TASI Lectures on Black Holes in String Theory

Abstract

This is a write-up of introductory lectures on black holes in string theory given at TASI-99. Topics discussed include: black holes, thermodynamics and the Bekenstein-Hawking entropy, the information problem; supergravity actions, conserved quantum numbers, supersymmetry and BPS states, units, duality and dimensional reduction, solution-generating; extremal M-branes and D-branes, smearing, probe actions, nonextremal branes, the Gregory-Laflamme instability; breakdown of supergravity and the Correspondence Principle, limits in parameter space, singularities; making black holes with branes, intersectionology, the harmonic function rule, explicit d=5, 4 examples; string computations of extremal black hole entropy in d=5, 4, rotation, fractionation; nonextremality and entropy, the link to BTZ black holes, Hawking radiation and absorption cross-sections in the string/brane and supergravity pictures.

First order description of black holes in moduli space

“…In fact, as we will show, the squared prepotential is a viable candidate for such a function, sharing with it the monotonicity property in the radial variable and the value taken at the horizon. 1 This problem was first addressed in [14] where, by exploiting the formal analogy between extremal black holes and domain wall solutions, explicit examples of W corresponding to certain N = 2 non-BPS extremal solutions were found.…”

“…Since we know that the potential (3.2) has two minima for the N = 3 theory, W (1) and W (2) exhaust the possible minima of the general potential for this theory. This in particular implies that eq.…”

“…Recent progress in the understanding of extremal non-BPS black-hole solutions in extended supergravities (for a review on black holes in supergravity see for example [1,2]) have revived the interest in the physics of extremal black holes.…”

Non-supersymmetric black rings as thermally excited supertubes

“…Without loss of generality we can take R > 0. The parameters λ, ν, µ i are restricted as 17) while the α i can initially take any real value. These ranges of values are typically sufficient to avoid the appearance of naked curvature singularities.…”

“…Spherical five-dimensional black holes with three charges are the most thoroughly studied black holes in string theory [17], so having three-charge black rings should be instrumental to develop the proposal in ref. [3] for a microscopic understanding of non-uniqueness and non-spherical topologies.…”