Gravitational Bound State Perturbations Inside Black Holes and Isospectrality

Fuente: arXiv
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Autori principali: Firouzjahi, Hassan, Rezazadeh, Kazem, Molaei, Masoud
Natura: Preprint
Pubblicazione: 2025
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author Firouzjahi, Hassan
Rezazadeh, Kazem
Molaei, Masoud
author_facet Firouzjahi, Hassan
Rezazadeh, Kazem
Molaei, Masoud
contents We study the bound state solutions for the polar perturbations in the interior of the Schwarzschild black hole. It is shown that for a given value of the spherical harmonic index $\ell$, there are a total of $\ell-1$ bound states for polar perturbations. We show both analytically and numerically that the spectrum of $\ell-2$ of these perturbations coincides exactly with the spectrum of axial perturbations. Consequently, the isospectrality between the bound states of axial and polar perturbations in the interior of the black hole is preserved. Furthermore, the additional mode found in the spectrum of polar perturbations is the algebraically special mode, which also furnishes the ground state of polar perturbations. It is shown that the spectrum of the highly excited states is equally spaced, which, in the semi-classical approximation, yields the black hole area quantization $ΔA = 16 πl_{\mathrm{Pl}}^2$.
format Preprint
id arxiv_https___arxiv_org_abs_2511_15140
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gravitational Bound State Perturbations Inside Black Holes and Isospectrality
Firouzjahi, Hassan
Rezazadeh, Kazem
Molaei, Masoud
General Relativity and Quantum Cosmology
Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
We study the bound state solutions for the polar perturbations in the interior of the Schwarzschild black hole. It is shown that for a given value of the spherical harmonic index $\ell$, there are a total of $\ell-1$ bound states for polar perturbations. We show both analytically and numerically that the spectrum of $\ell-2$ of these perturbations coincides exactly with the spectrum of axial perturbations. Consequently, the isospectrality between the bound states of axial and polar perturbations in the interior of the black hole is preserved. Furthermore, the additional mode found in the spectrum of polar perturbations is the algebraically special mode, which also furnishes the ground state of polar perturbations. It is shown that the spectrum of the highly excited states is equally spaced, which, in the semi-classical approximation, yields the black hole area quantization $ΔA = 16 πl_{\mathrm{Pl}}^2$.
title Gravitational Bound State Perturbations Inside Black Holes and Isospectrality
topic General Relativity and Quantum Cosmology
Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
url https://arxiv.org/abs/2511.15140