TY - JOUR

T1 - Caged black holes

T2 - Black holes in compactified spacetimes. I. Theory

AU - Kol, Barak

AU - Sorkin, Evgeny

AU - Piran, Tsvi

PY - 2004

Y1 - 2004

N2 - In backgrounds with compact dimensions there may exist several phases of black objects including a black hole and a black string. The phase transition between them raises questions and touches on fundamental issues such as topology change, uniqueness, and cosmic censorship. No analytic solution is known for the black hole, and moreover one can expect approximate solutions only for very small black holes, while phase transition physics happens when the black hole is large. Hence we turn to numerical solutions. Here some theoretical background to the numerical analysis is given, while the results will appear in a subsequent paper. The goals for a numerical analysis are set. The scalar charge and tension along the compact dimension are defined and used as improved order parameters which put both the black hole and the black string at finite values on the phase diagram. The predictions for small black holes are presented. The differential and the integrated forms of the first law are derived, and the latter (Smarr’s formula) can be used to estimate the “overall numerical error.” Field asymptotics and expressions for physical quantities in terms of the numerical values are supplied. The techniques include the “method of equivalent charges”, free energy, dimensional reduction, and analytic perturbation for small black holes.

AB - In backgrounds with compact dimensions there may exist several phases of black objects including a black hole and a black string. The phase transition between them raises questions and touches on fundamental issues such as topology change, uniqueness, and cosmic censorship. No analytic solution is known for the black hole, and moreover one can expect approximate solutions only for very small black holes, while phase transition physics happens when the black hole is large. Hence we turn to numerical solutions. Here some theoretical background to the numerical analysis is given, while the results will appear in a subsequent paper. The goals for a numerical analysis are set. The scalar charge and tension along the compact dimension are defined and used as improved order parameters which put both the black hole and the black string at finite values on the phase diagram. The predictions for small black holes are presented. The differential and the integrated forms of the first law are derived, and the latter (Smarr’s formula) can be used to estimate the “overall numerical error.” Field asymptotics and expressions for physical quantities in terms of the numerical values are supplied. The techniques include the “method of equivalent charges”, free energy, dimensional reduction, and analytic perturbation for small black holes.

UR - http://www.scopus.com/inward/record.url?scp=2342442555&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.69.064031

DO - 10.1103/PhysRevD.69.064031

M3 - Article

AN - SCOPUS:2342442555

SN - 1550-7998

VL - 69

SP - 12

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 6

ER -