Quasinormal Modes in Noncommutative Schwarzschild black holes

Abstract

We investigate the quasinormal modes of a massless scalar field in a Schwarzschild black hole, which is deformed due to noncommutative corrections. We present the deformed Schwarzschild black hole solution, which depends on the noncommutative parameter Θ, and we extract the master equation as a Schrödinger-like equation, giving the explicit expression of the effective potential which is modified due to the noncommutative corrections. We solve the master equation numerically and we find that the noncommutative gravitational corrections "break" the stability of the scalar perturbations in the long time evolution of the massless scalar field. The significance of these results is twofold. Firstly, our results can be related to the detection of gravitational waves by the near future gravitational wave detectors, such as LISA, which will have a significantly increased accuracy. In particular, these observed gravitational waves produced by binary strong gravitational systems have oscillating modes which can provide valuable information. Secondly, our results can serve as an additional tool to test the predictions of general relativity, as well as to examine the possible detection of this kind of gravitational corrections.

Quasinormal modes of charged BTZ black holes

“…That seems to be the case in such spacetime independent of the logarithm term as in (2). Considering other modified theories of gravity in high dimensional spaces, such as that of [99,100] we point out two specific differences: in our thorough investigation the effective potential is always positive, not allowing for instabilities in the field evolution. The resulting scalar perturbation evolves consequently into a well-behaved tower of quasinormal modes.…”