THERMODYNAMICS OF EVENT HORIZONS IN (2+1)-DIMENSIONAL GRAVITY

Although gravity in 2 + 1 dimensions is very different in nature from gravity in 3 + 1 dimensions, it is shown that the laws of thermodynamics for event horizons can be manifested also for (2 + 1)-dimensional gravity. The validity of the classical laws of horizon mechanics is verified in general and exemplified for the (2 + 1)-dimensional analogues of Reissner-Nordstrom and Schwarzschild-de Sitter spacetimes. We find that the entropy is given by 1/4L, where L is the length of the horizon. A consequence of having consistent thermodynamics is that the second law fixes the sign of Newton's constant to be positive.