Caged black hole thermodynamics: Charge, the extremal limit, and finite size effects

Abstract

We extend the effective field theory treatment of the thermodynamics of small compactified black holes to the case of charged black holes. The relevant thermodynamic quantities are computed to second order in the parameter λ\sim(r_0/L)^(d-3). We discuss how the addition of charge to a caged black hole may delay the phase transition to a black string. In the extremal limit, we construct an exact black hole solution which serves as a check for our perturbative results. Finite size effects are also included through higher order operators in the worldline action. We calculate how the thermodynamic quantities are modified in the presence of these operators, and show they enter beyond order λ^2 as in the uncharged case. Finally, we use the exact solution to constrain the Wilson coefficients of the finite size operators in the extremal limit.

27 pages, 7 figures; published version & references added

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• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
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• Black hole stereotyping: Induced gravito-static polarization
• Next to leading order spin-orbit effects in the motion of inspiralling compact binaries
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Multipole expansion at the level of the action
• Comparing space+time decompositions in the post-Newtonian limit
• Einstein's action and the harmonic gauge in terms of Newtonian fields
• Dressing the Post-Newtonian two-body problem and Classical Effective Field Theory
• Classical Effective Field Theory for Weak Ultra Relativistic Scattering
• Caged black hole with Maxwell charge
• Field theory for gravity at all scales