Abstract
In this work, we find exact gravastar solutions in the context of noncommutative geometry, and explore their physical properties and characteristics. The energy density of these geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension \( \sqrt{\alpha } \) due to the intrinsic uncertainty encoded in the coordinate commutator. These solutions are then matched to an exterior Schwarzschild spacetime. We further explore the dynamical stability of the transition layer of these gravastars, for the specific case of β = M 2/α < 1.9, where M is the black hole mass, to linearized spherically symmetric radial perturbations about static equilibrium solutions. It is found that large stability regions exist and, in particular, located sufficiently close to where the event horizon is expected to form.
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P.O. Mazur and E. Mottola, Gravitational condensate stars: an alternative to black holes, gr-qc/0109035 [INSPIRE].
P.O. Mazur and E. Mottola, Dark energy and condensate stars: Casimir energy in the large, gr-qc/0405111 [INSPIRE].
P.O. Mazur and E. Mottola, Gravitational vacuum condensate stars, Proc. Nat. Acad. Sci. 101 (2004) 9545 [gr-qc/0407075] [INSPIRE].
G. Chapline, E. Hohlfeld, R.B. Laughlin and D.I. Santiago, Quantum phase transitions and the breakdown of classical general relativity, Int. J. Mod. Phys. A 18 (2003) 3587 [gr-qc/0012094] [INSPIRE].
G. Chapline, Dark energy stars, eConf C 041213 (2004) 0205 [astro-ph/0503200] [INSPIRE].
F.S.N. Lobo, Stable dark energy stars, Class. Quant. Grav. 23 (2006) 1525 [gr-qc/0508115] [INSPIRE].
M. Visser and D.L. Wiltshire, Stable gravastars: an alternative to black holes?, Class. Quant. Grav. 21 (2004) 1135 [gr-qc/0310107] [INSPIRE].
B.M.N. Carter, Stable gravastars with generalised exteriors, Class. Quant. Grav. 22 (2005) 4551 [gr-qc/0509087] [INSPIRE].
P. Rocha, R. Chan, M.F.A. da Silva and A. Wang, Stable and ‘bounded excursion’ gravastars and black holes in Einstein’s theory of gravity, JCAP 11 (2008) 010 [arXiv:0809.4879] [INSPIRE].
C. Cattoen, T. Faber and M. Visser, Gravastars must have anisotropic pressures, Class. Quant. Grav. 22 (2005) 4189 [gr-qc/0505137] [INSPIRE].
A. DeBenedictis, D. Horvat, S. Ilijic, S. Kloster and K.S. Viswanathan, Gravastar solutions with continuous pressures and equation of state, Class. Quant. Grav. 23 (2006) 2303 [gr-qc/0511097] [INSPIRE].
F.S.N. Lobo and A.V.B. Arellano, Gravastars supported by nonlinear electrodynamics, Class. Quant. Grav. 24 (2007) 1069 [gr-qc/0611083] [INSPIRE].
N. Bilic, G.B. Tupper and R.D. Viollier, Born-Infeld phantom gravastars, JCAP 02 (2006) 013 [astro-ph/0503427] [INSPIRE].
A. DeBenedictis, R. Garattini and F.S.N. Lobo, Phantom stars and topology change, Phys. Rev. D 78 (2008) 104003 [arXiv:0808.0839] [INSPIRE].
O. Bertolami and J. Paramos, The Chaplygin dark star, Phys. Rev. D 72 (2005) 123512 [astro-ph/0509547] [INSPIRE].
S.S. Yazadjiev, Exact dark energy star solutions, Phys. Rev. D 83 (2011) 127501 [arXiv:1104.1865] [INSPIRE].
F.S.N. Lobo, Van der Waals quintessence stars, Phys. Rev. D 75 (2007) 024023 [gr-qc/0610118] [INSPIRE].
A.E. Broderick and R. Narayan, Where are all the gravastars? Limits upon the gravastar model from accreting black holes, Class. Quant. Grav. 24 (2007) 659 [gr-qc/0701154] [INSPIRE].
C.B.M.H. Chirenti and L. Rezzolla, How to tell a gravastar from a black hole, Class. Quant. Grav. 24 (2007) 4191 [arXiv:0706.1513] [INSPIRE].
D. Horvat and S. Ilijic, Gravastar energy conditions revisited, Class. Quant. Grav. 24 (2007) 5637 [arXiv:0707.1636] [INSPIRE].
V. Cardoso, P. Pani, M. Cadoni and M. Cavaglia, Ergoregion instability of ultracompact astrophysical objects, Phys. Rev. D 77 (2008) 124044 [arXiv:0709.0532] [INSPIRE].
C.B.M.H. Chirenti and L. Rezzolla, On the ergoregion instability in rotating gravastars, Phys. Rev. D 78 (2008) 084011 [arXiv:0808.4080] [INSPIRE].
D. Horvat, S. Ilijic and A. Marunovic, Electrically charged gravastar configurations, Class. Quant. Grav. 26 (2009) 025003 [arXiv:0807.2051] [INSPIRE].
B.V. Turimov, B.J. Ahmedov and A.A. Abdujabbarov, Electromagnetic fields of slowly rotating magnetized gravastars, Mod. Phys. Lett. A 24 (2009) 733 [arXiv:0902.0217] [INSPIRE].
T. Harko, Z. Kovacs and F.S.N. Lobo, Can accretion disk properties distinguish gravastars from black holes?, Class. Quant. Grav. 26 (2009) 215006 [arXiv:0905.1355] [INSPIRE].
E. Mottola, New horizons in gravity: the trace anomaly, dark energy and condensate stars, Acta Phys. Polon. B 41 (2010) 2031 [arXiv:1008.5006] [INSPIRE].
J.P.S. Lemos, F.S.N. Lobo and S. Quinet de Oliveira, Morris-Thorne wormholes with a cosmological constant, Phys. Rev. D 68 (2003) 064004 [gr-qc/0302049] [INSPIRE].
S.V. Sushkov, Wormholes supported by a phantom energy, Phys. Rev. D 71 (2005) 043520 [gr-qc/0502084] [INSPIRE].
F.S.N. Lobo, Phantom energy traversable wormholes, Phys. Rev. D 71 (2005) 084011 [gr-qc/0502099] [INSPIRE].
E.F. Eiroa, Stability of thin-shell wormholes with spherical symmetry, Phys. Rev. D 78 (2008) 024018 [arXiv:0805.1403] [INSPIRE].
F.S.N. Lobo, Surface stresses on a thin shell surrounding a traversable wormhole, Class. Quant. Grav. 21 (2004) 4811 [gr-qc/0409018] [INSPIRE].
F.S.N. Lobo, Energy conditions, traversable wormholes and dust shells, Gen. Rel. Grav. 37 (2005) 2023 [gr-qc/0410087] [INSPIRE].
J.P.S. Lemos and F.S.N. Lobo, Plane symmetric traversable wormholes in an anti-de Sitter background, Phys. Rev. D 69 (2004) 104007 [gr-qc/0402099] [INSPIRE].
F.S.N. Lobo, Exotic solutions in general relativity: traversable wormholes and ‘warp drive’ spacetimes, arXiv:0710.4474 [INSPIRE].
P.R. Brady, J. Louko and E. Poisson, Stability of a shell around a black hole, Phys. Rev. D 44 (1991) 1891 [INSPIRE].
M. Ishak and K. Lake, Stability of transparent spherically symmetric thin shells and wormholes, Phys. Rev. D 65 (2002) 044011 [gr-qc/0108058] [INSPIRE].
E.F. Eiroa and G.E. Romero, Linearized stability of charged thin shell wormholes, Gen. Rel. Grav. 36 (2004) 651 [gr-qc/0303093] [INSPIRE].
F.S.N. Lobo and P. Crawford, Stability analysis of dynamic thin shells, Class. Quant. Grav. 22 (2005) 4869 [gr-qc/0507063] [INSPIRE].
F.S.N. Lobo, Stability of phantom wormholes, Phys. Rev. D 71 (2005) 124022 [gr-qc/0506001] [INSPIRE].
E.F. Eiroa and C. Simeone, Cylindrical thin shell wormholes, Phys. Rev. D 70 (2004) 044008 [gr-qc/0404050] [INSPIRE].
E.F. Eiroa and C. Simeone, Thin-shell wormholes in dilaton gravity, Phys. Rev. D 71 (2005) 127501 [gr-qc/0502073] [INSPIRE].
M. Thibeault, C. Simeone and E.F. Eiroa, Thin-shell wormholes in Einstein-Maxwell theory with a Gauss-Bonnet term, Gen. Rel. Grav. 38 (2006) 1593 [gr-qc/0512029] [INSPIRE].
F. Rahaman, M. Kalam and S. Chakraborty, Thin shell wormholes in higher dimensional Einstein-Maxwell theory, Gen. Rel. Grav. 38 (2006) 1687 [gr-qc/0607061] [INSPIRE].
C. Bejarano, E.F. Eiroa and C. Simeone, Thin-shell wormholes associated with global cosmic strings, Phys. Rev. D 75 (2007) 027501 [gr-qc/0610123] [INSPIRE].
F. Rahaman, M. Kalam and S. Chakraborti, Thin shell wormhole in heterotic string theory, Int. J. Mod. Phys. D 16 (2007) 1669 [gr-qc/0611134] [INSPIRE].
E.F. Eiroa and C. Simeone, Stability of Chaplygin gas thin-shell wormholes, Phys. Rev. D 76 (2007) 024021 [arXiv:0704.1136] [INSPIRE].
F. Rahaman, M. Kalam, K.A. Rahman and S. Chakraborti, A theoretical construction of thin shell wormhole from tidal charged black hole, Gen. Rel. Grav. 39 (2007) 945 [gr-qc/0703143] [INSPIRE].
M.G. Richarte and C. Simeone, Traversable wormholes in a string cloud, Int. J. Mod. Phys. D 17 (2008) 1179 [arXiv:0711.2297] [INSPIRE].
E. Poisson and M. Visser, Thin shell wormholes: linearization stability, Phys. Rev. D 52 (1995) 7318 [gr-qc/9506083] [INSPIRE].
F.S.N. Lobo and P. Crawford, Linearized stability analysis of thin shell wormholes with a cosmological constant, Class. Quant. Grav. 21 (2004) 391 [gr-qc/0311002] [INSPIRE].
D. Horvat, S. Ilijic and A. Marunovic, Radial stability analysis of the continuous pressure gravastar, Class. Quant. Grav. 28 (2011) 195008 [arXiv:1104.3537] [INSPIRE].
S.S. Yazadjiev and D.D. Doneva, Possible dark energy imprints in gravitational wave spectrum of mixed neutron-dark-energy stars, JCAP 03 (2012) 037 [arXiv:1112.4375] [INSPIRE].
E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
A. Smailagic and E. Spallucci, Feynman path integral on the noncommutative plane, J. Phys. A 36 (2003) L467 [hep-th/0307217] [INSPIRE].
P. Nicolini, A. Smailagic and E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole, Phys. Lett. B 632 (2006) 547 [gr-qc/0510112] [INSPIRE].
E. Di Grezia, G. Esposito and G. Miele, Black hole evaporation in a spherically symmetric non-commutative space-time, J. Phys. A 41 (2008) 164063 [arXiv:0707.3318] [INSPIRE].
R. Casadio and P. Nicolini, The decay-time of non-commutative micro-black holes, JHEP 11 (2008) 072 [arXiv:0809.2471] [INSPIRE].
P. Nicolini, Noncommutative black holes, the final appeal to quantum gravity: a review, Int. J. Mod. Phys. A 24 (2009) 1229 [arXiv:0807.1939] [INSPIRE].
E. Spallucci, A. Smailagic and P. Nicolini, Non-commutative geometry inspired higher-dimensional charged black holes, Phys. Lett. B 670 (2009) 449 [arXiv:0801.3519] [INSPIRE].
S. Ansoldi, P. Nicolini, A. Smailagic and E. Spallucci, Noncommutative geometry inspired charged black holes, Phys. Lett. B 645 (2007) 261 [gr-qc/0612035] [INSPIRE].
P. Nicolini, A model of radiating black hole in noncommutative geometry, J. Phys. A 38 (2005) L631 [hep-th/0507266] [INSPIRE].
R. Garattini and F.S.N. Lobo, Self sustained phantom wormholes in semi-classical gravity, Class. Quant. Grav. 24 (2007) 2401 [gr-qc/0701020] [INSPIRE].
R. Garattini and F.S.N. Lobo, Self-sustained wormholes in modified dispersion relations, Phys. Rev. D 85 (2012) 024043 [arXiv:1111.5729] [INSPIRE].
R. Garattini and F.S.N. Lobo, Self-sustained traversable wormholes in noncommutative geometry, Phys. Lett. B 671 (2009) 146 [arXiv:0811.0919] [INSPIRE].
K. Lanczos, Flächenhafte Verteiliung der Materie in der Einsteinschen Gravitationstheorie, Ann. Phys. (Leipzig) 74 (1924) 518.
G. Darmois, Les équations de la gravitation einsteinienne, in Mémorial des sciences mathématiques, Fascicule XXV, Gauthier-Villars, Paris France (1927).
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44 (1966) 1 [Erratum ibid. B 48 (1967) 463] [INSPIRE].
A. Papapetrou and A. Hamoui, Simple material layers in general relativity, Ann. Inst. Henri Poincaré 9 (1968) 179.
N.M. Garcia, F.S.N. Lobo and M. Visser, Generic spherically symmetric dynamic thin-shell traversable wormholes in standard general relativity, Phys. Rev. D 86 (2012) 044026 [arXiv:1112.2057] [INSPIRE].
P. Martin Moruno, N. Montelongo Garcia, F.S.N. Lobo and M. Visser, Generic thin-shell gravastars, JCAP 03 (2012) 034 [arXiv:1112.5253] [INSPIRE].
K.A. Bronnikov, R.A. Konoplya and A. Zhidenko, Instabilities of wormholes and regular black holes supported by a phantom scalar field, Phys. Rev. D 86 (2012) 024028 [arXiv:1205.2224] [INSPIRE].
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Lobo, F.S.N., Garattini, R. Linearized stability analysis of gravastars in noncommutative geometry. J. High Energ. Phys. 2013, 65 (2013). https://doi.org/10.1007/JHEP12(2013)065
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DOI: https://doi.org/10.1007/JHEP12(2013)065