Abstract
By incorporating the electrical stability condition into the discussion, we continue the study on the thermodynamic phase structures of the Dp-D(p + 4) black brane in GG, GC, CG, CC ensembles defined in our previous paper [27]. We find that including the electrical stability conditions in addition to the thermal stability conditions does not modify the phase structure of the GG ensemble but puts more constraints on the parameter space where black branes can stably exist in GC, CG, CC ensembles. In particular, the van der Waals-like phase structure which was supposed to be present in these ensembles when only thermal stability condition is considered would no longer be visible, since the phase of the small black brane is unstable under electrical fluctuations. However, the symmetry of the phase structure by interchanging the two kinds of brane charges and potentials is still preserved, which is argued to be the result of T-duality.
Highlights
A dynamical quantum object instead of just a fixed background
By incorporating the electrical stability condition into the discussion, we continue the study on the thermodynamic phase structures of the Dp-D(p + 4) black brane in GG, GC, CG, CC ensembles defined in our previous paper [27]
We find that including the electrical stability conditions in addition to the thermal stability conditions does not modify the phase structure of the GG ensemble but puts more constraints on the parameter space where black branes can stably exist in GC, CG, CC ensembles
Summary
A Dp-D(p+4)-brane system can be described by the following Euclideanized metric, dilaton and form fields (see section 2 of [27] for more details), where ds. For p = 0 case it is possible that in some region of the Q-φ or q-Φ plane and at some specific b which depends on the value of the other two parameters, a van der Waals-like first order phase. In CC ensemble, the van der Waals-like phase transition cannot happen only in the p = 2 case For both p = 0, 1, this liquid-gas-like phase transition is found in certain region of the q-Q plane at some specific b, and terminates at a second order phase transition point. What we will show later in this paper is that after the electrical stability is considered, the small black brane phase in the van der Waals-like phase transition is not stable any more, which rules out the possibility of this phase transition. In that case the only stable phase is the large black brane phase
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