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Scalar and Spinor Quasi Normal Modes of a 2D Dilatonic Blackhole

Pabitra Gayen, Ratna Koley

TL;DR

This work analyzes quasinormal modes of a (1+1)D Mandal-Sengupta-Wadia dilatonic black hole under non-minimally coupled scalar and Dirac perturbations. For the scalar field with a power-law dilaton coupling h(r) ∝ sigma and under the parameter constraint M = sqrt{k}, the radial equation admits exact QNM frequencies, with ω' = -i (4 n^2 + 4 n sigma - k m^2) / (2 sqrt{k} (2 n + sigma)) and ω'' = -i (4 (n+1)(n+1 - sigma) - k m^2) / (2 sqrt{k} (2 n + 2 - sigma)). For the massless Dirac field, the two chiral modes have spectra with real parts linear in the coupling Q: ω_I = Q/(2 sqrt{M}) - i (n+1/2)/M and ω_II = -Q/(2 sqrt{M}) - i (n+1/2)/M, while the imaginary parts depend only on M and n. These exact results show that scalar QNMs are purely imaginary while Dirac QNMs are damped oscillations; damping grows with the overtone number and the spectra depend on the black hole parameters k and M. The authors discuss stability, time-domain behavior, and potential links to black hole area quantization via Maggiore's proposal, with future directions to explore other couplings and connections to microscopic black hole properties.

Abstract

External non-minimally coupled scalar and spinor field perturbations have been studied in a (1 + 1) dimensional dilatonic blackhole spacetime [1, 2]. Exact analytical expressions of the quasi- normal mode frequencies have been found for both the cases. In the scalar perturbations the quasi-normal mode frequencies turn out to be purely imaginary and negative. Furthermore we have found that the quasi-normal frequencies for Dirac field exhibit both real and imaginary part. The QNM frequencies decay monotonically with the overtone number under certain class of the blackhole parameters. The decay profile ensures the stability of the blackhole spacetime under these perturbations.

Scalar and Spinor Quasi Normal Modes of a 2D Dilatonic Blackhole

TL;DR

This work analyzes quasinormal modes of a (1+1)D Mandal-Sengupta-Wadia dilatonic black hole under non-minimally coupled scalar and Dirac perturbations. For the scalar field with a power-law dilaton coupling h(r) ∝ sigma and under the parameter constraint M = sqrt{k}, the radial equation admits exact QNM frequencies, with ω' = -i (4 n^2 + 4 n sigma - k m^2) / (2 sqrt{k} (2 n + sigma)) and ω'' = -i (4 (n+1)(n+1 - sigma) - k m^2) / (2 sqrt{k} (2 n + 2 - sigma)). For the massless Dirac field, the two chiral modes have spectra with real parts linear in the coupling Q: ω_I = Q/(2 sqrt{M}) - i (n+1/2)/M and ω_II = -Q/(2 sqrt{M}) - i (n+1/2)/M, while the imaginary parts depend only on M and n. These exact results show that scalar QNMs are purely imaginary while Dirac QNMs are damped oscillations; damping grows with the overtone number and the spectra depend on the black hole parameters k and M. The authors discuss stability, time-domain behavior, and potential links to black hole area quantization via Maggiore's proposal, with future directions to explore other couplings and connections to microscopic black hole properties.

Abstract

External non-minimally coupled scalar and spinor field perturbations have been studied in a (1 + 1) dimensional dilatonic blackhole spacetime [1, 2]. Exact analytical expressions of the quasi- normal mode frequencies have been found for both the cases. In the scalar perturbations the quasi-normal mode frequencies turn out to be purely imaginary and negative. Furthermore we have found that the quasi-normal frequencies for Dirac field exhibit both real and imaginary part. The QNM frequencies decay monotonically with the overtone number under certain class of the blackhole parameters. The decay profile ensures the stability of the blackhole spacetime under these perturbations.
Paper Structure (5 sections, 46 equations, 8 figures, 1 table)

This paper contains 5 sections, 46 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Quasi-normal modes for massive scalar perturbations
  3. Quasi-normal modes for massless Dirac field non-minimally coupled with dilaton field
  4. Conclusions
  5. Acknowledgements

Figures (8)

  • Figure 1: Effective potential experienced by a massive scalar field in tortoise coordinates.
  • Figure 2: Variation of imaginary part of QNFs for massive ($m=0.5$) scalar field with $n$ for different $\sqrt{k}$ values. Considering the values of the parameters $M=1$ and $\sigma=0.5$.
  • Figure 3: Time evolution of square of different massive scalar modes in logarithmic scale at $r=10$ corresponding to the frequency $\omega '$. Considering the value of the parameter $\sqrt{k}=1$.
  • Figure 4: Time evolution of square of different massive scalar modes in logarithmic scale at $r=10$ corresponding to the frequency $\omega "$.
  • Figure 5: Effective potential experienced by $Z_+$ mode for different $Q$ in tortoise coordinates with parameters $\sigma=-\frac{1}{2}$, $M=1$ and $\sqrt{k}=1$.
  • ...and 3 more figures