Phase Structures Of Black Dp-D(P+4)-Brane Systems In Various Ensembles

There has been a great success on the research of the thermodynamics of black hole systems since Bekenstein and Hawking discovered that black holes have entropy and can radiate. Hawking and his collaborators first established the link between the action of a gravitational system and the partition function of statistical physics, and then they applied this to the research on the phase structure of AdS black holes. However, this approach cannot be applied to the research on the black holes in asymptotically flat spacetime due to the fact that the heat capacity of this kind of black holes is negative which indicates the instability of the system. York et al. improved the method used by Hawking and Page by placing the black hole in a finite cavity such that this finite system can have a positive heat capacity. They then used the refined approach to investigate the thermodynamic phase structure of the Schwarzshild black hole in canonical ensemble and charged black holes in grand canonical ensemble in asymptotically flat spacetime. Later, there are subsequent attempts to investigate the phase structure of charged black holes in canonical ensemble using methods derived from theirs.On the other hand, due to the existence of D-branes in string theory, richer space-time structures such as black branes emerge in the effective low-energy theory of string theory. Lu and his colaborators extended York’s method to black brane systems. They elaborately examined the phase structure of black Dp-branes in canonical/grand canon-ical ensembles and black Dp-D(p+4)-branes in canonical ensemble. Based on their work, we further examine the thermodynamic stability and phase structure of black Dp-D(p+4)-branes in all possible ensembles.In chapter 2, we first give the spacetime geometry of a black Dp-D(p+4)-brane system, then we calculate the action of the this system and use the value of this action to establish equations of equilibrium state of Dp-D(p+4) system. In chapter 3, we drive the thermal and electrical stability conditions from the principle of minimum energy and simplify these conditions. In chapter 4 to 6, we utilize the stability conditions derived in chapter 3 to find the range of parameters for thermal stability and electrical stability of Dp-D(p+4)system in GG, GC, CG, CC ensembles. We then give the phase struc- tures of Dp-D (p+4) system by combining the thermal stability result and the electrical stability result. Since p can take values of 0,1 and 2, we will discuss cases for each value of p seperately. In the last chapter, we give a brief conclusion of this thesis.