The entropy increase during the black hole formation

Details The entropy increase during the black hole formation The entropy increase during the black hole formation

Apr 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007iaus..238..377h&link_type=abstract

Black Holes from Stars to Galaxies -- Across the Range of Masses. Edited by V. Karas and G. Matt. Proceedings of IAU Symposium #

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Scientific paper

Since the research of black hole thermodynamics was born a little over three decades ago, several striking concepts have been accepted. One of them is that the entropy is proportional to the surface area of the black hole. However there are still questions about the black hole entropy in its microscopic interpretation and its enormous increase through the black hole formation. In this paper, we investigate this problem from the viewpoint of the entropy increase. For the radiation dominated star, the temperature has decreased from the almost gravitational equilibrium one to the so-called Hawking temperature of the black hole. This decreased temperature could be estimated from the uncertainty principle. At the fundamental level, black holes are genuine quantum objects, where the de-Brogile length corresponding to the black hole temperature is comparable to the gravitational length. After the black hole formation, it is difficult to estimate the volume within the horizon, where time and radial coordinates are interchanged. For the Kerr solution, the volume within the horizon is considered to be infinite. The falling radiation can pass through the sphere of r=0 into another part of the space-time of negative value of r. If we interpret the temperature decrease as the volume increase of the black hole, the entropy increase could be understandable as the free expansion of radiation through the enlarged effective volume. The expected volume size is inferred from the temperature decrease. If we accept the increase of the effective black hole volume, it is derived that the entropy is proportional to the horizon surface area and the microscopic states of the black hole entropy could be understood as the statistical states of the enlarged phase space. Although this viewpoint is rather different from the current interpretation of the black hole entropy, it would stimulate to understand pedagogical and/or deeper meaning on the entropy increase in the black hole formation.

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