Uncertainty principle for the entropy of black holes, de Sitter and Rindler spaces

Details Uncertainty principle for the entropy of black holes, de Sitter and Rindler spaces Uncertainty principle for the entropy of black holes, de Sitter and Rindler spaces

Apr 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007iaus..238..379h&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 #

Mathematics

Logic

Scientific paper

One of the striking concepts of black hole is that the entropy of the black hole is proportional to the surface. The key concept to understand this statement is the uncertainty principle. As the black hole has the gravitational radius, there is the corresponding momentum. It can be speculated that the temperature of the black hole is proportional to the energy of the corresponding particle (photon). If the black hole is formed by such photons or particles, it could be explained that the temperature of the black hole is proportional to the surface gravity and the entropy of the black hole is proportional to the surface of the black hole. Recently it is confirmed the existence of cosmological constant. In the space with the cosmological constant (de Sitter space), each observer is surrounded by the event horizon of the cosmological scale. There is the characteristic length derived from the cosmological constant, so it could be speculated the temperature of the horizon from the uncertainty principle. If we assume that the universe is composed of particles (photons) with such de Brogile length, it could be derived that the entropy of the universe is related to the surface of the horizon. The similar consideration is applied to the uniformly accelerated coordinate (Rindler coordinate), where it has the characteristic length due to its acceleration. If we assume that the acceleration is due to the gravity of the gravitational mass of particles, it is derived that the entropy per surface is constant.

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