Extremal Black Holes and Elementary String States

Abstract

Some of the extremal black hole solutions in string theory have the same quantum numbers as the Bogomol'nyi saturated elementary string states. We explore the possibility that these black holes can be identified to elementary string excitations. It is shown that stringy effects could correct the Bekenstein-Hawking formula for the black hole entropy in such a way that it correctly reproduces the logarithm of the density of elementary string states. In particular, this entropy has the correct dependence on three independent parameters, the mass and the left-handed charge of the black hole, and the string coupling constant.Comment: 16 pages, LaTeX file, Example of a specific scenario modified, footnote and references adde

Non-renormalization of mass of some non-supersymmetric string states

“…For the supersymmetric states this is certainly true. As shown by Sen [3], the entropy given by the area of the stretched horizon of four dimensional, supersymmetric, electrically charged, black holes does agree, up to a proportionality constant, with the statistical entropy given by the logarithm of the perturbative degeneracy of the super states. This works in other dimensions as well [4].…”

Near-BPS-saturated rotating electrically charged black holes as string states

“…Alternatively, one may want to evaluate such quantities at the "stretched" horizons as proposed by Sen [24] for the static electrically charged BPS-saturated black holes. In this case the stretched horizon can be chosen to be by O( √ α ′ ) distance away from the singular horizon and the thermodynamic entropy is in qualitative agreement (up to a factor of O (1)) [24,25] with the statistical entropy, i.e., the logarithm of the degeneracy of BPS-saturated elementary string states with the same quantum numbers. On the other hand, the area of the rotating BPS-saturated black holes, evaluated at the stretched horizon (whose value is chosen to be independent of the angular momenta and electric charges), turns out to be independent of the angular momenta.…”

Effectiveness of one-dimensional gas models for black holes

“…Let us now provide a gas model counting of states for such black holes. We will use the convention used in [17,16]. The generic black hole is (G = 1) The ADM mass and the charge are given by…”