Phase transitions and critical behavior of black branes in canonical ensemble

Abstract

We study the thermodynamics and phase structure of asymptotically flat nondilatonic as well as dilatonic black branes in a cavity in arbitrary dimensions (D). We consider the canonical ensemble and so the charge inside the cavity and the temperature at the wall are fixed. We analyze the stability of the black brane equilibrium states and derive the phase structures. For the zero charge case we find an analog of Hawking-Page phase transition for these black branes in arbitrary dimensions. When the charge is non-zero, we find that below a critical value of the charge, the phase diagram has a line of first-order phase transition in a certain range of temperatures which ends up at a second order phase transition point (critical point) as the charge attains the critical value. We calculate the critical exponents at that critical point. Although our discussion is mainly concerned with the nondilatonic branes, we show how it easily carries over to the dilatonic branes as well.

Modulating the phase structure of black D6 branes in canonical ensemble

“…We have recently found [10,11] that the same characteristic phase structure (including a Hawking-Page transition) of stabilized uncharged (Schwarzschild) black holes was also shared by the stabilized uncharged black p-branes in D-dimensional asymptotically flat spacetime (with the brane worldvolume dimensions d = 1 + p ) in string/M theory. However, in the charged case, the van der Waals-Maxwell liquid-gas type phase structure mentioned earlier, with its characteristic behavior 4 shown in Fig.…”

“…x min x max Figure 1: The typical behavior of b q (x) vs x for q > q c and q < q c and q < q c (like thed > 2 cases), but we don't actually have a critical point in the usual sense and for each subcase the phase structure looks more like that of thed = 1 case (see [10] for detail). Hence this case can be viewed as a borderline in phase structure which distinguishes thed = 1 case from thed > 2 cases.…”

“…where the metric is in Einstein frame, each form field is obtained following [8,10] in such a way that the form field vanishes at the horizon so that it is well defined in the local 8 We actually use the configuration given in [14] with some modifications. The magnetic part of one form A 1 has now been changed to an electric seven-form potential A 7 which represents the presence of D6 branes.…”

“…4 The so-called reduced quantities b q (x),b, x, q, q c in Fig. 1 are defined in [10] and will also be given later in section 3 for D6-branes. b q (x) is the reduced inverse of local temperature of charged black Dp branes under consideration at the surface of cavity.b is the reduced inverse of the given temperature of cavity.…”

“…In drawing analogy with the usual van der Waals-Maxwell liquid-gas system, we have here b q (x) the analog of pressure, x the analog of volume and q the analog of temperature in the liquid-gas system. The detail analysis of phase structure and the related phase transitions for black p-branes is given in [10] and will also be briefly discussed later after (54). In drawing further analogy from the right phase graph in Fig.1, we have the small stable black p-brane phase the analog of the liquid phase while the large stable one the analog of the gas phase in the usual liquid-gas case.…”