An approach to the quantization of black hole quasi-normal modes

Abstract

In this work, we derive the asymptotic quasi-normal modes of a Banados-Teitelboim-Zanelli (BTZ) black hole using a quantum field theoretic Lagrangian. The BTZ black hole is a very popular system in the context of 2 + 1-dimensional quantum gravity. However, to our knowledge the quasi-normal modes of the BTZ black hole have been studied only in the classical domain. Here we show a way to quantize the quasi-normal modes of the BTZ black hole by mapping it to the Bateman-Feschbach-Tikochinsky oscillator and the Caldirola-Kanai oscillator. We have also discussed a couple of other black hole potentials to which this method can be applied. Int. J. Mod. Phys. D Downloaded from www.worldscientific.com by CAMBRIDGE UNIVERSITY on 08/22/15. For personal use only. S. Pal, K. Rajeev and S. Shankaranarayanan 1550083-2 Int. J. Mod. Phys. D Downloaded from www.worldscientific.com by CAMBRIDGE UNIVERSITY on 08/22/15. For personal use only. 1550083-3 Int. J. Mod. Phys. D Downloaded from www.worldscientific.com by CAMBRIDGE UNIVERSITY on 08/22/15. For personal use only.

On the effect of scalar fields on Hawking radiation and quasinormal modes of black holes

“…The completeness of the quasinormal modes is another subtle issue [20]. The quasinormal modes, in general, do not form a complete set and as such the gravitational wave signal cannot be represented by a sum of the quasinormal modes at all times [21][22][23].…”

Astroseismology of neutron stars from gravitational waves in the limit of perfect measurement

“…Spacetimes which allow for such a decomposition are said to be complete with respect to QNMs; in this context, completeness means that it is possible to express the evolution of a wavefunction as a sum over eigenfunctions (Price & Husain 1992;Nollert 1999). In fact, this is largely still an open problem within general relativity (Andersson 1993;Ching et al 1995;Beyer 1999;Pal et al 2015). For example, it has been argued that if the potential V has a significant tail at large radii, the GWs emitted due to the perturbation may only have power-law decays at late times, which means that the signal cannot be represented through QNMs, which decay exponentially (12) (Price & Husain 1992;Ching et al 1996).…”