A charged anisotropic well-behaved Adler–Finch–Skea solution satisfying Karmarkar condition
02 Feb 2017-International Journal of Modern Physics D (World Scientific Publishing Company)-Vol. 26, Iss: 08, pp 1750078
TL;DR: In this paper, a new well-behaved charged anisotropic solution of the field equations was discovered, which can represent a physically possible configuration with the inclusion of some net electric charge, i.e. the solution can become a wellbehaved solution with decreasing sound speed radially outward.
Abstract: In the present paper, we discover a new well-behaved charged anisotropic solution of Einstein–Maxwell’s field equations. We ansatz the metric potential g00 of the form given by Maurya el al. (Eur. Phys. J. C 76(2) (2016) 693) with n = 2. In their paper, it is mentioned that for n = 2, the solution is not well-behaved for neutral configuration as the speed of sound is nondecreasing radially outward. However, the solution can represent a physically possible configuration with the inclusion of some net electric charge, i.e. the solution can become a well-behaved solution with decreasing sound speed radially outward for a charged configuration. Due to the inclusion of electric charge, the solution leads to a very stiff equation-of-state (EoS) with the velocity of sound at the center vr02 = 0.819, vt02 = 0.923 and the compactness parameter u = 0.823 is close to the Buchdahl limit 0.889. This stiff EoS support a compact star configuration of mass 5.418M⊙ and radius of 10.1km.
Citations
More filters
TL;DR: In this article, a new anisotropic solution for spherically symmetric spacetimes was obtained by analyzing the Karmarkar embedding condition, which can be used to construct realistic static fluid spheres.
Abstract: We obtain a new anisotropic solution for spherically symmetric spacetimes by analyzing the Karmarkar embedding condition. For this purpose we construct a suitable form of one of the gravitational potentials to obtain a closed form solution. This form of the remaining gravitational potential allows us to solve the embedding equation and integrate the field equations. The resulting new anisotropic solution is well behaved, which can be utilized to construct realistic static fluid spheres. Also we estimated the masses and radii of fluid spheres for LMC X-4, EXO 1785-248, PSR J1903+327 and 4U 1820-30 by using observational data set values. The masses and radii obtained show that our anisotropic solution can represent fluid spheres to a very good degree of accuracy. The physical validity of the solution depends on the parameter values of a, b and c. The solution is well behaved for the wide range of parameters values $$0.00393\le a \le 0.0055$$
, $$0.0002 \le b \le 0.0025$$
and $$0.0107 \le c \le 0.0155$$
. The range of corresponding physical parameters for the different compact stars are $$0.3266\le v_{r0} \le 0.3708$$
, $$0.1583\le v_{t0} \le 0.2558$$
, $$0.3256\le z_{s} \le 0.4450$$
and $$4.3587\le \Gamma _{0} \le 5.6462$$
.
99 citations
TL;DR: In this article, a well-behaved solution to Einstein's field equations describing anisotropic matter distribution was proposed in the embedding class one spacetime framework using Karmarkar's condition.
Abstract: In this work, we present a new class of analytic and well-behaved solution to Einstein’s field equations describing anisotropic matter distribution. It’s achieved in the embedding class one spacetime framework using Karmarkar’s condition. We perform our analysis by proposing a new metric potential $$g_{rr}$$ which yields us a physically viable performance of all physical variables. The obtained model is representing the physical features of the solution in detail, analytically as well as graphically for strange star candidate SAX J1808.4-3658 ($$Mass=0.9 ~M_{\odot }$$, $$radius=7.951$$ km), with different values of parameter n ranging from 0.5 to 3.4. Our suggested solution is free from physical and geometric singularities, satisfies causality condition, Abreu’s criterion and relativistic adiabatic index $$\varGamma $$, and exhibits well-behaved nature, as well as, all energy conditions and equilibrium condition are well-defined, which implies that our model is physically acceptable. The physical sensitivity of the moment of inertia (I) obtained from the solutions is confirmed by the Bejger−Haensel concept, which could provide a precise tool to the matching rigidity of the state equation due to different values of n viz., $$n=0.5, 1.08, 1.66, 2.24, 2.82$$ and 3.4.
88 citations
TL;DR: In this article, the existence of compact spherical systems representing anisotropic matter distributions within the scenario of alternative theories of gravitation, specifically f(R, T) gravity theory, is studied.
Abstract: The main aim of this work is devoted to studying the existence of compact spherical systems representing anisotropic matter distributions within the scenario of alternative theories of gravitation, specifically f(R, T) gravity theory. Besides, a noteworthy and achievable choice on the formulation of f(R, T) gravity is made. To provide the complete set of field equations for the anisotropic matter distribution, it is considered that the functional form of f(R, T) as $$f(R, T)=R+2\chi T$$, where R and T correspond to scalar curvature and trace of the stress–energy tensor, respectively. Following the embedding class one approach employing the Eisland condition to get a full space–time portrayal interior the astrophysical structure. When the space–time geometry is identified, we construct a suitable anisotropic model by using a new gravitational potential $$g_{rr}$$ which often yields physically motivated solutions that describe the anisotropic matter distribution interior the astrophysical system. The physical availability of the obtained model, represents the physical characteristics of the solution is affirmed by performing several physical tests. It merits referencing that with the help of the observed mass values for six compact stars, we have predicted the exact radii for different values of $$\chi $$-coupling parameter. From this one can convince that the solution predicted the radii in good agreement with the observed values. Since the radius of MSP J0740+6620, the most massive neutron star observed yet is still unknown, we have predicted its radii for different values of $$\chi $$-coupling parameter. These predicted radii exhibit a monotonic diminishing nature as the parameter $$\chi $$ going from $$-1$$ to 1 gradually. The M–R curve generated from our solution can accommodate a variety of compact stars from the less massive (Her X-1) to super massive (MSP J0740+6620). So the present study uncovers that the modified f(R, T) gravity is an appropriate theory to clarify massive astrophysical systems, in any case, for $$\chi =0.0$$ the standard consequences of the general relativity are recovered.
46 citations
TL;DR: In this paper, a non-singular solution satisfying the Karmarkar condition is presented, which yields finite values of metric potentials, density, pressure, redshift, etc.
Abstract: A new solution satisfying the Karmarkar condition is presented here. We were first to have discovered a hypergeometric function metric potential representing embedding class I spacetime. This new solution yields finite values of metric potentials, density, pressure, redshift, etc. and hence a non-singular solution. The solution is well behaved with respect to the parameter $$n=12$$
to $$n=24$$
corresponding to a stable configuration of mass $$2.01M_\odot $$
and radius 9.1 km. The internal properties of the solution are very different for $$n=12$$
to $$n=24$$
; however, the total mass and radius is independent of the parameter n. The energy conditions are also holds good by the solution which thus can represent a physically viable matter distribution. The equilibrium condition and stability are also discussed through TOV-equation, cracking method and $$\Gamma >4/3$$
. The static stability criterion is also well satisfied and the turning point corresponds to $$4.46M_\odot $$
for a radius of 9.1 km.
46 citations
TL;DR: In this paper, a new mass function was proposed to obtain an exact analytic solution of the Einstein field equations of a compact star within embedding class one spacetime i.e., four dimensional spacetime embedded in five dimensional pseudo Euclidean space.
45 citations
References
More filters
TL;DR: In this article, the authors review and discuss possible causes for the appearance of local anisotropy (principal stresses unequal) in self-gravitating systems and present its main consequences.
907 citations
TL;DR: In the two years since the review of Hewish (1970) the number of observed pulsars has increased modestly from 50 to 58 (November 1971), accompanied by a plethora of over three hundred theoretical papers.
Abstract: As is so often the case either the poet has an insight so far denied to the rest of us or his theory of pulsars is quite muddled. A great deal now seems under stood about these delightful surprising objects-except for details of how they pulse. But there are already so many clues from pulsar observations that one cannot be optimistic that continued observations of the periodic radio signals will offer crucial new evidence. In the two years since the review of Hewish (1970) the number of observed pulsars has increased modestly from 50 to 58 (November 1971), accompanied by a plethora of over three hundred theoretical papers. There have been.no novel revelations: The rotating neutron star still has no serious competitor as the pulsar clock; its spin is almost certainly coupled to its environment by a huge magnetic field for which a consensus of estimates gives a value at the stellar surface of order 1012 G; the observed variations in radio in tensity (and also in optical, X-ray, and ')I-ray fluxes for the pulsar in the Crab nebula) are usually assumed to be associated with nonalignment of the stellar dipole magnetic field and spin axis. Some kind of coherent emission process is necessary to account for the enormous radio intensities of pulsars. All of these entrenched ideas have become even more established. There have been activity and progress in the following areas: (1) The rich variety of pulse shapes, polarizations, and intensity variations have been further confirmed and explored. In a given pulsar there can be marked correlation over many pulses as well as remarkable differences. The main problem now is deciding which among the numerous data are fundamental and how many of them a tentative theory must fit. (2) An enormous amount of detail about the Crab pulsar (NP 0532) radia tion is now available: radio, optical, X-ray and ')I-ray pulses, their structure, and correlations between pulses in different regimes. Changes in the surrounding nebula have been described that may be associated with pulsar variations. Very precise timing measurements before and after period discontinuities ("glitches")
781 citations
TL;DR: In this article, the authors explore the influence that density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity and show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions.
Abstract: Using the concept of cracking we explore the influence that density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity. This concept, conceived to describe the behavior of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of self-gravitating compact objects. We show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions. In fact, it is found that these regions could occur when, at a particular point within the distribution, the tangential speed of sound is greater than the radial one.
488 citations
TL;DR: In this article, the role of local anisotropy and radiation in the onset of dynamical instabilities in free-streaming regime was investigated. But the role played by local anotropy was not investigated.
Abstract: We study the role played by local anisotropy and radiation (in the free-streaming regime) in the onset of dynamical instabilities. In the case of anisotropy we find that, for Newtonian and post-Newtonian approximations, the relevant quantity is the anisotropy of the unperturbed fluid, and that small anisotropies may, in principle, drastically change the stability of the system. The influence of the free-streaming radiation upon stability appears to be qualitatively of the same type as that of radiative diffusion. Some speculations and prospective applications to astrophysical scenarios are presented
420 citations
TL;DR: In this article, the authors explore the influence of density fluctuations and local anisotropy on the stability of local and non-local anisotropic matter configurations in general relativity and show that potentially unstable regions within a configuration can be identified as a function of the difference of propagations of sound along tangential and radial directions.
Abstract: Using the the concept of cracking we explore the influence of density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity. This concept, conceived to describe the behaviour of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of selfgravitating compact objects. We show that potentially unstable regions within a configuration can be identify as a function of the difference of propagations of sound along tangential and radial directions. In fact, it is found that these regions could occur when, at particular point within the distribution, the tangential speed of sound is greater than radial one.
411 citations