Bohr's semiclassical model of the black hole thermodynamics
We propose a simple procedure for evaluating the main attributes of a Schwarzschild's black hole: Bekenstein-Hawking entropy, Hawking temperature and Bekenstein's quantization of the surface area. We make use of the condition that the circumference of a great circle on the black hole horiz...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Astronomical Observatory, Department of Astronomy, Belgrade
2008-01-01
|
| Series: | Serbian Astronomical Journal |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-698X/2008/1450-698X0876015P.pdf |
| _version_ | 1818541725197533184 |
|---|---|
| author | Panković V. Predojević M. Grujić P. |
| author_facet | Panković V. Predojević M. Grujić P. |
| author_sort | Panković V. |
| collection | DOAJ |
| description | We propose a simple procedure for evaluating the main attributes of a Schwarzschild's black hole: Bekenstein-Hawking entropy, Hawking temperature and Bekenstein's quantization of the surface area. We make use of the condition that the circumference of a great circle on the black hole horizon contains finite and whole number of the corresponding reduced Compton's wavelength. It is essentially analogous to Bohr's quantization postulate in Bohr's atomic model interpreted by de Broglie's relation. It implies the standard meaning of the black hole entropy corresponding to surface of the quantum variation of the great circles on the black hole horizon surface area. We present black hole radiation in the form conceptually analogous to Bohr's postulate on the photon emission by discrete quantum jump of the electron within the Old quantum theory. This enables us, in accordance with Heisenberg's uncertainty relation and Bohr's correspondence principle, to make a rough estimate of the time interval for black hole evaporation, which turns out very close to time interval predicted by the standard Hawking's theory. Our calculations confirm Bekenstein's semiclassical result for the energy quantization, in variance with Frasca's (2005) calculations. Finally we speculate about the possible source-energy distribution within the black hole horizon. |
| first_indexed | 2024-12-11T22:12:57Z |
| format | Article |
| id | doaj.art-a0d31e55c0c7443ca28f6347afbb5877 |
| institution | Directory Open Access Journal |
| issn | 1450-698X 1820-9289 |
| language | English |
| last_indexed | 2024-12-11T22:12:57Z |
| publishDate | 2008-01-01 |
| publisher | Astronomical Observatory, Department of Astronomy, Belgrade |
| record_format | Article |
| series | Serbian Astronomical Journal |
| spelling | doaj.art-a0d31e55c0c7443ca28f6347afbb58772022-12-22T00:48:42ZengAstronomical Observatory, Department of Astronomy, BelgradeSerbian Astronomical Journal1450-698X1820-92892008-01-012008176152210.2298/SAJ0876015P1450-698X0876015PBohr's semiclassical model of the black hole thermodynamicsPanković V.0Predojević M.1Grujić P.2Department of Physics, Faculty of Sciences, Novi SadDepartment of Physics, Faculty of Sciences, Novi SadInstitute of Physics, BelgradeWe propose a simple procedure for evaluating the main attributes of a Schwarzschild's black hole: Bekenstein-Hawking entropy, Hawking temperature and Bekenstein's quantization of the surface area. We make use of the condition that the circumference of a great circle on the black hole horizon contains finite and whole number of the corresponding reduced Compton's wavelength. It is essentially analogous to Bohr's quantization postulate in Bohr's atomic model interpreted by de Broglie's relation. It implies the standard meaning of the black hole entropy corresponding to surface of the quantum variation of the great circles on the black hole horizon surface area. We present black hole radiation in the form conceptually analogous to Bohr's postulate on the photon emission by discrete quantum jump of the electron within the Old quantum theory. This enables us, in accordance with Heisenberg's uncertainty relation and Bohr's correspondence principle, to make a rough estimate of the time interval for black hole evaporation, which turns out very close to time interval predicted by the standard Hawking's theory. Our calculations confirm Bekenstein's semiclassical result for the energy quantization, in variance with Frasca's (2005) calculations. Finally we speculate about the possible source-energy distribution within the black hole horizon.http://www.doiserbia.nb.rs/img/doi/1450-698X/2008/1450-698X0876015P.pdfblack hole physics |
| spellingShingle | Panković V. Predojević M. Grujić P. Bohr's semiclassical model of the black hole thermodynamics Serbian Astronomical Journal black hole physics |
| title | Bohr's semiclassical model of the black hole thermodynamics |
| title_full | Bohr's semiclassical model of the black hole thermodynamics |
| title_fullStr | Bohr's semiclassical model of the black hole thermodynamics |
| title_full_unstemmed | Bohr's semiclassical model of the black hole thermodynamics |
| title_short | Bohr's semiclassical model of the black hole thermodynamics |
| title_sort | bohr s semiclassical model of the black hole thermodynamics |
| topic | black hole physics |
| url | http://www.doiserbia.nb.rs/img/doi/1450-698X/2008/1450-698X0876015P.pdf |
| work_keys_str_mv | AT pankovicv bohrssemiclassicalmodeloftheblackholethermodynamics AT predojevicm bohrssemiclassicalmodeloftheblackholethermodynamics AT grujicp bohrssemiclassicalmodeloftheblackholethermodynamics |