Bose-Einstein condensate general relativistic stars

Chavanis, Pierre‐Henri; Harkó, Tiberiu

doi:10.1103/physrevd.86.064011

Cited by 235 publications

(318 citation statements)

References 109 publications

Supporting

Mentioning

308

Contrasting

Unclassified

Order By: Relevance

“…This result, along with the fact that all N excitations in the mode k c are confined within the radius R H λ c , 14) immediately leads to the conclusion that the system is indeed a black hole,…”

Section: Hairless Black Holementioning

confidence: 88%

“…(2.7). However, the problem of self-gravitating scalar fields in general relativity has been know for decades [12] and analytical solutions have yet to be found [13,14]. Moreover, it is not a priori guaranteed that such a semiclassical approach remains valid for the type of quantum sources we are dealing with, since the quantum fluctuations of the source could be large enough to spoil the possibility of employing a curved background geometry to describe the region where the source is located 5 .…”

Section: Stars and Self-sustained Scalar Statesmentioning

confidence: 99%

See 1 more Smart Citation

Black holes as self-sustained quantum states and Hawking radiation

Casadio

Giugno

Micu³

et al. 2014

Phys. Rev. D

View full text Add to dashboard Cite

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. *

show abstract

Section: Hairless Black Holementioning

confidence: 88%

Section: Stars and Self-sustained Scalar Statesmentioning

confidence: 99%

Black holes as self-sustained quantum states and Hawking radiation

Casadio

Giugno

Micu³

et al. 2014

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…On the other hand, for realistic dark matter densities the corresponding mass of the star will exceed the general relativistic stability limit. Hence the realistic description of the dark stars requires the inclusion of general relativistic effects in the study of their structure [31].…”

Section: Discussion and Final Remarksmentioning

confidence: 99%

“…The possibility that due to their superfluid properties some compact astrophysical objects may contain a significant part of their matter in the form of a BoseEinstein condensate was investigated in [31]. To study the condensate the Gross-Pitaevskii equation was used, with arbitrary non-linearity.…”

Section: Introductionmentioning

confidence: 99%

Gravitational collapse of Bose-Einstein condensate dark matter halos

Harkó

2014

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schrödinger equation (the Gross-Pitaevskii equation), with repulsive inter-particle interactions. By using a variational approach, and by choosing an appropriate trial wave function, we reformulate the Gross-Pitaevskii equation with spherical symmetry as Newton's equation of motion for a particle in an effective potential, which is determined by the zero point kinetic energy, the gravitational energy, and the particles interaction energy, respectively. The velocity of the condensate is proportional to the radial distance, with a time dependent proportionality function. The equation of motion of the collapsing dark matter condensate is studied by using both analytical and numerical methods. The collapse of the condensate ends with the formation of a stable configuration, corresponding to the minimum of the effective potential. The radius and the mass of the resulting dark matter object are obtained, as well as the collapse time of the condensate. The numerical values of these global astrophysical quantities, characterizing condensed dark matter systems, strongly depend on the two parameters describing the condensate, the mass of the dark matter particle, and of the scattering length, respectively. The stability of the condensate under small perturbations is also studied, and the oscillations frequency of the halo is obtained. Hence these results show that the gravitational collapse of the condensed dark matter halos can lead to the formation of stable astrophysical systems with both galactic and stellar sizes.

show abstract

“…In particular, polytropic models with n = 1 can be used to model Bose-Einstein Condensate dark matter (Boehmer & Harko 2007), and Bose-Einstein Condensate stars (Chavanis & Harko 2012), respectively. For a polytropic system, the interior structure of the compact objects can be described by an equation of state of the form…”

Section: Exact Power Series Solutions Of the Relativistic Mass Equatimentioning

confidence: 99%

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

Harkó

Mak

2016

Astrophys Space Sci

View full text Add to dashboard Cite

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state T. Harko 1,2 • M. K. Mak 3Abstract Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n = 1, and for the indexes n = 1/2 and n = 1/5, respectively. The case of n = 3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven

show abstract

Bose-Einstein condensate general relativistic stars

Cited by 235 publications

References 109 publications

Black holes as self-sustained quantum states and Hawking radiation

Black holes as self-sustained quantum states and Hawking radiation

Gravitational collapse of Bose-Einstein condensate dark matter halos

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

Contact Info

Product

Resources

About