Static Isolated Horizons: SU(2) Invariant Phase Space, Quantization, and Black Hole Entropy
Static Isolated Horizons: SU(2) Invariant Phase Space, Quantization, and Black Hole Entropy
复制标题
静态孤立视界：SU(2) 不变相空间、量化和黑洞熵
作者：
Alejandro Perez;D. Pranzetti
我们在一个明显的SU（2）不变的表述中研究静态一般孤立视界的经典场论表述。我们表明，通常的经典描述需要修订的非静态的情况下，由于打破了在地平线上的非同态不变性，导致通常的前辛结构的非保守。我们认为，如何避免这种困难可以通过简单的扩大领域的内容在地平线上，恢复同形不变性。限制我们的注意力静态孤立的视野，我们研究有效的理论描述的边界自由度。提出了一种水平自由度的量化方法。通过定义一个统计力学系综，其中只有视界的面积aH是宏观固定的-允许远离球对称的波动状态-我们表明，它是可能获得与霍金面积定律的一致性（S = aH /（4l 2 p）），无需将Immirzi参数固定为任何特定值：与面积定律的一致性只在Immirzi参数和涉及视界自由度的有效描述的Chern-Simons理论的水平之间强加了一种关系。
We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2) invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non-conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance. Restricting our attention to static isolated horizons we study the effective theories describing the boundary degrees of freedom. A quantization of the horizon degrees of freedom is proposed. By defining a statistical mechanical ensemble where only the area aH of the horizon is fixed macroscopically—states with fluctuations away from spherical symmetry are allowed—we show that it is possible to obtain agreement with the Hawkings area law (S = aH /(4l 2p)) without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom.