Entropy and black hole horizons

The standard approach of counting the number of eigenmodes of N scalar fields near the horizon is used as a basis to provide a simple statistical mechanical derivation of the black hole entropy in two and four dimensions. The Bekenstein formula S = A4Gh̷h and the two-dimensional entropy 2Mlh̷h are naturally obtained (up to a numerical constant of order 1). This approach provides an explanation on why the black hole entropy is of order 1h̷h and why it is independent of the number of field-theoretical degrees of freedom.