Thermal BEC Black Holes

Abstract

Abstract: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 energy ω > m (representing the Hawking radiation and modeled with a Planckian distribution at the expected Hawking temperature). Assuming the main effect of the internal scatterings is the Hawking radiation, the N -particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy M = N m and Entropy 2015, 17 6894 a Planckian distribution for E > M at the same Hawking temperature. This can be used to compute the partition function and to find the usual area law for the entropy, with a logarithmic correction related to the Hawking component. The backreaction of modes with ω > m is 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.

Horizon quantum mechanics of rotating black holes

“…[10]. 1 This model can be considered as a working realization of the corpuscular black holes proposed by Dvali and Gomez [12][13][14][15][16][17][18][19], and it turns out to be simple enough, so as to allow one to determine explicitly the probability that the chosen states are indeed black holes. Furthermore, we will investigate the existence of the inner horizon and likelihood of extremal configurations for these states.…”

Horizon quantum fuzziness for non-singular black holes

“…In particular, it has been proposed [34] that N → ∞ is the limit, in which a purely classical geometry shall emerge from the effective description of the corpuscular black hole model. This statement is enforced by the present analysis, since…”

“…Although approximating the binding potential with a square well leads to interesting results [34], a more appropriate approximation for such a potential is provided by the harmonic black hole model [21,35], for which we have that V (r ) = V 0 (r ) (λ μ − r ), where…”

Born-Kothari Condensation for Fermions

“…It is generally assumed that the density of states is proportional to the volume element in the p-space as we considered here in Equation (10). This is true in the description of BEC which is derived by assuming a discrete set of plane wave modes in a large box, and then allowing the box length to infinity to recover the integral as a limit of the sum.…”

“…It was only after the discovery of superfluidity [3] in 1938, the phenomenon received tremendous impetus which eventually led to its experimental realization in 1995 [4][5][6]. The study of BEC in dilute gases exhibits quantum phenomena on a large scale and has become one of the most active fields of research in atomic, molecular, and condensed matter physics in recent times [7][8][9][10][11].…”