Canadian Journal of Physics Dark energy stars: Stable configurations Journal: Canadian Journal of Physics ManuscriptFor ID cjp-2017-0526 Review Only Manuscript Type: Article Date Submitted by the Author: 19-Jul-2017 Complete List of Authors: Bhar, Piyali; Jadavpur University, Mathematics Manna, Tuhina; St. Xavier's College, Commerce Rahaman, Farook; Jadavpur University, Mathematics Banerjee, Ayan; Jadavpur Univ, Mathematics Dark energy, Stellar equilibrium, Exact solution, Specific mass function, Keyword: junction conditions Is the invited manuscript for consideration in a Special N/A Issue? : https://mc06.manuscriptcentral.com/cjp-pubs Page 1 of 10 Canadian Journal of Physics Dark energy stars: Stable configurations Piyali Bhar∗ Department of Mathematics, Government General Degree College, Singur, Hooghly 712 409, West Bengal, India Tuhina Mannay Department of Commerce (Evening), St. Xaviers College, 30 Mother Teresa Sarani, Kolkata 700016, West Bengal, India Farook Rahamanz and Ayan Banerjeex Department of Mathematics, Jadavpur University, Kolkata-700032, India (Dated: April 12, 2018) In present paper a spherically symmetric stellar configuration has been analyzed by assuming the matter distribution of the stellar configuration is anisotropic in nature and compared with the realistic objects, namely, the low mass X-ray binaries (LMXBs) and X-ray pulsars. The analytic solution has been obtained by utilizing the dark energy equation of state for the interior solution corresponding to the Schwarzschild exterior vacuum solution at the junction interface. Several phys- ical properties like energy conditions, stability, mass-radius ratio, and surface redshift are described through mathematical calculations as well as graphical plots. It is found that obtained mass-radius ration of the compact stars candidates like 4U 1820-30, PSR J 1614-2230, Vela X-1 and Cen X- 3are very much consistent with the observed data by Gangopadhyay et al. (Mon. Not. R. Astron. Soc. 431, 3216 (2013)).For So our Review proposed model would Only be useful in the investigation of the possible clustering of dark energy. PACS numbers: I. INTRODUCTION and dark matter. There is hardly any other topic in general relativity In 2005 physicist George Chaplin proposed that, grav- which is as extensively researched as black holes. Since itational collapse of objects with masses greater than a Oppenheimer and Snyder [4] first attempt at explaining few solar masses should lead to the formation of a com- the state of gravitational collapse of a black hole, there pact object called dark energy star whose surface corre- have been various observational data favouring the exis- sponds to a quantum critical surface for space-time, and tence of event horizon, but nonesoever proving it [5]. This whose interior differs from ordinary space-time only in in turn has lead to the developement of a plura of fasci- having a much larger vacuum energy [1]. He claimed nating alternative ideas. One such popular model is that that the current picture of gravitational collapse as ex- of a gravastar or gravitationally vacuum star as proposed plained in terms of event horizon is physically inconsis- by Mazur and Mottola [6]. Its a compact object having tent since it conflicts with quantum mechanics [2]. The an interior de Sitter condensate defined by the equation theory states that infalling matter gets converted to dark of state p = −ρ , matched to a shell of finite thickness energy as it falls through the event horizon causing the with an equation of state p = ρ , which is again matched space inside the event horizon to have a high value of cos- to an exterior Schwarzschild vacuum solution. This star mological constant and hence a high negative pressure to has no singularity at the origin and no event horizon since exert against gravity. This high negative pressure may the thick shell surface with a radius slightly greater than counter the mass the star gains thus avoiding a singu- the Schwarzschild radius, replaces both the de Sitter and larity. Thus there is a sort of phase transition occurring the Schwarzschild horizons. The charged and uncharged in the phase of space at the event horizon [2, 3]. In fact model of gravastar was obtained in our earlier works [7]. Dark energy star may account for high energy cosmic ray A modified version of the gravastar was studied by Cat- sources and positron sources since infalling masses decays toen et al. [8] using a continuous pressure profile without into lighter masses at the event horizon accelerating pro- thin shells. It strongly suggested an anisotropic pres- ton decay. This proposal may provide a new perspective sure model. Later an alternative model termed as Born- on spectacular astrophysical phenomena including super- Infeld phantom gravastar was constructed replacing the novae explosions, gamma ray bursts, positron emission, de-Sitter spacetime by an interior spacetime governed by the Chaplygin gas equation of state [9]. In this paper the authors have investigated a generalized case in which the equation of state is governed by the equation of state ∗Electronic address: [email protected] yElectronic address: [email protected] p = !ρ matched to an exterior vacuum solution. The zElectronic address: [email protected] proposed stellar model consists of five zones : an inte- xElectronic address: [email protected] rior core, a thin shell between the core and the interior https://mc06.manuscriptcentral.com/cjp-pubs Canadian Journal of Physics Page 2 of 10 2 spacetime, the interior spacetime and a thin shell which the exterior vacuum region is obtained [15]. Yadav et acts as a junction interface between the interior and the al. [16] have given a dark energy model with a variable exterior Schwarzschild spacetime. This kind of compact equation of state parameter. Inspired by the prior men- object which generalizes a gravatus model by using equa- tioned works of Cattoen et al. [8] and Ruderman(1972) tion of state p = !ρ with ! < −1=3 is called a dark [20] we have taken the pressure inside the fluid sphere in energy gravastar or simply a dark energy star , as re- our model to be anisotropic. For an anisotropy distribu- ferred by Chapline. This terminology is motivated by the tion, the pressure inside the fluid sphere is decomposed fact that dark energy is still unknown component of our into two orthogonal components: radial pressure pr and Universe has relativistic negative pressure. The 1998 ob- transverse pressure pt where obviously pr =6 pt. Stud- servations of Type la Supernova [10] confirms that dark ies on X-ray pulsars, Her-x-1, X-ray buster 4U 1820-30, energy is responsible for the phase of cosmic accelera- millisecond pulsar SAXJ1804.4-3658 etc. suggests that tion. Numerous other recent observations of Cosmic Mi- nuclear matter tends to become anisotropic in nature at crowave Background(CMB) anisotropies and Large Scale very high densities ( 1015gm=cc.) [21, 22]. Anisotropy Structure(LSS) [11] reconfirm this characteristics of small may occur due to any of the following reasons : exis- redshift evolution of our Universe. The simplest explana- tence of solid core, a type 3A superfluid [23], phase transi- tion of dark energy is the cosmological constant Λ which tion [24], pion condensation [25], rotation, magnetic field, is usually interpreted physically as a vacuum energy, with mixture of two fluid, existence of external field etc. p = −ρ. Another possible way to explain the dark energy We organised the paper as follows : In Sec. II. deals is by invoking an equation of state, p = !ρ with ! < 0 , with the basic field equations and their solutions, then where p is the spatially homogeneous pressure and ρ the the junction conditions have been discussed in Sec. III. energy density of the dark energy,For instead Review of the constant In Only Sec. IV. the physical properties with the stability con- vacuum energy density. The models of dark energy with ditions have been studied. Finally, in Sec. V. we discuss ! > −1 mainly comprises of quintessence , k-essence and some specific comments regarding the results obtained in chaplygin gas among others. the study. This idea of dark energy star theorizes that the sur- face of a compact object is a quantum critical shell with II. INTERIOR SPACE-TIME AND THE FIELD some thickness z [12]. When ordinary elementaryq par- EQUATIONS M0 ticles which have energy beyond Q0 = 100MeV , M We consider a static spherically symmetric space-time where M is the solar mass, enter this quantum critical 0 given by the following line element: region they decay into substituent products and radiation [ Z ] that gets directed backwards from the surface of dark en- 1 dr2 ds2 = −exp −2 g(~r)dr~ dt2 + + r2dΩ2; (1) ergy star perpendicular to the critical surface. However − 2m r 1 r for particles with energy < Q0 will pass through the crit- ical surface and follow diverging geodesics in the interior where r denotes the radial coordinate. Here g(r) denote of a dark energy star. Now compact objects at the cen- an arbitrary function of the radial coordinate represent- tre of galaxies contains quarks and gluons inside nucle- ing the locally measured gravitational acceleration, which ons whose energies exceed this value [13]. According to according to general convention is assumed to be positive Georgi-Glashow grand unified model nucleons can decay in case of an inward directed gravitational attraction, and by a process in which a quark decays into a positron and negative in the case an outward directed gravitational re- two antiquarks. Interestingly an excess of positrons have pulsion. Also the function m(r) denotes the gravitational been detected in the centre of galaxies which may be the mass contained within a sphere of radius r. best evidence for dark energy stars. In addition to that, We proceed now to describe the matter distribution of primordial dark energy stars can form out of fluctuations the spherical body which is anisotropic in nature, and of spacetime analogous to a quantum critical instability the energy-momentum tensor is characterized by the fol- [2].