Boundary Effects on Bose-Einstein Condensation in Ultra-Static Space-Times

Akant, Levent; Ertugrul, Emine; Gül, Yusuf; Turgut, O. Teoman

doi:10.48550/arxiv.1501.02743

Cited by 1 publication

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“…In the following we will work in the ultrarelativistic regime where the mass parameter m of the field is much smaller than the temperature T , m << T , and employ an expansion in terms of the small parameter βm (β = T −1 ) (sometimes called the high temperature expansion) to study the free energy and the entropy of the quantum field in the presence of Dirichlet walls. We will also present an alternative derivation [18] of the high temperature expansion based on Mellin transform methods which does not make use of the zeta function regularization. The resulting expansion is in complete agreement with the one obtained by the latter method [19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Boundary Effects on the Thermodynamics of Quantum Fields Near a Black Hole

Akant,

Debir,

Ertugrul

2015

Preprint

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We study the thermodynamics of a quantum field in a spherical shell around a static black hole. We implement brick wall regularization by imposing Dirichlet boundary conditions on the field at the boundaries and analyze their effects on the free energy and the entropy. We also consider the possibility of using Neumann boundary conditions. We examine both bosonic and fermionic fields in Schwarzschild, Reissner-Nordström (RN), extreme RN, and dilatonic backgrounds. We show that the horizon divergences get contributions from the boundary (brick wall) which at the Hawking temperature are comparable to the bulk contributions. It is also shown that the leading divergence is the same for all the backgrounds considered and that the subleading logarithmic divergence is given by a specific function of surface gravity and horizon area. We will also consider the near horizon geometry and show the existence of a finite term generated by the logarithmic divergence which involves the logarithm of the horizon area. The thermodynamics of quantum fields is examined in the ultrarelavisitc regime through the high temperature/small mass expansion. We derive the high temperature expansion in the presence of chemical potential by Mellin transform and heat kernel methods as applied to the harmonic sum representation of the free energy.

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