Quasi-exactly solvable quasinormal modes

Ho, Choon‐Lin; Cho, Hing‐Tong

doi:10.1063/1.2823815

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…13 Therefore the modified Pöschl-Teller potential is .11) where the factors ν and c can be adjusted to approximate actual black hole potentials, 22 subject to the condition (ν 2 + c 2 ) > 0. Here we have considered the quasi-exactly solvable form of the Poschl-Teller potential, 34,35 a special form of the more general Scarf II potential. The Schrödinger -like equation for the Pöschl-Teller potential is…”

Section: Discussionmentioning

confidence: 99%

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

Pal

Rajeev

Shankaranarayanan

2015

Int. J. Mod. Phys. D

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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.

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Section: Discussionmentioning

confidence: 99%

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

Pal

Rajeev

Shankaranarayanan

2015

Int. J. Mod. Phys. D

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“…Via quasi-exactly solvable theory, Ref. [41] found the exact solutions of equation (2.4) with V = V P T to be given as [14]:…”

Section: The Deepxde Packagementioning

confidence: 99%

Determining QNMs using PINNs

Cornell¹,

Ncube²,

Harmsen³

2022

Preprint

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In recent years there has been an increased interest in neural networks, particularly with regard to their ability to approximate partial differential equations. In this regard, research has begun on so-called physics-informed neural networks (PINNs) which incorporate into their loss function the boundary conditions of the functions they are attempting to approximate. In this paper, we investigate the viability of obtaining the quasi-normal modes (QNMs) of non-rotating black holes in 4-dimensional space-time using PINNs, and we find that it is achievable using a standard approach that is capable of solving eigenvalue problems (dubbed the eigenvalue solver here). In comparison to the QNMs obtained via more established methods (namely, the continued fraction method and the 6th-order Wentzel, Kramer, Brillouin method) the PINN computations share the same degree of accuracy as these counterparts. In other words, our PINN approximations had percentage deviations as low as (δω Re , δω Im ) = (< 0.01%, < 0.01%). In terms of efficiency, however, the PINN approach falls short, leading to our conclusion that the method is currently not to be recommended when considering overall performance.

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Quasi-exactly solvable quasinormal modes

Cited by 2 publications

References 15 publications

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

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

Determining QNMs using PINNs

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