2024/09/13 by Carpio, Wilfredo Yupanqui, Octavio Obregón, Obregón, Octavio · 1 citation
Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2409.09181
openalex publication_date 2024/09/13 · openalex created_date 2024/10/23 · openalex updated_date 2026/07/30
Starting from the eigenvalue equation for the mass of a black hole derived by Mäkelä and Repo, we show that, by reparametrizing the radial coordinate and the wave function, it can be rewritten as the eigenvalue equation of a quantum harmonic oscillator. We then study the interior of a Schwarzschild black hole using two quantization approaches. In the standard quantization, the area and mass spectra are discrete, characterized by a quantum number n, but the wave function is not square-integrable, limiting its physical interpretation. In contrast, a minimal-uncertainty quantization approach yields an area spectrum that grows as n2, and consequently the mass M also increases. In this framework, the wave function is finite and square-integrable, with convergence requiring that the deformation parameter β be regulated by a discrete quantum number m. The wave function exhibits quantum tunneling connecting the black hole interior with both its exterior and a white hole region, effects that disappear in the limit β→ 0. These results demonstrate how minimal-length effects both regularize the wave function and modify the semiclassical structure of the black hole.