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In this article we try to present spherically symmetric isotropic strange star model under the framework of $f(R,mathcal{T})$ theory of gravity. To this end, we consider that the Lagrangian density is an arbitrary linear function of the Ricci scalar $R$ and the trace of the energy momentum tensor~$mathcal{T}$ given as $fleft(R,mathcal{T}right)=R+2chi T$. We also assume that the quark matter distribution is governed by the simplest form of the MIT bag model equation of state (EOS) as $p=frac{1}{3}left(rho-4Bright)$, where $B$ is the bag constant. We have obtained an exact solution of the modified form of the the Tolman-Oppenheimer-Volkoff (TOV) equation in the framework of $f(R,mathcal{T})$ gravity theory and studied the dependence of different physical properties, viz., total mass, radius, energy density and pressure on the chosen values of $chi$. Further, to examine physical acceptability of the proposed stellar model in detail, we conducted different tests, viz. energy conditions, modified TOV equation, mass-radius relation, causality condition etc. We have precisely explained the effects arising due to the coupling of the matter and geometry on the compact stellar system. For a chosen value of the Bag constant we have predicted numerical values of different physical parameters in tabular format for the different strange stars. It is found that as the factor $chi$ increases the strange stars shrink gradually and become less massive to turn into a more compact stellar system. The maximum mass point is well within the observational limits and hence our proposed model is suitable to explain the ultra dense compact stars. For $chi=0$ we retrieve as usual the standard results of general relativity (GR).
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For the accurate understanding of compact objects such as neutron stars and strange stars, the Tolmann-Openheimer-Volkof (TOV) equation has proved to be of great use. Hence, in this work, we obtain the TOV equation for the energy-momentum-conserved $f(R,T)$ theory of gravity to study strange quark stars. The $f(R,T)$ theory is important, especially in cosmology, because it solves certain incompleteness of the standard model. In general, there is no intrinsic conservation of the energy-momentum tensor in the $f(R,T)$ gravity. Since this conservation is important in the astrophysical context, we impose the condition $ abla T_{mu u}=0$, so that we obtain a function $f(R,T)$ that implies conservation. This choice of a function $f(R,T)$ that conserves the momentum-energy tensor gives rise to a strong link between gravity and the microphysics of the compact object. We obtain the TOV by taking into account a linear equation of state to describe the matter inside strange stars, such as $p=omegarho$ and the MIT bag model $p=omega(rho-4B)$. With these assumptions it was possible to derive macroscopic properties of these objects.
We investigate effects of the modified $f(R, mathcal{T})$ gravity on the charged strange quark stars with the standard choice of $f(R, mathcal{T})=R+2chi mathcal{T}$. 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 $p=frac{1}{3}(rho-4B)$, where $B$ is the bag constant, while the form of charge distribution is chosen to be $qleft(rright)=Qleft(r/Rright)^3=alpha r^3$ with $alpha$ as a constant. We derive the values of the unknown parameters by matching the interior spacetime to the exterior Reissner-Nordstr{o}m metric followed by the appropriate choice of the values of the parameters $chi$ and $alpha$. 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).
The article presents modeling of inflationary scenarios for the first time in the $f(R,T)$ theory of gravity. We assume the $f(R,T)$ functional from to be $R + eta T$, where $R$ denotes the Ricci scalar, $T$ the trace of the energy-momentum tensor and $eta$ the model parameter (constant). We first investigated an inflationary scenario where the inflation is driven purely due to geometric effects outside of GR. We found the inflation observables to be independent of the number of e-foldings in this setup. The computed value of the spectral index is consistent with latest Planck 2018 dataset while the scalar to tensor ratio is a bit higher. We then proceeded to analyze the behavior of an inflation driven by $f(R,T)$ gravity coupled with a real scalar field. By taking the slow-roll approximation, we generated interesting scenarios where a Klein Gordon potential leads to observationally consistent inflation observables. Our results makes it clear-cut that in addition to the Ricci scalar and scalar fields, the trace of energy momentum tensor also play a major role in driving inflationary scenarios.
In the current article, we study anisotropic spherically symmetric strange star under the background of $f(R,T)$ gravity using the metric potentials of Tolman-Kuchowicz type~cite{Tolman1939,Kuchowicz1968} as $lambda(r)=ln(1+ar^2+br^4)$ and $ u(r)=Br^2+2ln C$ which are free from singularity, satisfy stability criteria and also well behaved. We calculate the value of constants $a$, $b$, $B$ and $C$ using matching conditions and the observed values of the masses and radii of known samples. To describe the strange quark matter (SQM) distribution, here we have used the phenomenological MIT bag model equation of state (EOS) where the density profile ($rho$) is related to the radial pressure ($p_r$) as $p_r(r)=frac{1}{3}(rho-4B_g)$. Here quark pressure is responsible for generation of bag constant $B_g$. Motivation behind this study lies in finding out a non-singular physically acceptable solution having various properties of strange stars. The model shows consistency with various energy conditions, TOV equation, Herreras cracking condition and also with Harrison-Zel$$dovich-Novikovs static stability criteria. Numerical values of EOS parameter and the adiabatic index also enhance the acceptability of our model.
We study a specific model of anisotropic strange stars in the modified $fleft(R,mathcal{T}right)$-type gravity by deriving solutions to the modified Einstein field equations representing a spherically symmetric anisotropic stellar object. We take a standard assumption that $f(R,mathcal{T})=R+2chimathcal{T}$, where $R$ is Ricci scalar, $mathcal{T}$ is the trace of the energy-momentum tensor of matter, and $chi$ 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 $p_r=frac{1}{3}left(rho-4Bright)$, 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 $chi$. 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 $fleft(R,mathcal{T}right)$ gravity theory. Our study shows that with decreasing the value of $chi$, the stellar systems under investigations become gradually massive and larger in size, turning them into less dense compact objects. It also reveals that for $chi<0$ the $fleft(R,mathcal{T}right)$ 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).
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