Two-charge Black Hole Research Articles

Revisiting α′ corrections to heterotic two-charge black holes

We find solutions of the heterotic string effective action describing the first-order α′ corrections to two-charge black holes at finite temperature. Making explicit use of these solutions, we compute the corrections to the thermodynamic quantities: temperature, chemical potentials, mass, charges and entropy. We check that the first law of black hole mechanics is satisfied and that the thermodynamics agrees with the one extracted from the Euclidean on-shell action. Finally, we show that our results are in agreement with the corrections for the thermodynamics recently predicted by Chen, Maldacena and Witten.

Shockwaves in black hole microstate geometries

Gravitational solutions involving shockwaves have attracted significant recent interest in the context of black holes and quantum chaos. Certain classes of supersymmetric two-charge black hole microstates are described by supergravity solutions containing shockwaves, that are horizonless and smooth away from the shockwave. These configurations have been used to describe how black hole microstates absorb and scramble perturbations. In this paper we construct the first family of asymptotically flat supersymmetric three-charge microstate solutions that contain shockwaves. We identify a family of holographically dual states of the D1-D5 CFT and show that these pass a set of tests, including a precision holographic test. We find precise agreement between gravity and CFT. Our results may prove useful for constructing more general families of black hole microstate solutions.

The fuzzball nature of two-charge black hole microstates

It has been suggested by A. Sen that the entropy of two-charge supersymmetric bound states in string theory should be accounted for by adding the entropy of source-free horizonless supergravity solutions to the entropy associated with the horizons of small black holes. This would imply that the entropy arises differently depending on the duality frame: in the D1-D5 frame one would count source-free horizonless solutions, while in the NS1-P frame one would compute the area of a horizon. This might lead to the belief that the microstates are described by fuzzball solutions in the D1-D5 duality frame but by a black hole with a horizon in the latter. We argue that this is not the case, and that the microstates are fuzzballs in all duality frames. We observe that the scaling argument used by Sen fails to account for the entropy in the D1-P and other duality frames. We also note that the traditional extremal black hole solution is not a complete string background, since finite-action paths connect the exterior near-horizon extremal throat to the region inside the horizon, including the singularity. The singularity of the traditional black hole solution does not give a valid boundary condition for a fundamental string; correcting this condition by resolving the singularity modifies the black hole to a fuzzball with no horizon. We argue that for questions of counting states, the traditional black hole solution should be understood through its Euclidean continuation as a saddle point, and that the Lorentzian states being counted are fuzzballs in all duality frames.

A new approach to two-charge fuzzball geometries

A few years ago, Mathur proposed a ‘fuzzball’ conjecture to give a microscopic description of black hole entropy. In the fuzzball scenario, the entropy in a two-charge black hole corresponds to microstates of a two-charge string (brane) system, e.g., a winding fundamental string with momentum modes. The geometry of such a two-charge system is fuzzy near the horizon, and is very difficult to get analytically in general. In this paper, we show a new method to get geometries of two-charge fuzzball. Our method is based on the multipole expansion. We find that the method is powerful enough to get a clean analytic form of metric of the fuzzball with one-momentum mode. It is expected to get multi-mode geometries using this method in the near future.

Microstate Counting of 3-charge Black Hole from Supergravity

where A is the area of the horizon. Statistical mechanics then suggests that there should be e states of the black hole, but the geometry of the black hole is completely determined by its mass, charge and angular momentum : so called ‘Black holes have no hair’. This statement implies that the entropy of the black hole is S = ln 1 = 0. This is the ‘black hole entropy puzzle’, which is closely related to the ‘black hole information problems’. String theory has a rich structure and admits black-hole solutions in higher dimensions [2–4]. Then, the black holes in string theory may give an understanding of these puzzles. Black holes in string theory are widely studied by using a chiral null model [5–11]. This model provides a class of exact solutions of oscillating strings in various cases. From these solutions, Mathur proposed the ‘fuzzy ball’ conjecture for the black hole [12,13]. He constructed a geometry of the two-charge black hole by performing a chain of duality transformations from the metric of the oscillating fundamental string. The result gives a family of geometries for the D1-D5 system characterized by a single function ~ F , the vibration profile of the fundamental string. Moreover these geometries have no horizons and no singularity which corresponds to the so-called ‘black hole microstate geometries’. By quantizing the single function ~ F , we can obtain the number of geometries for the black hole [14]. This result agrees with the one from the calculation in the CFT side.

Three-charge black holes on a circle

We study phases of five-dimensional three-charge black holes with a circle in their transverse space. In particular, when the black hole is localized on the circle we compute the corrections to the metric and corresponding thermodynamics in the limit of small mass. When taking the near-extremal limit, this gives the corrections to the constant entropy of the extremal three-charge black hole as a function of the energy above extremality. For the partial extremal limit with two charges sent to infinity and one finite we show that the first correction to the entropy is in agreement with the microscopic entropy by taking into account that the number of branes shift as a consequence of the interactions across the transverse circle. Beyond these analytical results, we also numerically obtain the entire phase of non- and near-extremal three- and two-charge black holes localized on a circle. More generally, we find in this paper a rich phase structure, including a new phase of three-charge black holes that are non-uniformly distributed on the circle. All these three-charge black hole phases are found via a map that relates them to the phases of five-dimensional neutral Kaluza-Klein black holes.

String-corrected black holes

We investigate the geometry of four dimensional black hole solutions in the presence of stringy higher curvature corrections to the low energy effective action. For certain supersymmetric two charge black holes these corrections drastically alter the causal structure of the solution, converting seemingly pathological null singularities into timelike singularities hidden behind a finite area horizon. We establish, analytically and numerically, that the string-corrected two-charge black hole metric has the same Penrose diagram as the extremal four-charge black hole. The higher derivative terms lead to another dramatic effect -- the gravitational force exerted by a black hole on an inertial observer is no longer purely attractive! The magnitude of this effect is related to the size of the compactification manifold.

Massive-scalar absorption by extremal p-branes

We study the absorption probability of minimally-coupled massive scalars by extremal p-branes. In particular, we find that the massive scalar wave equation under the self-dual string background has the same form as the massless scalar wave equation under the dyonic string background. Thus it can be cast into the form of a modified Mathieu equation and solved exactly. Another example that we can solve exactly is that of the D=4 two-charge black hole with equal charges, for which we obtain the closed-form absorption probability. We also obtain the leading-order absorption probabilities for D3-, M2- and M5-branes.

Closed-form absorption probability of certain D = 5 and D = 4 black holes and leading-order cross-section of generic extremal p-branes

We obtain the closed-form absorption probabilities for minimally-coupled massless scalars propagating in the background of D=5 single-charge and D=4 two-charge black holes. These are the only two examples of extremal black holes with non-vanishing absorption probabilities that can be solved in closed form for arbitrary incident frequencies. In both cases, the absorption probability vanishes when the frequency is below a certain threshold, and we discuss the connection between this phenomenon and the behaviour of geodesics in these black hole backgrounds. We also obtain leading-order absorption cross-sections for generic extremal p-branes, and show that the expression for the cross-section as a function of frequency coincides with the leading-order dependence of the entropy on the temperature in the corresponding near-extremal p-branes.