THERMODYNAMICS OF BLACK-HOLE IN (N-BRANE THEORY(3) DIMENSIONS FROM EUCLIDEAN N)

In this letter we consider an N-brane description of an (N + 3)-dimens ional black hole horizon. First of all, we start by examining in more detail a previous work where a string theory is used in describing the dynamics of the event horizon of a four-dimensional black hole. This is an attempt to understand the black hole thermodynamics by an effect ive two-dimensional field theory of the event horizon of a black hole. Then we consider a particle model defined on one-dimensional Euclidea n line in a three-dimensional black hole as a target spacetime metric. By solving the held equations we find a ''worldline instanton'' which connects the past event horizon with the future one. This solution gi ves us the exact value of the Hawking temperature and to leading order the Bekenstein-Hawking formula of black hole entropy. We also show th at this formalism is extensible to an arbitrary spacetime dimension. F inally we make a comment of many recent works of one-loop quantum corr ection to the black hole entropy.