arXiv subjects

Saibal Ray

Publications and source records attributed to Saibal Ray.

At least 73 records · Page 4Linked to original sources

arXiv2020

Study of gravastars under $f(\mathbb{T})$ gravity

In the present paper we propose a stellar model under the $f(\mathbb{T})$ gravity following the conjecture of Mazur-Mottola~[Report number: LA-UR-01-5067 (2001); Proc. Natl. Acad. Sci. USA 101 (2004) 9545] known in literature as {\it gravastar}, a viable alternative to the black hole. This gravastar has three different regions, viz., (A) Interior core region, (B) Intermediate thin shell, and (C) Exterior spherical region. It is assumed that in the interior region the fluid pressure is equal to a negative matter-energy density providing a constant repulsive force over the spherical thin shell. This shell at the intermediate region is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zeldovich's conjecture of stiff fluid~[Zeldovich, Mon. Not. R. Astron. Soc. 160 (1972) 1], does nullify the repulsive force exerted by the interior core region for a stable configuration. On the other hand, the exterior spherical region can be described by the exterior Schwarzschild-de Sitter solution. With all these specifications we have found out a set of exact and singularity-free solutions of the gravastar which presents several physically interesting as well as valid features within the framework of alternative gravity.

gr-qc↗

arXiv2020

Gravastars in $f(\mathbb{T},\mathcal{T})$ gravity

We propose a stellar model under the $f(\mathbb{T},\mathcal{T})$ gravity following Mazur-Mottola's conjecture [Mazur (2001), Mazur (2004)] known as gravastar which is generally believed as a viable alternative to black hole. The gravastar consists of three regions, viz., (I) Interior region, (II) Intermediate shell region, and (III) Exterior region. The pressure within the interior core region is assumed to be equal to the constant negative matter-energy density which provides a constant repulsive force over the thin shell region. The shell is assumed to be made up of fluid of ultrarelativistic plasma and following the Zel'dovich's conjecture of stiff fluid [Zeldovich (1972)] it is also assumed that the pressure which is directly proportional to the matter-energy density according to Zel'dovich's conjecture, does cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum and it can be described by the Schwarzschild solution. Under all these specifications we find out a set of exact and singularity-free solutions of the gravastar presenting several physically valid features within the framework of alternative gravity, namely $f(\mathbb{T},\mathcal{T})$ gravity [Harko (2014)], where the part of the gravitational Lagrangian in the corresponding action is taken as an arbitrary function of torsion scalar $\mathbb{T}$ and the trace of the energy-momentum tensor $\mathcal{T}$.

gr-qc↗

arXiv2019

Inflation in anisotropic brane universe using tachyon field

Cosmological solution to the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I geometry and perfect fluid as matter sources has been considered. The matter on the brane is described by a tachyonic field. The solution admits inflationary era and at a later epoch the anisotropy of the universe washes out. We obtain two classes of cosmological scenario, in the first case universe evolves from singularity and in the second case universe expands without singularity.

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arXiv2019

Neutron star under homotopy perturbation method

We obtain a mass function solving the Tolman-Oppenheimer-Volkoff (TOV) equation for isotropic and spherically symmetric system via homotopy perturbation method (HPM). Using the mass function we construct a stellar model which can be determined from the equation of state (EOS) parameter ($ω$) and a model parameter ($n$). With the help of Einstein field equations we develop three solutions which can describe different properties and the core-crust structure of neutron star (NS). Solution I is valid for NS having the inner and outer radius near the surface of the star. The star is physical up to the inner radius whereas negative density occurs and the energy conditions are violated in the upper region from the inner to outer radius. Solution II represents NS with high gravitational redshift as well as compactification factor. All the features of NS can be given by solution III which involves only the EOS parameter. Our model predicts maximum mass for a NS with the central density $5.5\times10^{15}~g/cm^{3}$ and surface redshift 0.69 is to be $2.01~M_\odot$ for the EOS parameter $ω=0.73$. The predicted range for the surface redshift is $0.57<Z_s<1.95$ for the allowed ranges $8.4<n<10.9$ and $1/3<ω<1$ in the presented NS model.

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arXiv2019

Relativistic strange stars in Tolman-Kuchowicz spacetime

In this article we propose a relativistic model of a static spherically symmetric anisotropic strange star with the help of Tolman-Kuchowicz (TK) metric potentials [Tolman, Phys. Rev. {\bf55}, 364 (1939) and Kuchowicz, Acta Phys. Pol. {\bf33}, 541 (1968)]. The form of the potentials are $λ(r)=\ln(1+ar^2+br^4)$ and $ν(r)=Br^2+2\ln C$ where $a$, $b$, $B$ and $C$ are constants which we have to evaluate using boundary conditions. We also consider the simplest form of the phenomenological MIT bag equation of state (EOS) to represent the strange quark matter (SQM) distribution inside the stellar system. Here, the radial pressure $p_r$ relates with the density profile $ρ$ as follows, $p_r(r)=\frac{1}{3}[ρ(r)-4B_g]$, where $B_g$ is the Bag constant. To check the physical acceptability and stability of the stellar system based on the obtained solutions, we have performed various physical tests. It is shown that the model satisfies all the stability criteria, including nonsingular nature of the density and pressure, implies stable nature. Here, the Bag constant for different strange star candidates are found to be $(68-70)$~MeV/{fm}$^3$ which satisfies all the acceptability criteria and remains in the experimental range.

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arXiv2019

Generating Realistic Sequences of Customer-level Transactions for Retail Datasets

In order to better engage with customers, retailers rely on extensive customer and product databases which allows them to better understand customer behaviour and purchasing patterns. This has long been a challenging task as customer modelling is a multi-faceted, noisy and time-dependent problem. The most common way to tackle this problem is indirectly through task-specific supervised learning prediction problems, with relatively little literature on modelling a customer by directly simulating their future transactions. In this paper we propose a method for generating realistic sequences of baskets that a given customer is likely to purchase over a period of time. Customer embedding representations are learned using a Recurrent Neural Network (RNN) which takes into account the entire sequence of transaction data. Given the customer state at a specific point in time, a Generative Adversarial Network (GAN) is trained to generate a plausible basket of products for the following week. The newly generated basket is then fed back into the RNN to update the customer's state. The GAN is thus used in tandem with the RNN module in a pipeline alternating between basket generation and customer state updating steps. This allows for sampling over a distribution of a customer's future sequence of baskets, which then can be used to gain insight into how to service the customer more effectively. The methodology is empirically shown to produce baskets that appear similar to real baskets and enjoy many common properties, including frequencies of different product types, brands, and prices. Furthermore, the generated data is able to replicate most of the strongest sequential patterns that exist between product types in the real data.

cs.LG↗

arXiv2019

Study on charged strange stars in $f\left(R,\mathcal{T}\right)$ gravity

We investigate effects of the modified $f(R, \mathcal{T})$ gravity on the charged strange quark stars with the standard choice of $f(R, \mathcal{T})=R+2χ\mathcal{T}$. Those types of stars are supposed to be made of strange quark matter (SQM) whose distribution is governed by the phenomenological MIT bag EOS as $p=\frac{1}{3}(ρ-4B)$, where $B$ is the bag constant, while the form of charge distribution is chosen to be $q\left(r\right)=Q\left(r/R\right)^3=αr^3$ with $α$ as a constant. We derive the values of the unknown parameters by matching the interior spacetime to the exterior Reissner-Nordstr{ö}m metric followed by the appropriate choice of the values of the parameters $χ$ and $α$. Our study reveals that besides SQM, a new kind of matter distribution originates due to the interaction between the matter and the extra geometric term, while the modification of the Tolman-Oppenheimer-Volkoff (TOV) equation invokes the presence of a new force $F_c$. The accumulation of the electric charge distribution reaches its maximum at the surface, and the predicted values of the corresponding electric charge and electric field are of the order of $10^{19-20}$ C and $10^{21-22}$ V/cm, respectively. To examine the physical validity of our solutions, we perform several tests and find that the proposed $f(R, \mathcal{T})$ model survives all these critical tests. Therefore, our model can describe the non-singular charged strange stars and justify the supermassive compact stellar objects having their masses beyond the maximum mass limit for the compact stars in the standard scenario. Our model also supports the existence of several exotic astrophysical objects like super-Chandrasekhar white dwarfs, massive pulsars, and even magnetars, which remain unexplained in the framework of General Relativity (GR).

gr-qc↗

arXiv2019

Noncommutative black hole in the Finslerian spacetime

We study the behavior of the noncommutative radiating Schwarzschild black hole in the Finslerian spacetime. The investigation shows that black hole possesses either (i) two horizons, or (ii) a single horizon, or (iii) no horizon corresponding to a minimal mass. We obtain that the minimal mass significantly changes with the Finslerian parameter, keeping minimal horizon remain unchanged. It turns out that under Finslerian spacetime, the maximum temperature before cooling down to absolute zero varies with Finslerian parameter. We then study the stability of the black hole by analyzing the specific heat and free energy. The energy conditions, their violation limit also scrutinized. Our findings suggest a stable black hole remnant, whose mass and size are uniquely determined in terms of the Finslerian parameter $\overline{Ric}$ and noncommutative parameter $θ$. The physical relevance of these results are discussed in a brief.

physics.gen-ph↗

arXiv2019

Constraining values of bag constant for strange star candidates

We provide a strange star model under the framework of general relativity by using a general linear equation of state (EOS). The solution set thus obtained is employed on altogether 20 compact star candidates to constraint values of MIT bag model. No specific value of the bag constant ($B$) a-priori is assumed rather possible range of values for bag constant is determined from observational data of the said set of compact stars. To do so the Tolman-Oppenheimer-Volkoff (TOV) equation is solved by homotopy perturbation method (HPM) and hence we get a mass function for the stellar system. The solution to the Einstein field equations represents a non-singular, causal and stable stellar structure which can be related to strange stars. Eventually we get an interesting result on the range of the bag constant as 41.58~MeV~fm$^{-3}< B <$319.31~MeV~fm$^{-3}$. We have found the maximum surface redshift $Z^{max}_{s}=0.63$ and shown that the central redshift ($Z_c$) can not have value larger than $2k$, where $k=2.010789 \pm 0.073203$. Also we provide a possible value of bag constant for neutron star (NS) with quark core using hadronic as well as quark EOS.

gr-qc↗

arXiv2019

Inflationary phase and role of dark energy: Revisited

The inflationary phase of the Universe is explored by proposing a toy model related to the scalar field, termed as {\it inflaton}. The potential part of the energy density in the said era is assumed to have a constant vacuum energy density part and a variable part containing the inflaton. The prime idea of the proposed model constructed in the framework of the closed Universe is based on a fact that the inflaton is the root cause of the orientation of the space. According to this model the expansion of the Universe in the inflationary epoch is not approximately rather exactly exponential in nature and thus it can solve some of the fundamental puzzles, viz. flatness as well as horizon problems. It is also predicted that the constant energy density part in the potential may be associated to the dark energy, which is eventually different from the vacuum energy, at least in the inflationary phase of the Universe. However, the model keeps room for the end of inflationary era.

physics.gen-ph↗

arXiv2019

Exploring physical features of anisotropic strange stars beyond standard maximum mass limit in $f\left(R,\mathcal{T}\right)$ gravity

We study a specific model of anisotropic strange stars in the modified $f\left(R,\mathcal{T}\right)$-type gravity by deriving solutions to the modified Einstein field equations representing a spherically symmetric anisotropic stellar object. We take a standard assumption that $f(R,\mathcal{T})=R+2χ\mathcal{T}$, where $R$ is Ricci scalar, $\mathcal{T}$ is the trace of the energy-momentum tensor of matter, and $χ$ is a coupling constant. To obtain our solution to the modified Einstein equations, we successfully apply the `embedding class 1' techniques. We also consider the case when the strange quark matter (SQM) distribution is governed by the simplified MIT bag model equation of state given by $p_r=\frac{1}{3}\left(ρ-4B\right)$, where $B$ is bag constant. We calculate the radius of the strange star candidates by directly solving the modified TOV equation with the observed values of the mass and some parametric values of $B$ and $χ$. The physical acceptability of our solutions is verified by performing several physical tests. Interestingly, besides the SQM, another type of matter distribution originates due to the effect of coupling between the matter and curvature terms in the $f\left(R,\mathcal{T}\right)$ gravity theory. Our study shows that with decreasing the value of $χ$, the stellar systems under investigations become gradually massive and larger in size, turning them into less dense compact objects. It also reveals that for $χ<0$ the $f\left(R,\mathcal{T}\right)$ gravity emerges as a suitable theory for explaining the observed massive stellar objects like massive pulsars, super-Chandrasekhar stars and magnetars, etc., which remain obscure in the standard framework of General Relativity (GR).

gr-qc↗

arXiv2019

Anisotropic strange star in Finsler geometry

In the present paper, we report on a study of the anisotropic strange stars under Finsler geometry. Keeping in mind that Finsler spacetime is not merely a generalization of Riemannian geometry rather the main idea is the projectivized tangent bundle of the manifold $\mathpzc{M}$, we have developed the respective field equations. Thereafter, we consider the strange quark distribution inside the stellar system followed by the MIT bag model equation of state (EOS). To find out the stability and also the physical acceptability of the stellar configuration, we perform in detail some basic physical tests of the proposed model. The results of the testing show that the system is consistent with the Tolman-Oppenheimer-Volkoff (TOV) equation, Herrera cracking concept, different energy conditions and adiabatic index. One important result that we observe is that the anisotropic stress reaches to the maximum at the surface of the stellar configuration. We calculate (i) the maximum mass as well as corresponding radius, (ii) the central density of the strange stars for finite values of bag constant $B_g$ and (iii) the fractional binding energy of the system. This study shows that Finsler geometry is especially suitable to explain massive stellar systems.

gr-qc↗

arXiv2019

Charged anisotropic strange stars in Finslerian geometry

We investigate a simplified model for the strange stars in the framework of Finslerian spacetime geometry, composed of charged fluid. It is considered that the fluid consisting of three flavor quarks including a small amount of non-interacting electrons to maintain the chemical equilibrium and assumed that the fluid is compressible by nature. To obtain the simplified form of charged strange star we considered constant flag curvature. Based on geometry, we have developed the field equations within the localized charge distribution. We considered that the strange quarks distributed within the stellar system are compiled with the MIT bag model type of equation of state (EOS) and the charge distribution within the system follows a power law. We represent the exterior spacetime by the Finslerian Ressiner-Nordstr{ö}m space-time. The maximum anisotropic stress is obtained at the surface of the system. Whether the system is in equilibrium or not, has been examined with respect to the Tolman-Oppenheimer-Volkoff (TOV) equation, Herrera cracking concept, different energy conditions and adiabatic index. We obtain that the total charge is of the order of 10$^{20}$ C and the corresponding electric field is of around 10$^{22}$ V/m. The central density and central pressure vary inversely with the charge. Varying the free parameter (charge constant) of the model, we find the generalized mass-radius variation of strange stars and determine the maximum limited mass with the corresponding radius. Furthermore, we also considered the variation of mass and radius against central density respectively.

gr-qc↗

arXiv2018

Strange stars in Krori-Barua space-time under f(R; T) gravity

In the present work, we study about highly dense compact stars which are made of quarks, specially strange quarks, adopting the Krori-Barua (KB)~\cite{Krori1975} metric in the framework of $f(R,T)$ gravity. The equation of state (EOS) of a strange star can be represented by the MIT bag model as $p_r(r)=\frac{1}{3}[ρ(r)-4B_g]$ where $B_g$ is the bag constant, arises due to the quark pressure. Main motive behind our study is to find out singularity free and physically acceptable solutions for different features of strange stars. Here we also investigate the effect of alternative gravity in the formation of strange stars. We find that our model is consistent with various energy conditions and also satisfies Herrera's cracking condition, TOV equation, static stability criteria of Harrison-Zel$'$dovich-Novikov etc. The value of the adiabatic indices as well as the EOS parameters re-establish the acceptability of our model. Here in detail we have studied specifically three different strange star candidates, viz. $PSRJ~1614~2230, Vela~X-1$ and $Cen~X-3$. As a whole, present model fulfils all the criteria for stability. Another fascinating point we have discussed is the value of the bag constant which lies in the range $(40-45)$~MeV/fm$^{3}$. This is quite smaller than the predicted range, i.e., $(55-75)$~MeV/fm$^{3}$ ~\cite{Farhi1984,Alcock1986}. The presence of the constant ($χ$), arises due to the coupling between matter and geometry, is responsible behind this reduction in $B_g$ value. For $χ=0$, we get the higher value for $B_g$ as the above mentioned predicted range.

gr-qc↗

arXiv2018

Anisotropic compact stars in f(T) gravity under Karmarkar condition

In this study, we present a generalized spherically symmetric, anisotropic and static compact stellar model in $f(T)$ gravity, where $T$ represents the torsion scalar. By employing the Karmarkar condition we have obtained embedding class 1 metric from the general spherically metric of class 2 and the solutions of the Einstein field equations (EFE) has been presented with the choice of suitable parametric values of $n$ under a simplified linear form of $f(T)$ gravity reads as $f(T)=A+BT$, where $A$ and $B$ are two constants. By matching the interior spacetime metric with the exterior Schwarzschild metric at the surface and considering the values of mass and radius of the compact stars we obtain the values of the unknown constants. We have presented further a detailed analysis of the physical acceptability and examined the stability of the stellar configuration by studying the energy conditions, generalized Tolman-Oppenheimer-Volkov (TOV) equation, Herrera cracking concept, adiabatic index, etc. In the investigation, we predict numerical values of the central density, surface density, central pressure, etc., in a tabular form taking different values of $n$ specifically for $LMC~X-4$, $Cen~X-3$ and $SMC~X-1$ as the representative of compact star candidates.

gr-qc↗

arXiv2018

Solar system tests in constraining parameters of dyon black holes

In the present letter we examine the possibility of constraining dyon black holes based on the available observational data at the scale of the Solar system. For this we consider the classical tests of general relativity, viz., the perihelion precession of the planet Mercury and the deflection of light by the Sun. In connection to mathematical analysis we are considering static and spherically symmetric dyon black hole which carries both the electric and magnetic charge simultaneously, which are encoded it by the parameters $λ_0$ and $β_0$. We constrain these two parameters using the Solar system tests and obtain the permissible range from the observations.

gr-qc↗

arXiv2018

A New Model for Strange Stars

In the present work, we attempt to find a new class of solutions for the spherically symmetric perfect fluid sphere by employing the Homotopy Perturbation Method (HPM), a new tool via which the mass polynomial function facilitates to tackle the Einstein field equations. A set of interior solutions found on the basis of the simplest MIT bag model equation of state (EOS) in the form $p=\frac{1}{3}(ρ-4B)$ where $B$ is the bag constant. The proposed interior metric for the stellar system is consistent with the exterior Schwarzschild spacetime on the boundary. In addition, we also conduct a detailed study on different tests, viz. the energy conditions, TOV equation, adiabatic index, Buchdahl limit, etc., to verify the physical validity of the proposed model. The numerical value of the used parameters is predicted for different strange star candidates, for different chosen values of the bag constant. In a nutshell, by exploiting HPM technique first time ever in the field of relativistic astrophysics, we have predicted in the present literature a singularity-free and stable stellar model which is suitable to describe ultra-dense objects, like strange (quark) stars.

gr-qc↗

arXiv2018

Anisotropic strange stars in Tolman-Kuchowicz spacetime

We attempt to study a singularity-free model for the spherically symmetric anisotropic strange stars under Einstein's general theory of relativity by exploiting the Tolman-Kuchowicz metric. Further, we have assumed that the cosmological constant $Λ$ is a scalar variable dependent on the spatial coordinate $r$. To describe the strange star candidates we have considered that they are made of strange quark matter (SQM) distribution, which is assumed to be governed by the MIT bag equation of state. To obtain unknown constants of the stellar system we match the interior Tolman-Kuchowicz metric to the exterior modified Schwarzschild metric with the cosmological constant, at the surface of the system. Following Deb et al. we have predicted the exact values of the radii for different strange star candidates based on the observed values of the masses of the stellar objects and the chosen parametric values of the $Λ$ as well as the bag constant $\mathcal{B}$. The set of solutions satisfies all the physical requirements to represent strange stars. Interestingly, our study reveals that as the values of the $Λ$ and $\mathcal{B}$ increase the anisotropic system becomes gradually smaller in size turning the whole system into a more compact ultra-dense stellar object.

gr-qc↗