The Connection Between Entropy and the Absorption Spectra of Schwarzschild Black Holes for Light and Massless Scalar Fields

Entropy

Sergio Mendoza¹  Xavier Hernandez¹  Pablo L. Rendón¹  C. S. Lopez-Monsalvo¹ 

[1]¹Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, AP 70-264, Distrito Federal 04510, Mexico

关键词: Physics of black holes;    Classical black holes;    Quantum aspects of black holes;    evaporation;    thermodynamics;   

DOI  :  10.3390/e11010017

来源: mdpi

【 摘 要 】

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 R_s, in the vicinity of R_s. 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.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.