Further Evidence for the Conformal Structure of a Schwarzschild Black Hole in an Algebraic Approach

We study the excitations of a massive Schwarzschild black hole of mass M resulting from the capture of infalling matter described by a massless scalar field. The near-horizon dynamics of this system is governed by a Hamiltonian which is related to the Virasoro algebra and admits a one-parameter family of self-adjoint extensions described by a parameter z ∈ R. The density of states of the black hole can be expressed equivalently in terms of z or M , leading to a consistent relation between these two parameters. The corresponding black hole entropy is obtained as S = S(0) − 3 2 logS(0) + C, where S(0) is the Bekenstein-Hawking entropy, C is a constant with other subleading corrections exponentially suppressed. The appearance of this precise form for the black hole entropy within our formalism, which is expected on general grounds in any conformal field theoretic description, provides strong evidence for the near-horizon conformal structure in this system.