English

Gravitational Bound State Perturbations Inside Black Holes and Isospectrality

General Relativity and Quantum Cosmology 2025-12-01 v2 Cosmology and Nongalactic Astrophysics High Energy Physics - Theory

Abstract

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 1\ell-1 bound states for polar perturbations. We show both analytically and numerically that the spectrum of 2\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=16πlPl2\Delta A = 16 \pi l_{\mathrm{Pl}}^2.

Keywords

Cite

@article{arxiv.2511.15140,
  title  = {Gravitational Bound State Perturbations Inside Black Holes and Isospectrality},
  author = {Hassan Firouzjahi and Kazem Rezazadeh and Masoud Molaei},
  journal= {arXiv preprint arXiv:2511.15140},
  year   = {2025}
}

Comments

8 pages, 3 figures. v2: discussions on black hole area quantization added