Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-07-06
Rev.Mex.Fis.52:515,2006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, 1 figure. Added discussion on relativistic Jeans criterion and a more formal statistical mechanical treatment. Accept
Scientific paper
We show that if the total internal energy of a black hole is constructed as the sum of $N$ photons all having a fixed wavelength chosen to scale with the Schwarzschild radius as $\lambda=\alpha R_{s}$, then $N$ will scale with $R_{s}^{2}$. A statistical mechanical calculation of the configuration proposed yields (\alpha = 4 \pi^2 / \ln(2)) and a total entropy of the system $S=k_{B}N \ln(2)$, in agreement with the Bekenstein entropy of a black hole . It is shown that the critical temperature for Bose-Einstein condensation for relativistic particles of $\lambda=\alpha R_{s}$ is always well below the Hawking temperature of a black hole, in support of the proposed internal configuration. We then examine our results from the point of view of recent loop quantum gravity ideas and find that a natural consistency of both approaches appears. We show that the Jeans criterion for gravitational instability can be generalised to the special and general relativistic regimes and holds for any type of mass--energy distribution.
Hernandez Xabier
Lopez-Monsalvo C. S.
Mendoza Sergio
Sussman Roberto A.
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