entropy and Thermodynamical Gravity
We show that the classical equations of gravity follow from a thermodynamic relation, dQ = T dS, where S is taken to be the Wald entropy, applied to a local Rindler horizon at any point in spacetime. Our approach works for all diffeomorphism-invariant theories of gravity. This suggests that classical gravity may be thermodynamic in origin.
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.
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
118399350
The black hole membrane paradigm in f (R) gravity
To an outside observer, a black hole?s event horizon appears to behave exactly like a dynamical fluid membrane. We extend this membrane paradigm to black holes in general f(R) theories of gravity. We derive the stress tensor and various transport coefficients of the fluid and find that the membrane behaves as a non-Newtonian fluid except for the special case of Einstein gravity. Using Euclidean methods, we study the thermodynamics of the membrane. We speculate on what theories of gravity admit horizons with fluid properties.
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, $S^3 \times R$.
121595572
Dimensional regularisation and broken conformal Ward identities
Abstract Dimensional regularization is used to give a simple treatment of broken conformal Ward identities. The method reproduces the known answers for standard theories. In addition it permits a derivation of the relevant identities for non-Abelian gauge theories which have not been obtained by other means. For the latter class of theories asymptotic scale invariance is found not to imply asymptotic conformal invariance for gauge variant Green functions. This is due to two gauge dependent insertions occurring in the identities. One can be predicted classically, whereas the other contains a new term dependent on Faddeev-Popov ghosts.
119169856
New shell closure for neutron-rich Sn isotopes
The evolution of shell structure away from stability [1]has been a topic of intense theoretical [2, 3] and experi-mental [4–6] studies since last decade. Theoretical stud-ies have identiﬁed diﬀerent reasons for the phenomenonof shell evolution with neutron or proton excess. Amongthe various components of the nucleon - nucleon interac-tion, the spin-orbit, tensor part and three - body eﬀectplay important roles in the shell evolutions [1]. Due totensor interactions, nuclear mean ﬁeld undergoes varia-tions with neutron excess. This leads to monopole mi-gration [2]. It is observed for both proton-rich as well asneutron-rich nuclei. While approaching the neutron dripline, the neutron density becomes very diﬀused [3] whichcan also lead to shell quenching. For exotic light nucleithe well established magic numbers for the stable nu-clei are found to be modiﬁed or new magic numbers haveevolved. At least four doubly magic oxygen isotopes havebeen observed [6–8]. They are
119360725
What is between Fermi-Dirac and Bose-Einstein Statistics?
(a) Institute of Theoretical Physics, Warsaw University, ul. Hoz˙a 69, 00-681 Warszawa, Poland(b) Institute of Physics, Jagellonian University, ul. Reymonta 4, 30-059 Krak´ow, Poland(c) Wheatstone Physics Laboratory, King’s Collage, Strand, London WC2R 2LS, UKWe overwiev the properties of a quantum gas of particles with the intermediate statistics deﬁnedby Haldane. Although this statistics has no direct connection to the symmetry of the multiparticlewave function, the statistical distribution function interpolates continuously between the Fermi-Dirac and the Bose-Einstein limits. We present an explicit solution of the transcendental equationfor the didtribution function in a general case, as well as determine the thermodynamic propertiesin both low- and high-temperature limits.Published in Acta Physica Polonica B 26, 2167 (1995)
15306576
On the UV renormalizability of noncommutative field theories
UV/IR mixing is one of the most important features of noncommutative field theories. As a consequence of this coupling of the UV and IR sectors, the configuration of fields at the zero momentum limit in these theories is a very singular configuration. We show that the renormalization conditions set at a particular momentum configuration with a fixed number of zero momenta, renormalizes the Green's functions for any general momenta only when this configuration has same set of zero momenta. Therefore only when renormalization conditions are set at a point where all the external momenta are nonzero, the quantum theory is renormalizable for all values of nonzero momentum. This arises as a result of different scaling behaviors of Green's functions with respect to the UV cutoff (Λ) for configurations containing different set of zero momenta. We study this in the noncommutative 4 theory and analyse similar results for the Gross-Neveu model at one loop level. We next show this general feature using Wilsonian RG of Polchinski in the globally O(N) symmetric scalar theory and prove the renormalizability of the theory to all orders with an infrared cutoff. In the context of spontaneous symmetry breaking (SSB) in noncommutative scalar theory, it is essential to note the different scaling behaviors of Green's functions with respect to Λ for different set of zero momenta configurations. We show that in the broken phase of the theory the Ward identities are satisfied to all orders only when one keeps an infrared regulator by shifting to a nonconstant vacuum.
119598948
Asymptotic analysis of the Boltzmann equation for dark matter relics
This paper presents an asymptotic analysis of the Boltzmann equations (Riccati differential equations) that describe the physics of thermal dark-matter-relic abundances. Two different asymptotic techniques are used, boundary-layer theory, which makes use of asymptotic matching, and the delta expansion, which is a powerful technique for solving nonlinear differential equations. Two different Boltzmann equations are considered. The first is derived from general relativistic considerations and the second arises in dilatonic string cosmology. The global asymptotic analysis presented here is used to find the long-time behavior of the solutions to these equations. In the first case, the nature of the so-called freeze-out region and the post-freeze-out behavior is explored. In the second case, the effect of the dilaton on cold dark-matter abundances is calculated and it is shown that there is a large-time power-law fall off of the dark-matter abundance.