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The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields
Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, AP 70-264, Distrito Federal 04510, Mexico
GEPI, Observatoire de Paris, 5 Place Jules Janssen, 92195 Meudon, France
CCADET, Universidad Nacional Autonoma de Mexico, Distrito Federal 04510, Mexico
School of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom
* Author to whom correspondence should be addressed.
Received: 11 June 2008 / Accepted: 11 January 2009 / Published: 23 January 2009
Abstract: We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value c, for wavelengths larger than Rs, in the vicinity of Rs. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent ’particle’ description fails, and the wave nature becomes apparent.
Keywords: Physics of black holes; Classical black holes; Quantum aspects of black holes; evaporation; thermodynamics
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Mendoza, S.; Hernandez, X.; Rendón, P.L.; Lopez-Monsalvo, C.S.; Velasco-Segura, R. The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields. Entropy 2009, 11, 17-31.
Mendoza S, Hernandez X, Rendón PL, Lopez-Monsalvo CS, Velasco-Segura R. The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields. Entropy. 2009; 11(1):17-31.
Mendoza, Sergio; Hernandez, Xavier; Rendón, Pablo L.; Lopez-Monsalvo, C. S.; Velasco-Segura, Roberto. 2009. "The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields." Entropy 11, no. 1: 17-31.