Gravitational Bound State Perturbations Inside Black Holes and Isospectrality
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910280582168576 |
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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 |