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Register a new userEquation of State in the Presence of Gravity
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We investigate how an equation of state for matter is affected when a gravity is present. For this purpose, we consider a box of ideal gas in the presence of Newtonian gravity. In addition to the ordinary thermodynamic quantities, a characteristic variable that represents a weight per unit area relative to the average pressure is required in order to describe a macroscopic state of the gas. Although the density and the pressure are not uniform due to the presence of gravity, the ideal gas law itself is satisfied for the thermodynamic quantities when averaged over the system. Assuming that the system follows an adiabatic process further, we obtain a {it new} relation between the averaged pressure and density, which differs from the conventional equation of state for the ideal gas in the absence of gravity. Applying our results to a small volume in a Newtonian star, however, we find that the conventional one is reliable for most astrophysical situations when the characteristic scale is small. On the other hand, gravity effects become significant near the surface of a Newtonian star.
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New high-precision observations are now possible to constrain different gravity theories. To examine the accelerated expansion of the Universe, we used the newly proposed $f(Q,T)$ gravity, where $Q$ is the non-metricity, and $T$ is the trace of the energy-momentum tensor. The investigation is carried out using a parameterized effective equation of state with two parameters, $m$ and $n$. We have also considered the linear form of $f(Q,T)= Q+bT$, where $b$ is constant. By constraining the model with the recently published 1048 Pantheon sample, we were able to find the best fitting values for the parameters $b$, $m$, and $n$. The model appears to be in good agreement with the observations. Finally, we analyzed the behavior of the deceleration parameter and equation of state parameter. The results support the feasibility of $f(Q,T)$ as a promising theory of gravity, illuminating a new direction towards explaining the Universes dark sector.
In this article, the bulk viscosity is introduced in a modified gravity model. The gravitational action has a general $f(R,T)$ form, where $R$ and $ T $ are the curvature scalar and the trace of energy momentum tensor respectively. An effective equation of state (EoS) has been investigated in the cosmological evolution with bulk viscosity. In the present scenario, the Hubble parameter which has a scaling relation with the redshift can be obtained generically. The role of deceleration parameter $q$ and equation of state parameter $omega $ is discussed to explain the late-time accelerating expansion of the universe. The statefinder parameters and Om diagnostic analysis are discussed for our obtained model to distinguish from other dark energy models together with the analysis of energy conditions and velocity of sound for the model. We have also numerically investigated the model by detailed maximum likelihood analysis of $580$ Type Ia supernovae from Union $ 2.1$ compilation datasets and updated $57$ Hubble datasets ($31$ data points from differential age method and $26$ points from BAO and other methods). It is with efforts found that the present model is in good agreement with observations.
In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schr{o}dinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein-Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gravity model. In order to achieve the results of this paper we considered three different rainbow gravity models mostly used in the literature and compare the resulting modifications in the Landau levels with the standard case, namely without rainbow gravity.
In this paper, we study static and spherically symmetric black hole (BH) solutions in the scalar-tensor theories with the coupling of the scalar field to the Gauss-Bonnet (GB) term $xi (phi) R_{rm GB}$, where $R_{rm GB}:=R^2-4R^{alphabeta}R_{alphabeta}+R^{alphabetamu u}R_{alphabetamu u}$ is the GB invariant and $xi(phi)$ is a function of the scalar field $phi$. Recently, it was shown that in these theories scalarized static and spherically symmetric BH solutions which are different from the Schwarzschild solution and possess the nontrivial profiles of the scalar field can be realized for certain choices of the coupling functions and parameters. These scalarized BH solutions are classified in terms of the number of nodes of the scalar field. It was then pointed out that in the case of the pure quadratic order coupling to the GB term, $xi(phi)=eta phi^2/8$, scalarized BH solutions with any number of nodes are unstable against the radial perturbation. In order to see how a higher order power of $phi$ in the coupling function $xi(phi)$ affects the properties of the scalarized BHs and their stability, we investigate scalarized BH solutions in the presence of the quartic order term in the GB coupling function, $xi(phi)=eta phi^2 (1+alpha phi^2)/8$. We clarify that the existence of the higher order term in the coupling function can realize scalarized BHs with zero nodes of the scalar field which are stable against the radial perturbation.
In the Einstein-bumblebee gravity, the Lorentz symmetry is spontaneously broken by a vector field. In this paper, we attempt to test the Lorentz symmetry via the observation of the shadow cast by the Kerr-like black hole with or without plasma. A novel phenomenon of the Lorentz-violating parameter on the shadow is observed. The result shows that when the observer gradually moves from the poles to the equatorial plane, the shadow radius $R_{rm s}$ firstly decreases and then increases with the Lorentz-violating parameter. Such nonmonotonic behavior provides us an important understanding on the black hole shadow in the Einstein-bumblebee gravity. Besides, three more distortion observables are calculated, and found to increase with the Lorentz-violating parameter. Moreover, when a homogeneous plasma is present, the motion of the photon is analyzed. We further observe that the refractive index shrinks the size, while enhances the deformation of the shadow. Finally, adopting the observed data of the diameter of M87$^*$, we find the refractive index is more favored in (0.914, 1).
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