Black hole spectroscopy via an action invariance in noncommutative spacetimes

Abstract

Spectroscopy for a modified Schwarzschild black hole in noncommutative spacetimes is investigated. By utilizing an action invariance of black holes, the equally spaced entropy spectrum characteristic of Bekenstein’s original derivation is recovered. The derived spectrum is independent of the noncommutative parameter θ, and holds for all the existed noncommutative black holes independent of mass. On the other hand, the obtained area spectrum is not always equidistant due to the noncommutativity effects of the modified spacetimes. For large black holes, the equally spaced area spectrum spectrum can be obtained at the leading order in θ. But, for small black holes, the derived area spectrum is not equidistant, and it depends the noncommutative parameter. In addition, the one loop back reaction effect on the spectroscopy of the noncommutative Schwarzschild black hole is discussed. In this calculation, due to the back reaction effect, the equidistant area spectrum can not be obtained for all the noncommutative black holes with both large and small mass. Conversely, the back reaction effect has no influence on the entropy spectrum. The obtained entropy spectrum is equidistant and consistent with the original Bekenstein’s spectrum for all the existed noncommutative Schwarzschild black holes.

Keywords

• black hole spectroscopy
• noncommutative spacetimes
• action invariance