Dynamical origin of the entropy of a black hole

Abstract

Modes of physical fields which are located inside a horizon and which cannot be observed by a distant observer are identified with the dynamical degrees of freedom of a black hole. A new invariant statistical mechanical definition of black-hole entropy is proposed. It is shown that the main contribution to the entropy is given by thermally excited "invisible" modes propagating in the close vicinity of the horizon. A calculation based on the proposed definition yields a value of the entropy which is in good agreement with the usually adopted value $\frac{A^H}{\left(4\mathrm{}{l}_{\mathrm{Pl}}^2\right)}$, where $A^H$ is the black-hole surface area and $l_{\mathrm{Pl}}$ is the Planck length.