Classical Solutions in Einstein's Gravity and Study of some Collapsing   Models
  My research work can be classified into two parts namely, (i) Cosmological phenomena with varying speed of light and (ii) Gravitational collapse and black holes.   We have investigated several cosmological phenomena when velocity of light varies with time. We have considered the variation of light as power-law in time and have studied the Brans-Dicke cosmology, Quintessence problem and others. We have also examined whether some cosmological problems can be solved using it for anisotropic space-time model.   In brane scenario we have studied some cosmological implications namely, the Cosmic No-Hair Conjecture (CNHC) and variable gravity theory. In CNHC we have shown that in realistic situation no more extra conditions are needed in brane scenario.   In gravitational collapse, we have mainly concentrated to spherical collapse for dust distribution. We have considered both four and higher dimensional space-time and have examined the possibility for formation of black hole or naked singularity. In marginally bound case we have found naked singularity is possible only for four and five dimension, while for non-marginally bound case the possibility of black hole increases with the increase in the dimension of the space-time.   In quasi-spherical gravitational collapse for dust distribution, we have (n+2) dimensional Szekeres space-time and have examined the possibility for formation of black hole or naked singularity. In marginally bound case, we have found that possibility of naked singularity depends on dimension of the space-time. 
Ujjal Debnath