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

Jul, 1996
3 pages
Published in:
  • Phys.Rev.Lett. 77 (1996) 4992-4995
e-Print:
Report number:
  • SU-ITP-96-35

Citations per year

1996200320102017202405101520
Abstract:
We show that under variation of moduli fields ϕ\phi the first law of black hole thermodynamics becomes dM=κdA8π+ΩdJ+ψdq+χdpΣdϕdM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq + \chi dp - \Sigma d\phi, where Σ\Sigma are the scalar charges. We also show that the ADM mass is extremized at fixed AA, JJ, (p,q)(p,q) when the moduli fields take the fixed value ϕfix(p,q)\phi_{\rm fix}(p,q) which depend only on electric and magnetic charges. It follows that the least mass of any black hole with fixed conserved electric and magnetic charges is given by the mass of the double-extreme black hole with these charges. Our work allows us to interpret the previously known observation that for all extreme black holes the moduli fields at the horizon take a value ϕ=ϕfix(p,q)\phi= \phi_{\rm fix}(p,q) depending only on the electric and magnetic conserved charges: ϕfix(p,q) \phi_{\rm fix}(p,q) is such that the scalar charges Σ(ϕfix,(p,q))=0\Sigma (\phi_{\rm fix}, (p,q))=0.
  • string model
  • moduli space
  • black hole
  • thermodynamics