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Register a new userA conservative energy-momentum tensor in the $f(R,T)$ gravity and its implications for the phenomenology of neutron stars
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Added by
Geanderson Carvalho Mr
Publication date
2018
fields
Physics
and research's language is
English
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The solutions for the Tolmann-Oppenheimer-Volkoff (TOV) equation bring valuable informations about the macroscopical features of compact astrophysical objects as neutron stars. They are sensitive to both the equation of state considered for nuclear matter and the background gravitational theory. In this work we construct the TOV equation for a conservative version of the $f(R,T)$ gravity. While the non-vanishing of the covariant derivative of the $f(R,T)$ energy-momentum tensor yields, in a cosmological perspective, the prediction of creation of matter throughout the universe evolution as shown by T. Harko, in the analysis of the hydrostatic equilibrium of compact astrophysical objects, this property still lacks a convincing physical explanation. The imposition of $ abla^{mu}T_{mu u}=0$ demands a particular form for the function $h(T)$ in $f(R,T)=R+h(T)$, which is here derived. Therefore, the choice of a specific equation of state for the star matter demands a unique form of $h(T)$, manifesting a strong connection between conserved $f(R,T)$ gravity and the star matter constitution. We construct and solve the TOV equation for the general equation of state for $p=krho^{Gamma}$, with $k$ being the EoS parameter, $rho$ {it the energy density} and $Gamma$ is the adiabatic index. We also derive the macroscopical properties of neutron stars ($Gamma=5/3$) within this approach.
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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.
In $f(R)$ gravity and Brans-Dicke theory with scalar potentials, we study the structure of neutron stars on a spherically symmetric and static background for two equations of state: SLy and FPS. In massless BD theory, the presence of a scalar coupling $Q$ with matter works to change the star radius in comparison to General Relativity, while the maximum allowed mass of neutron stars is hardly modified for both SLy and FPS equations of state. In Brans-Dicke theory with the massive potential $V(phi)=m^2 phi^2/2$, where $m^2$ is a positive constant, we show the difficulty of realizing neutron star solutions with a stable field profile due to the existence of an exponentially growing mode outside the star. As in $f(R)$ gravity with the $R^2$ term, this property is related to the requirement of extra boundary conditions of the field at the surface of star. For the self-coupling potential $V(phi)=lambda phi^4/4$, this problem can be circumvented by the fact that the second derivative $V_{,phi phi}=3lambdaphi^2$ approaches 0 at spatial infinity. In this case, we numerically show the existence of neutron star solutions for both SLy and FPS equations of state and discuss how the mass-radius relation is modified as compared to General Relativity.
Deviations from the predictions of general relativity due to energy-momentum squared gravity (EMSG) are expected to become pronounced in the high density cores of neutron stars. We derive the hydrostatic equilibrium equations in EMSG and solve them numerically to obtain the neutron star mass-radius relations for four different realistic equations of state. We use the existing observational measurements of the masses and radii of neutron stars to constrain the free parameter, $alpha ,$ that characterizes the coupling between matter and spacetime in EMSG. We show that $-10^{-38},mathrm{cm^{3}/erg}<alpha <+10^{-37},mathrm{cm^{3}/erg}$. Under this constraint, we discuss what contributions EMSG can provide to the physics of neutron stars, in particular, their relevance to the so called textit{hyperon puzzle} in neutron stars. We also discuss how EMSG alters the dynamics of the early universe from the predictions of the standard cosmological model. We show that EMSG leaves the standard cosmology safely unaltered back to $tsim 10^{-4}$ seconds at which the energy density of the universe is $sim 10^{34},mathrm{erg,cm^{-3}}$.
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).
In this paper, we study the stellar structure in terms of alternative theory of gravity specially by f (R;T) gravity theory. Here, we consider the function f (R;T) = R+2VT where R is the Ricci scalar, T is the stress-energy momentum and V is the coupling constant. Using it we developed a stellar model that briefly explains the isotropic matter distribution within the compact object filled with perfect fluid. The stability of the model is shown by several physical and stability conditions. With the accecptibility of our theory, we were able to collect data for compact stars like PSR-B0943+10, CEN X-3, SMC X-4, Her X-1 and 4U1538-52 with great accuracy.
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