Bose-Einstein condensates with derivative and long-range interactions as set-ups for analog black holes

Kühnel, Florian

doi:10.1103/physrevd.90.084024

Cited by 14 publications

(11 citation statements)

References 56 publications

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“…Recent works by Dvali and Gomez have offered a new perspective on the quantum aspects of black hole physics [1], and are drawing more and more attention [2,3,4,5,6,7,8,9]. The idea is very simple: a black hole can be modelled as a Bose-Einstein condensate (BEC) of gravitons interacting with each other.…”

Section: Introductionmentioning

confidence: 99%

Black holes as self-sustained quantum states and Hawking radiation

Casadio

Giugno

Micu³

et al. 2014

Phys. Rev. D

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We employ the recently proposed formalism of the "horizon wave-function" to investigate the emergence of a horizon in models of black holes as Bose-Einstein condensates of gravitons. We start from the Klein-Gordon equation for a massless scalar (toy graviton) field coupled to a static matter current. The (spherically symmetric) classical field reproduces the Newtonian potential generated by the matter source, and the corresponding quantum state is given by a coherent superposition of scalar modes with continuous occupation number. Assuming an attractive self-interaction that allows for bound states, one finds that (approximately) only one mode is allowed, and the system can be confined in a region of the size of the Schwarzschild radius. This radius is then shown to correspond to a proper horizon, by means of the horizon wave-function of the quantum system, with an uncertainty in size naturally related to the expected typical energy of Hawking modes. In particular, this uncertainty decreases for larger black hole mass (with larger number of light scalar quanta), in agreement with semiclassical expectations, a result which does not hold for a single very massive particle. We finally speculate that a phase transition should occur during the gravitational collapse of a star, ideally represented by a static matter current and Newtonian potential, that leads to a black hole, again ideally represented by the condensate of toy gravitons, and suggest an effective order parameter that could be used to investigate this transition. *

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Section: Introductionmentioning

confidence: 99%

Black holes as self-sustained quantum states and Hawking radiation

Casadio

Giugno

Micu³

et al. 2014

Phys. Rev. D

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“…This also means that we expect the occurrence of Hawking radiation [12,21] (see also Ref. [22]). (5) There is a coordinate singularity when v r → 1 (i.e., when it approaches the local speed of sound), and a curvature singularity for r → 0.…”

Section: Eulerian Metricmentioning

confidence: 96%

“…In recent years, it has become very fruitful not only to study BECs in the laboratory but also to interpret macroscopic objects-such as (primordial) black holes [19][20][21][22], neutron/boson stars [23][24][25], white dwarfs [26], and/or darkmatter halos as BECs [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Astrophysical Bose-Einstein condensates and superradiance

Kühnel

Rampf

2014

Phys. Rev. D

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We investigate gravitational analogue models to describe slowly rotating objects (e.g., dark-matter halos, or boson stars) in terms of Bose-Einstein condensates, trapped in their own gravitational potentials. We begin with a modified Gross-Pitaevskii equation, and show that the resulting background equations of motion are stable, as long as the rotational component is treated as a small perturbation. The dynamics of the fluctuations of the velocity potential are effectively governed by the Klein-Gordon equation of an "Eulerian metric," where we derive the latter by the use of a relativistic Lagrangian extrapolation. Superradiant scattering on such objects is studied. We derive conditions for its occurrence and estimate its strength. Our investigations might give an observational handle to phenomenologically constrain BoseEinstein condensates.

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“…The simple and intuitive corpuscular model recently introduced by Dvali and Gomez in [16][17][18][19][20][21][22] and widely developed in [36][37][38][39][40][41][42][43][44], puts gravitation under a new light. The model is based on the assumption that the classical geometry should be viewed as an effective description of a quantum state with a large graviton occupation number, where gravitons play the role of space-time quanta, very much like photons are light quanta in a laser beam.…”

Section: Corpuscular Modelmentioning

confidence: 99%

Thermal BEC Black Holes

Casadio

Giugno

Micu

et al. 2015

Entropy

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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.

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Bose-Einstein condensates with derivative and long-range interactions as set-ups for analog black holes

Cited by 14 publications

References 56 publications

Black holes as self-sustained quantum states and Hawking radiation

Black holes as self-sustained quantum states and Hawking radiation

Astrophysical Bose-Einstein condensates and superradiance

Thermal BEC Black Holes

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