正则系综下双黑膜系统热力学相行为的研究
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摘要
自从了0年代初贝肯斯坦(J.D.Bekenstein)和霍金(S.W.Hawking)等人的开创性的工作以来,由于关系到量子论的幺正性、信息守恒和引力量子化等深刻的问题,黑洞的热力学就一直是理论物理研究的前沿和热点之一。这是因为,黑洞作为一个宏观引力系统,其态函数熵和温度等热力学量本质上都是量子的,因此对应的热力学在一定意义下也是量子的,所以黑洞成为了研究上述问题,特别是量子引力的一个很好的对象。
黑膜可以看作是超弦／M理论中对黑洞的高维推广,对黑D膜以及双黑膜系统的热力学相行为的研究,可以看作是对黑洞热力学在维数方面更一般的推广,同时也希望为建立M理论更完整的框架提供重要的非微扰信息。
由于黑洞存在霍金辐射,因此渐近平坦的黑洞在热力学上并不稳定。为了研究球对称黑洞的热力学相结构,约克(J.W.York)等人把这样的黑洞放入一个与其同心的球形空腔中。由于引力沿径向的非均匀性,对这样的系统,我们必须给定空腔沿径向的位置(空腔的半径应大于黑洞视界半径)、空腔壁处的温度等,换句话说我们不仅要考虑黑洞还要考虑环境即考虑的是一个系综。根据空腔壁处的电势固定还是空腔内的电荷固定,我们分别定义了所谓的巨正则系综和正则系综。在本论文中,我们将局限于考虑正则系综,即空腔内的电荷固定。
于是我们按照这个方法,把渐进平坦的黑Dp膜放到一个腔中,在正则系综下来研究它们的热力学相结构。不带荷的情况,有发生类似于霍金-佩吉(D.N.Page)相变的黑膜-热平坦空间相变。对带荷的情况,当Dp膜的维数p<5时,就可能出现类似范德瓦尔斯(J.D.van der Waals)-麦克斯韦(J.C.Maxwell)气液相变的大小黑膜之间的相变：当荷低于临界值,相图在一定温度范围内表现为可能发生类似上述气液相变的一级相变;当荷刚好达到临界值时,相图就表现为可能发生二级相变,出现二级相变点,也就是所谓的临界点。带荷的黑D5膜和D6膜都不会出现临界现象,也就不会发生大小黑膜间类似气液相变的相变,不过它们的情况也不尽相同。
于是我们考虑对原先十维弦理论中的黑Dp,膜,加入相对低维的非定域D膜(即均匀分布在沿高维Dp膜的其它方向上),来组成一个带荷的黑D(p-2)/Dp或D(p-4)/Dp)或者D0/D6系统,看看会不会从性质上改变原先黑膜的相结构.结果多数双黑膜系统还是保持原有的相结构,原来有或者没有发生类似范德瓦尔斯-麦克斯韦气液相变的一级相变还是保持原状。只有D(?)/D5(也考虑了它的S(?)F/NS5).D0,D6这两个系统发生了期望的变化(D2/D6系统虽然有些变化,但仅类似D5系统,没有给出类似范德瓦尔斯-麦克斯韦气液相变的译级相变结构。)
带荷的黑D1/D5(F/NS5)和D0/D6系统将是本文的焦点,因为加入非局域的D1(F)和D0分别使原先的D5(XS5)和D6从没有类似范德瓦尔斯-麦克斯韦气液相变的大小黑膜相变,改变到有发生这种相变(这里是大小双黑膜系统之间的相变)。
最后我们在临界点计算了一些临界指数,讨论了上述变化是如何发生的,可能的原因是什么,可以把这个变化实际上看作是在热力学层面上,膜荷与原先膜的横向维度的增加之间的关联等问题。可以肯定的是,系统中黑膜之间的相互作用(引力与荷两部分),是表现出这些相行为的重要原因。
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.
黑膜可以看作是超弦／M理论中对黑洞的高维推广,对黑D膜以及双黑膜系统的热力学相行为的研究,可以看作是对黑洞热力学在维数方面更一般的推广,同时也希望为建立M理论更完整的框架提供重要的非微扰信息。
由于黑洞存在霍金辐射,因此渐近平坦的黑洞在热力学上并不稳定。为了研究球对称黑洞的热力学相结构,约克(J.W.York)等人把这样的黑洞放入一个与其同心的球形空腔中。由于引力沿径向的非均匀性,对这样的系统,我们必须给定空腔沿径向的位置(空腔的半径应大于黑洞视界半径)、空腔壁处的温度等,换句话说我们不仅要考虑黑洞还要考虑环境即考虑的是一个系综。根据空腔壁处的电势固定还是空腔内的电荷固定,我们分别定义了所谓的巨正则系综和正则系综。在本论文中,我们将局限于考虑正则系综,即空腔内的电荷固定。
于是我们按照这个方法,把渐进平坦的黑Dp膜放到一个腔中,在正则系综下来研究它们的热力学相结构。不带荷的情况,有发生类似于霍金-佩吉(D.N.Page)相变的黑膜-热平坦空间相变。对带荷的情况,当Dp膜的维数p<5时,就可能出现类似范德瓦尔斯(J.D.van der Waals)-麦克斯韦(J.C.Maxwell)气液相变的大小黑膜之间的相变：当荷低于临界值,相图在一定温度范围内表现为可能发生类似上述气液相变的一级相变;当荷刚好达到临界值时,相图就表现为可能发生二级相变,出现二级相变点,也就是所谓的临界点。带荷的黑D5膜和D6膜都不会出现临界现象,也就不会发生大小黑膜间类似气液相变的相变,不过它们的情况也不尽相同。
于是我们考虑对原先十维弦理论中的黑Dp,膜,加入相对低维的非定域D膜(即均匀分布在沿高维Dp膜的其它方向上),来组成一个带荷的黑D(p-2)/Dp或D(p-4)/Dp)或者D0/D6系统,看看会不会从性质上改变原先黑膜的相结构.结果多数双黑膜系统还是保持原有的相结构,原来有或者没有发生类似范德瓦尔斯-麦克斯韦气液相变的一级相变还是保持原状。只有D(?)/D5(也考虑了它的S(?)F/NS5).D0,D6这两个系统发生了期望的变化(D2/D6系统虽然有些变化,但仅类似D5系统,没有给出类似范德瓦尔斯-麦克斯韦气液相变的译级相变结构。)
带荷的黑D1/D5(F/NS5)和D0/D6系统将是本文的焦点,因为加入非局域的D1(F)和D0分别使原先的D5(XS5)和D6从没有类似范德瓦尔斯-麦克斯韦气液相变的大小黑膜相变,改变到有发生这种相变(这里是大小双黑膜系统之间的相变)。
最后我们在临界点计算了一些临界指数,讨论了上述变化是如何发生的,可能的原因是什么,可以把这个变化实际上看作是在热力学层面上,膜荷与原先膜的横向维度的增加之间的关联等问题。可以肯定的是,系统中黑膜之间的相互作用(引力与荷两部分),是表现出这些相行为的重要原因。
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.
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