Quasiparticle picture of black holes and the entropy–area relation

We propose an effective description of 0-brane black holes, in which the black hole is modeled as a gas of non-interacting quasi-particles in the dual quantum mechanics. This simple model is shown to account for many of the static thermodynamic properties of the black hole. It also accounts for dynamical properties, such as the rate at which energy gets thermalized by the black hole. We use the model to show that the entropy of the quantum mechanics is proportional to the black hole horizon area in Planck units. The Hawking-Bekenstein relationship [1] between entropy and area is a fundamental property of quantum gravity. In recent years it has become possible to build microscopic models of black holes, and show that the entropy – area relationship indeed holds [2, 3, 4, 5, 6, 7]. But in these calculations the underlying reason for a universal connection between entropy and area remains obscure, since the black hole microstates are only explicitly constructed in a limit where the geometry is singular. The advent of the AdS/CFT correspondence [8] and its generalizations [9] should make it possible to better understand the relationship between entropy and area. In the AdS/CFT framework the entropy of the black hole can be identified with the thermal entropy of the CFT, while the area of the horizon should in principle be calculable within the CFT. However to date not much progress has been made in this direction. The problem is that we do not understand in detail how quasi-local bulk gravitational physics emerges from the dual CFT. This makes the direct CFT definition of horizon area difficult. We will work in the context of the duality between 0-brane quantum mechanics and 0-brane black holes [9]. In the regime where the black holes are well-described by supergravity the quantum mechanics is strongly coupled. In [10, 11, 12] we developed a mean-field approximation scheme for the strongly-coupled quantum mechanics, and showed that it captures some of the essential physics of the dual gravity theory. Similar approximations have been used in [13] in the framework of the IKKT matrix model [14]. In the end the mean-field approximation suggests the following very simple picture of the quantum mechanics. The finite-temperature quantum mechanics has an effective description in terms of a collection of non-interacting quasi-particles 1 , which we identify with the individual matrix elements appearing in the matrix fields X(t). There are a total …