General relativity characterizes gravity as a geometric property exhibited on spacetime by massive objects, while teleparallel gravity achieves the same results at the level of equations, by taking a torsional perspective of gravity. Similar to the f (R) theory teleparallel gravity can also be generalized to f (T ), with the resulting field equations being inherently distinct from f (R) gravity in that they are second order, while in the former case they turn out to be fourth order. In the present case, a minimally coupled scalar field is investigated in the f (T ) gravity context for several forms of the scalar field potential. A number of new f (T ) solutions are found for these potentials. Their respective state parameters are also being examined.

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 spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analysed at the expense of a high degree of symmetry in the spacetime, that of conformal flatness and self similarity. Indeed collapsing models, terminating into a curvature singularity can be obtained. The formation of black holes or the occurrence of naked singularities depend on the initial collapsing profiles.

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.Perhaps the most straightforward modification of GR is understood by writing the Einstein-Hilbert lagrangian as an analytic function f (R) of the Ricci scalar R instead of R itself. The so-called f (R) * email: soumya@cts.iitkgp.ernet.in † Goswami@ukzn.ac.za ‡ Maharaj@ukzn.ac.za §

The collapse scenario of a scalar field along with a perfect fluid distribution is investigated for a conformally flat spacetime. The theorem for the integrability of an anharmonic oscillator has been utilized. For a pure power law potential of the form φ n+1 , it is found that a central singularity is formed which is covered by an apparent horizon for n > 0 and n < −3. Some numerical results have also been presented for a combination of two different powers of φ in the potential. *