Phases of R-charged black holes, spinning branes and strongly coupled gauge theories

Abstract

We study the thermodynamic stability of charged black holes in gauged supergravity theories in D = 5, D = 4 and D = 7. We find explicitly the location of the Hawking-Page phase transition between charged black holes and the pure anti-de Sitter space-time, both in the grand-canonical ensemble, where electric potentials are held fixed, and in the canonical ensemble, where total charges are held fixed. We also find the explicit local thermodynamic stability constraints for black holes with one non-zero charge. In the grandcanonical ensemble, there is in general a region of phase space where neither the anti-de Sitter space-time is dynamically preferred, nor are the charged black holes thermodynamically stable. But in the canonical ensemble, anti-de Sitter space-time is always dynamically preferred in the domain where black holes are unstable.We demonstrate the equivalence of large R-charged black holes in D = 5, D = 4 and D = 7 with spinning near-extreme D3-, M2-and M5-branes, respectively. The mass, the charges and the entropy of such black holes can be mapped into the energy above extremality, the angular momenta and the entropy of the corresponding branes. We also note a peculiar numerological sense in which the grand-canonical stability constraints for large charge black holes in D = 4 and D = 7 are dual, and in which the D = 5 constraints are self-dual.

Drag force in a charged Script N = 4 SYM plasma

“…The latter theory is believed to be a consistent truncation of the Kaluza-Klein S 5 reduction of Type IIB supergravity, and in [37] it was shown that the STU and spinning D3 backgrounds are indeed related in this manner: the background described by equations (5.1)-(5.5) of [34] is shown there to be a non-trivial truncation of our (2.1), with the identifications κ 1 = (l/r H ) 2 , κ 2 = κ 3 = 0. The drag force deduced from the STU background in this case is given in equation (5.12) of [34], which is then to be compared with our spinning D3 result (3.20).…”

“…For simplicity we will restrict attention to the case where only one of the three SU(4) angular momenta is non-zero. The corresponding solution was obtained in [36] (see also [37]); 2 we will follow here the conventions of [39]. In the near-horizon limit, the metric is…”

From static to evolving geometries—R-charged hydrodynamics from supergravity

“…The scaling large τ limit of the diagonal equations (τ τ , zz, yy and xx components) is 14) where the explicit formulas for the R α β in the scaling limit are given in the appendix. Apart from these equations we also have the leading part of the off-diagonal equation R τ z = 0:…”

Black hole mass and Hamilton-Jacobi counterterms

“…In these systems it is possible to turn on conserved R-charges in addition to the temperature. It is then appropriate to work with the grand canonical ensemble, as discussed in [4]. The thermodynamic potential is related to the energy according to 2) where Q I are the set of conserved R-charges and Φ I are the corresponding electric potentials (which play the rôle of chemical potentials).…”

“…Here we consider only the particular case of the STU model, corresponding to the U(1) 3 truncation of maximal gauged supergravity. The black holes in this model, which may carry up to three charges, have been well studied [4]. The counterterm renormalization prescription for black holes in the STU model was recently examined in [26] for single-charge black holes and in [27] for three-charge black holes.…”