Thermal BEC Black Holes

Entropy

Roberto Casadio²  Andrea Giugno²  Octavian Micu¹  Alessio Orlandi²  Remo Garattini³ 

[1] Institute of Space Science, Atomistilor 409, 077125 Magurele, Ilfov, Romania; E-Mail:;Dipartimento di Fisica e Astronomia, Alma Mater Università di Bologna, via Irnerio 46, 40126 Bologna, Italy; E-Mails:Dipartimento di Fisica e Astronomia, Alma Mater Università di Bologna, via Irnerio 46, 40126 Bologna, Italy;

关键词: black holes;    horizon wave function;    Hawking radiation;    generalized uncertainty principle;   

DOI  :  10.3390/e17106893

来源: mdpi

【 摘 要 】

We review some features of Bose–Einstein condensate (BEC) models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical field reproduces the Newtonian potential generated by the matter source, while the corresponding quantum state is given by a coherent superposition of scalar modes with a continuous occupation number. An attractive self-interaction is needed for bound states to form, the case in which one finds that (approximately) one mode is allowed, and the system of N bosons can be self-confined in a volume of the size of the Schwarzschild radius. The horizon wave function formalism is then used to show that the radius of such a system corresponds to a proper horizon. The uncertainty in the size of the horizon is related to the typical energy of Hawking modes: it decreases with the increasing of the black hole mass (larger number of gravitons), resulting in agreement with the semiclassical calculations and which does not hold for a single very massive particle. The spectrum of these systems has two components: a discrete ground state of energy m (the bosons forming the black hole) and a continuous spectrum with energyis also shown to reduce the Hawking flux. The above corrections suggest that for black holes in this quantum state, the evaporation properly stops for a vanishing mass.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.