TY - JOUR

T1 - Moduli, scalar charges, and the first law of black hole thermodynamics

AU - Gibbons, Gary

AU - Kallosh, Renata

AU - Kol, Barak

PY - 1996

Y1 - 1996

N2 - We show that under variation of moduli fields φ the first law of black hole thermodynamics becomes dM = κdA/8 π + Ω dJ + ψdq + χdp - Σ dφ, where Σ are the scalar charges. Also the Arnowitt-Desner-Misner mass is extremized at fixed A, J, (p, q) when the moduli fields take the fixed value φfix(p, q) which depend only on electric and magnetic charges. Thus the double-extreme black hole minimizes the mass for fixed conserved charges. We can now explain the fact that extreme black holes fix the moduli fields at the horizon φ = φfix (p, q): φfix is such that the scalar charges vanish: Σ(φfix, (p, q)) = 0.

AB - We show that under variation of moduli fields φ the first law of black hole thermodynamics becomes dM = κdA/8 π + Ω dJ + ψdq + χdp - Σ dφ, where Σ are the scalar charges. Also the Arnowitt-Desner-Misner mass is extremized at fixed A, J, (p, q) when the moduli fields take the fixed value φfix(p, q) which depend only on electric and magnetic charges. Thus the double-extreme black hole minimizes the mass for fixed conserved charges. We can now explain the fact that extreme black holes fix the moduli fields at the horizon φ = φfix (p, q): φfix is such that the scalar charges vanish: Σ(φfix, (p, q)) = 0.

UR - http://www.scopus.com/inward/record.url?scp=0000640429&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.77.4992

DO - 10.1103/PhysRevLett.77.4992

M3 - Article

AN - SCOPUS:0000640429

SN - 0031-9007

VL - 77

SP - 4992

EP - 4995

JO - Physical Review Letters

JF - Physical Review Letters

IS - 25

ER -