Effects of Noncommutativity on the Black Hole Entropy

Abstract

The BTZ black hole geometry is probed with a noncommutative scalar field which obeys the κ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity.