Sumita Banerjee

Bio: Sumita Banerjee is an academic researcher from Budge Budge Institute of Technology. The author has contributed to research in topics: Wormhole & String theory. The author has an hindex of 6, co-authored 8 publications receiving 120 citations.

A charged anisotropic well-behaved Adler–Finch–Skea solution satisfying Karmarkar condition

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.

A charged anisotropic well-behaved Adler-Finch-Skea solution Satisfying Karmarkar Condition

Abstract: In the present article, we discover a new well-behaved charged anisotropic solution of Einstein-Maxwell's field equations. We ansatz the metric potential $g_{00}$ of the form given by Maurya el al. (arXiv:1607.05582v1) with $n=2$. In their article it is mentioned that for $n=2$ the solution is not well-behaved for neutral configuration as the speed of sound is non-decreasing radially outward. However, the solution can represent a physically possible configuration with the inclusion of some net electric charged 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 charged the solution leads to a very stiff equation of state (EoS) with the velocity of sound at the center $v_{r0}^2=0.819, ~v_{t0}^2=0.923$ and the compactness parameter $u=0.823$ is closed to the Buchdahl limit 0.889. This stiff EoS support a compact star configuration of mass $5.418M_\odot$ and radius of $10.1 km$.

Anisotropic stellar models admitting conformal motion

Abstract: We address the problem of finding static and spherically symmetric anisotropic compact stars in general relativity that admit conformal motions. The study is framed in the language of f(R) gravity theory in order to expose opportunity for further study in the more general theory. Exact solutions of compact stars are found under the assumption that spherically symmetric spacetimes admit conformal motion with anisotropic matter distribution in nature. In this work, two cases have been studied for the existence of such solutions: first, we consider the model given by $f(R)=R$ and then $f(R)=aR+b$ . Finally, specific characteristics and physical properties have been explored analytically along with graphical representations for conformally symmetric compact stars in f(R) gravity.

Singularity Free Stars in (2+1) Dimensions

Abstract: We present some new types of non-singular model for anisotropic stars with constant Λ and variable Λ based on the Krori and Barua (KB) metric in (2+1) dimensions. The solutions obtained here satisfy all the regularity conditions and its simple analytical form helps us to study the various physical properties of the configuration.

Study of gravastars in Finslerian geometry

Abstract: In this present article, we have proposed gravastar under Finslerian spacetime geometry, which can be claimed as an alternative to Finslerian black hole. This study can be considered as a sequel of our previous works based on the Finslerian geometry where we have constructed some phenomenological models for compact stars and wormholes. The concept of gravastar was first proposed by Mazur and Mottola (2001. arXiv:gr-qc/0109035; Proc Natl Acad Sci USA 101:9545, 2004) which consist of three regions in its configuration namely (I) the interior core, (II) the intermediate thin shell, and (III) the vacuum exterior. These three regions can be described by three different equation of state. Here we solve gravastar under the framework of Finsler geometry and obtain a set of exact and physically acceptable solutions for three different regions. We have also studied various physical parameters which are fulfilled by the physical requirement for validity of the present study on gravastar within the Finslerian spacetime geometry.

Anisotropic fluid spheres of embedding class one using Karmarkar condition

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 $$4.3587\le \Gamma _{0} \le 5.6462$$ .

Anisotropic relativistic fluid spheres: an embedding class I approach

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.

Anisotropic fluid spheres of embedding class one using Karmarkar condition

Abstract: We obtain a new anisotropic solution for spherically symmetric spacetimes by analysing of 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 masses and radii of fluid spheres for LMC X-4 and EXO 1785-248 by using observational data sets values. The obtained masses and radii show that our anisotropic solution can represent fluid spheres to a very good degree of accuracy.

Analytical study of anisotropic compact star models

Abstract: A simple classification is given of the anisotropic relativistic star models, resembling the one of charged isotropic solutions. On the ground of this database, and taking into account the conditions for physically realistic star models, a method is proposed for generating all such solutions. It is based on the energy density and the radial pressure as seeding functions. Numerous relations between the realistic conditions are found and the need for a graphic proof is reduced just to one pair of inequalities. This general formalism is illustrated with an example of a class of solutions with linear equation of state and simple energy density. It is found that the solutions depend on three free constants and concrete examples are given. Some other popular models are studied with the same method.

A conformally flat realistic anisotropic model for a compact star

Abstract: A physically realistic stellar model with a simple expression for the energy density and conformally flat interior is found. The relations between the different physical conditions are used without graphic proofs. It may represnet a real pulsar.