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Register a new userA complete study of conformally flat pseudo-symmetric spacetimes in the theory of F(R)-gravity
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We investigate the geometrical and physical structures of a pseudo-symmetric spacetime $(PS)_4$ with timelike vector under the condition of conformal flatness. We classify it into two possible types: constant Ricci scalar and closed velocity vector. We further study this spacetime as a solution of $F(R)$-gravity theory and show that the pressure and energy density of the effective cosmological perfect fluid separately possess certain typical relations with the geometry and the gravity sector of the theory. Based on this result, some observational and cosmological analyses are done for the $F(R)$-gravity model and the energy conditions are investigated, supporting the accelerated expansion of the universe.
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The present work includes an analytical investigation of a collapsing spherical star in f (R) gravity. The interior of the collapsing star admits a conformal flatness. Information regarding the fate of the collapse is extracted from the matching conditions of the extrinsic curvature and the Ricci curvature scalar across the boundary hypersurface of the star. The radial distribution of the physical quantities such as density, anisotropic pressure and radial heat flux are studied. The inhomogeneity of the collapsing interior leads to a non-zero acceleration. The divergence of this acceleration and the loss of energy through a heat conduction forces the rate of the collapse to die down and the formation of a zero proper volume singularity is realized only asymptotically.
Recent elaborated by T. Harko and collaborators, the $f(R,T)$ theories of gravity contemplate an optimistic alternative to dark energy, for which $R$ and $T$ stand for the Ricci scalar and the trace of the energy-momentum tensor, respectively. Although the literature has shown that the $T$ dependence on the gravitational part of the action - which is due to the consideration of quantum effects - may induce some novel features in the scope of late-time cosmological dynamics, in the radiation-dominated universe, when $T=0$, no contributions seem to rise from such theories. Apparently, $f(R,T)$ contributions to a radiation-dominated universe may rise only from the $f(R,T^varphi)$ approach, which is nothing but the $f(R,T)$ gravity in the case of a self-interacting scalar field whose trace of the energy-momentum tensor is $T^varphi$. We intend, in this article, to show how $f(R,T^varphi)$ theories of gravity can contribute to the study of the primordial stages of the universe. Our results predict a graceful exit from inflationary stage to a radiation-dominated era. They also predict a late-time cosmic acceleration after a matter-dominated phase, making the $f(R,T^varphi)$ theories able to describe, in a self-consistent way, all the different stages of the universe dynamics.
In this paper we consider conformally flat perturbations on the Friedmann Lemaitre Robertson Walker (FLRW) spacetime containing a general matter field. Working with the linearised field equations, we unearth some important geometrical properties of matter shear and vorticity and how they interact with the thermodynamical quantities in the absence of any free gravity powered by the Weyl curvature. As there are hardly any physically realistic rotating exact conformally flat solutions in general relativity, these covariant and gauge invariant results bring out transparently the role of vorticity in the linearised regime. Most interestingly, we demonstrate that the matter shear obeys a transverse traceless tensor wave equation, and the vorticity obeys a vector wave equation in this regime. These shear and vorticity waves replace the gravitational waves in the sense that they causally carry the information about local change in the curvature of these spacetimes.
The present work investigates the gravitational collapse of a perfect fluid in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.
A plane symmetric Bianchi-I model is explored in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of energy-momentum tensor. The solutions are obtained with the consideration of a specific Hubble parameter which yields a constant deceleration parameter. The various evolutionary phases are identified under the constraints obtained for physically viable cosmological scenarios. Although a single (primary) matter source is taken, due to the coupling between matter and $f(R,T)$ gravity, an additional matter source appears, which mimics a perfect fluid or exotic matter. The solutions are also extended to the case of a scalar field model. The kinematical behavior of the model remains independent of $f(R,T)$ gravity. The physical behavior of the effective matter also remains the same as in general relativity. It is found that $f(R,T)$ gravity can be a good alternative to the hypothetical candidates of dark energy to describe the present accelerating expansion of the universe.
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