Thermodynamics and statistical mechanics of induced Liouville gravity
Thermodynamics and statistical mechanics of induced Liouville gravity
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DOI：
10.1103/physrevd.60.024016
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发表时间：
1999-01
影响因子：
5
通讯作者：
V. Frolov;D. Fursaev;J. Gegenberg;G. Kunstatter
中科院分区：
文献类型：
--
作者：
V. Frolov;D. Fursaev;J. Gegenberg;G. Kunstatter
在本文中，我们描述了一个刘维尔引力，这是由一组量子场（成分）诱导，并表示一个二维模拟萨哈罗夫的诱导引力。所考虑的理论的重要特点是存在的无质量成分，这是负责的外观诱导刘维场。大质量组分的作用只是诱导宇宙常数。我们考虑具有负和零宇宙学常数的欧几里德刘维引力的瞬子解，某些瞬子被解释为二维反德西特黑洞。我们研究了所有溶液的热力学，并得出结论，它们的熵完全由无质量组分的热力学熵决定。这表明，特别是，诱导引力的成分是真正的自由度的$AdS_2$黑洞。特别注意的是在环面上的诱导刘维引力与零宇宙常数。我们证明了它的热力学与BTZ黑洞热力学的等价性，并对BTZ黑洞熵的计算进行了评述。
In this paper we describe a Liouville gravity which is induced by a set of quantum fields (constituents) and represents a two-dimensional analog of Sakharov's induced gravity. The important feature of the considered theory is the presence of massless constituents which are responsible for the appearance of the induced Liouville field. The role of the massive constituents is only to induce the cosmological constant. We consider the instanton solutions of the Euclidean Liouville gravity with negative and zero cosmological constants, some instantons being interpreted as two-dimensional anti-de Sitter $AdS_2$ black holes. We study thermodynamics of all the solutions and conclude that their entropy is completely determined by the statistical-mechanical entropy of the massless constituents. This shows, in particular, that the constituents of the induced gravity are the true degrees of freedom of $AdS_2$ black holes. Special attention is also paid to the induced Liouville gravity with zero cosmological constant on a torus. We demonstrate the equivalence of its thermodynamics to the thermodynamics of BTZ black holes and comment on computations of the BTZ black hole entropy.