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
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AN - SCOPUS:0000640429
SN - 0031-9007
VL - 77
SP - 4992
EP - 4995
JO - Physical Review Letters
JF - Physical Review Letters
IS - 25
ER -