M. Cvetic et I. Gaida, DUALITY-INVARIANT NON-EXTREME BLACK-HOLES IN TOROIDALLY COMPACTIFIED STRING THEORY, Nuclear physics. B, 505(1-2), 1997, pp. 291-306
We present a duality-invariant structure of the thermodynamic quantiti
es of non-extreme black hole solutions of toroidally compactified Type
II (M-theory) and heterotic string in five and four dimensions. These
quantities are parametrized by duality-invariant combination of charg
es and the non-extremality parameter, which measures a deviation from
the BPS-saturated limit. In particular, in D = 5 we find explicit S- a
nd T-duality- [U-duality]-invariant expressions for solutions of toroi
dally compactified heterotic string [Type II string]. In D = 4, we con
sider general S-duality-invariant expressions for non-extreme solution
s of pure N = 4 supergravity and find to the leading order in non-extr
emality parameter the T- and S-duality-invariant expressions of toroid
ally compactified heterotic string. General non-extreme solutions of t
oroidally compactified string in D = 4 are awaiting further investigat
ion. (C) 1997 Elsevier Science B.V.