Minimum Length Effects in Black Hole Physics
We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black holes and how mod
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Minimum Length Effects in Black Hole Physics Roberto Casadio, Octavian Micu and Piero Nicolini
Abstract We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black holes and how modified dispersion relations affect the Hawking decay, both in four space-time dimensions and in models with extra spatial dimensions. In the latter case, we briefly discuss possible phenomenological signatures. Keywords Minimum length · Black holes · Planck scale · Hawking effect · Extra spatial-dimensions
10.1 Gravity and Minimum Length Physics is characterized by a variety of research fields and diversified tools of investigation that strongly depend on the length scales under consideration. As a result, one finds an array of sub-disciplines, spanning from cosmology, to astrophysics, geophysics, molecular and atomic physics, nuclear and particle physics. In a nutshell, we can say that Physics concerns events occurring at scales between the radius of the Universe and the typical size of observed elementary particles. It is not hard to R. Casadio (B) Dipartimento di Fisica e Astronomia, Università di Bologna, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy e-mail: [email protected] R. Casadio I.N.F.N., Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy O. Micu Institute of Space Science, P.O. Box MG-23, 077125 Bucharest-Magurele, Bucharest, Romania e-mail: [email protected] P. Nicolini Frankfurt Institute for Advanced Studies (FIAS), Science Campus Riedberg, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main, Germany e-mail: [email protected] © Springer International Publishing Switzerland 2015 X. Calmet (ed.), Quantum Aspects of Black Holes, Fundamental Theories of Physics 178, DOI 10.1007/978-3-319-10852-0_10
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understand that such a rich array of physical phenomena requires specific formalisms. For instance, at macroscopic scales, models of the Universe are obtained in terms of general relativity, while at microscopic scales quantum physics has been proven to be the adequate theory for the miniaturised world. Despite the generality of such a scheme, it cannot be considered as complete. One may be tempted to conclude that at microscopic scales, we can, at least in principle, figure out arbitrarily small lengths. In quantum mechanics, or more precisely in quantum field theory, particle sizes are described by the Compton wavelength, which accounts for the Heisenberg uncertainty in localising a microscopic object at a given energy. From this, it descends a “rule of thumb” according to which the higher the energy, the smaller is the size one can probe in a particle physics experiment. Apparently there is no minimal length scale. The limitations to the accuracy in measuring a length seems to be only a technological problem related to the possibility of reaching higher and higher energy scales. In th
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