In this work, we analyze the wormhole solutions in $f(R)$ gravity. Specifically sought for geometry following three shape functions: (i) $b(r)=r_{0}+\rho_{0}r_{0}^{3}\ln\left(\frac{r_{0}}{r}\right)$, (ii) $b(r)=r_{0}+\gamma r_{0}\left(1-\dfrac{r_{0}}{r}\right)$, and (iii) $b(r)=\alpha +\beta r$, under some legitimate physical conditions on parameters as well constants involved here with functio...

The gravitational dynamics of a collapsing matter configuration which is simultaneously radiating heat flux studied in $f(R)$ gravity. Three particular functional forms gravity are considered to show that it possible envisage boundary conditions such the end state collapse has weak singularity and radiates away all its mass before reach central singularity.

We review the state of the art of f(R) theories of gravity (in their various formulations), which have been proposed as an explanation of the cosmic acceleration alternative to dark energy. The successes of f(R) gravity are discussed, together with the challenges imposed by minimal criteria for their viability. Presented at SIGRAV 2008, 18th Congress of the Italian Society of General Relativity...

Within the metric formalism of $f(R)$ theories gravity, where $R$ is Ricci scalar, we study hydrostatic equilibrium structure compact stars with inclusion anisotropic pressure. In particular, focus on $f(R)= R^{1+\epsilon}$ model and examine small deviations from General Relativity (GR) for $\vert \epsilon \vert \ll 1$. A suitable definition mass function explicitly formulated field equations v...

We consider the cosmology derived from f(T, B) gravity where T is the torsion scalar and [Formula: see text] a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel f(T) gravity, the curvature f(R) gravity, and the teleparallel-curvature f(R, T) gravity, which are particular cases of f(T, B). We adopt the Noether Symmetry Approach to st...