Phase Structure Of Double Black D-Brane Systems In Canonical Ensemble

Since the pioneering work by J. D. Bekenstein and S. W. Hawking in the early1970s, black hole thermodynamics has been one of active research topics in theoretical physics, for it leads to issues of quantum mechanical unitarity as well as information puzzle and to the nature of quantum gravity. This is because on one hand. Hawking radiation is a featureless thermal one while the objects have all their respective peculiar features before they fall into the black hole and on the other hand, black hole being a macroscopic gravitational system, its entropy and temperature are both in essence quantum mechanical, implying that the corresponding thermodynamics are also quantum mechanical in nature. Hence black holes are ideal systems for us to address the above raised issues.Black branes in string/M-theory can be considered as a higher dimensional generalization of black holes. So. understanding the thermodynamics and phase structure of black D-branes or the corresponding double black D-brane system-s, can be also considered as a higher dimensional generalization of black hole ones, while at the same time we expect to learn lessons about non-perturbative information for M-theory.Asymptotically flat black holes are thermodynamically unstable due to the Hawking radiation. To properly study the thermodynamics and phase structure of a spherically symmetric black hole, we need first to stabilize such a system. The standard approach for this is to place such a system in a finite concentric spherical cavity with its surface temperature fixed. In other words, a thermodynamical ensemble is considered which can be either canonical or grand canonical, depend-ing on whether the charge inside the cavity or the potential at the surface of the cavity is fixed. We focus in this thesis on the canonical ensemble, i.e., the charge inside the cavity is fixed.With this approach, the thermodynamics and phase structure of the simple asymptotically flat D=10black p-braues were studied in canonical ensemble. For the uncharged case. there is always a Hawking-Page-like phase transition between the black p-brane and the corresponding "hot empty space. When the charge is non-zero. the phase structure contains a van der Waals-Maxwell liquid-gas type phase transition when p <5with a line ot first-order phase transition ending at a second order pliase transit ion (critical) point. However, for p=5or6. we do not have such a phase structure.We then seek means which can be used lo modify the phase structure of p=5or6case to the expected one. For this, we consider specifically to add the lower dimensional D-branes to the Do or D6system, deloealized along their respective worldvolume directions. In particular, we consider a charged black D(p-2)/Dpor D(p-1)/Dp or D0/D6system for which the delocalized lower dimensional branes are D(p-2) or D(p-4) or DO. respectively. It turns out that tin’s can occur only for the D1/D5or D0/D6system.We calculate the critical exponents at the respective critical point for the relevant system under consideration. We discuss the underlying physical reason which gives rise to the dramatic change of phase structure of D5or D6when the deloealized D1or D0are added, and find out that this may be due to the nature of interaction between D1and D5or between DO and D6.