Extremal black holes inD= 5: SUSY vs. Gauss-Bonnet corrections

Abstract

We analyse near-horizon solutions and compare the results for the black hole entropy of five-dimensional spherically symmetric extremal black holes when the N = 2 SUGRA actions are supplied with two different types of higher-order corrections: (1) supersymmetric completion of gravitational Chern-Simons term, and (2) Gauss-Bonnet term. We show that for large BPS black holes lowest order α ′ corrections to the entropy are the same, but for non-BPS are generally different. We pay special attention to the class of prepotentials connected with K3 × T 2 and T 6 compactifications. For supersymmetric correction we find beside BPS also a set of non-BPS solutions. In the particular case of T 6 compactification (equivalent to the heterotic string on T 4 × S 1 ) we find the (almost) complete set of solutions (with exception of some non-BPS small black holes), and show that entropy of small black holes is different from statistical entropy obtained by counting of microstates of heterotic string theory. We also find complete set of solutions for K3 × T 2 and T 6 case when correction is given by Gauss-Bonnet term. Contrary to four-dimensional case, obtained entropy is different from the one with supersymmetric correction. We show that in Gauss-Bonnet case entropy of small "BPS" black holes agrees with microscopic entropy in the known cases.

Heterotic black holes

“…As shown in section 7 of Ref. [20], for large black holes (all three charges n, w, N nonvanishing) one gets the entropy which differs from statistical results, though in BPS case (n, w, N > 0) the result gives correct first α -correction. For small BPS black hole, given by N = 0 and nw > 0, we again obtain Wald entropy agreeing with statistical result S (BPS) stat = 4π √ nw .…”

“…α -corrections and heterotic black holes Predrag Dominis Prester When w < 0, the only change is c ↔ c. When used in Cardy formula (3.13) we obtain in the BPS case (nw > 0) S 20) while in the non-BPS case (nw < 0) we obtain…”

“…For some special sets of charges we then numerically checked that there are no other physically acceptable solutions. 13 However, one exception can be found in [20]. 14 While this review was in preparation this solution was presented in [71].…”

“…For this prepotential in [20] we constructed full set of near-horizon solutions of N = 2 supersymmetric R 2 action. We now present the results.…”

“…It is known (see, e.g., section 5.1 of [20]) at lowest order (two-derivative) supersymmetric action (6.1) with STU prepotential (6.33) can be put (by making Poincare duality transformation on A 1 gauge field, and then going from Einstein-to string-frame metric) in the form of the heterotic effective action (2.21), where 21…”