Abstract:
It is known now that a typical gravitational collapse in general relativity, evolving from regular initial data and under physically reasonable conditions would end in either a black hole or a naked singularity final state. An important question that needs to be answered in this connection is, whether the analogues of the laws of thermodynamics, as formulated for relativistic horizons are respected by the dynamical spacetimes for collapse that end in the formation of a naked singularity. We investigate here the thermodynamical behaviour of the dynamical horizons that form in spherically symmetric gravitational collapse and we show that the first and second laws of black hole thermodynamics, as extended to dynamical spacetimes in a suitable manner, are not violated whether the collapse ends in a black hole or a naked singularity. We then make a distinction between the naked singularities that result from gravitational collapse, and those that exist in solutions of Einstein equations in vacuum axially symmetric and stationary spacetimes, and discuss their connection with thermodynamics in view of the cosmic censorship conjecture and the validity of the third law of black hole mechanics.

Abstract:
We study numerically gravitational collapse of a spherically symmetric instanton particle in five dimensions. We show that the late stages of the process are characterized by a nearly constant ``free energy'', the value of which matches (within numerical uncertainties) the value obtained from standard black-hole thermodynamics. This suggests a purely classical interpretation of the free energy of a black hole.

Abstract:
We study the collapse of a homogeneous braneworld dust cloud in the context of the various curvature correction scenarios, namely, the induced-gravity, the Gauss-Bonnet, and the combined induced-gravity and Gauss-Bonnet. In accordance to the Randall-Sundrum model, and contrary to four-dimensional general relativity, we show in all cases that the exterior spacetime on the brane is non-static.

Abstract:
We study the fate of a collapsing star on the brane in a generalized braneworld gravity with bulk matter. Specifically, we investigate for the possibility of having a static exterior for a collapsing star in the radiative bulk scenario. Here, the nonlocal correction due to bulk matter is manifest in an induced mass that adds up to the physical mass of the star resulting in an effective mass. A Schwarzschild solution for the exterior in terms of this effective mass is obtained, which reveals that even if the star exchanges energy with the bulk, the exterior may appear to be static to a braneworld observer located outside the collapsing region. The possible explanation of the situation from the discussion on the role of bulk matter is provided. The nature of bulk matter and the corresponding bulk geometry have also been obtained and analyzed, which gives a complete picture of both brane and bulk viewpoints.

Abstract:
The existence of extremely dark and compact astronomical bodies is by now a well established observational fact. On the other hand, classical General Relativity predicts the existence of black holes which fit very well with the observations, but do lead to important conceptual problems. In this contribution we ask ourselves the straightforward question: Are the dark and compact objects that we have observational evidence for black holes in the sense of General Relativity? By revising the semiclassical scenario of stellar collapse we find out that as the result of a collapse some alternative objects could be formed which might supplant black holes.

Abstract:
Stars form by the gravitational collapse of interstellar gas. The thermodynamic response of the gas can be characterized by an effective equation of state. It determines how gas heats up or cools as it gets compressed, and hence plays a key role in regulating the process of stellar birth on virtually all scales, ranging from individual star clusters up to the galaxy as a whole. We present a systematic study of the impact of thermodynamics on gravitational collapse in the context of high-redshift star formation, but argue that our findings are also relevant for present-day star formation in molecular clouds. We consider a polytropic equation of state, P = k rho^Gamma, with both sub-isothermal exponents Gamma < 1 and super-isothermal exponents Gamma > 1. We find significant differences between these two cases. For Gamma > 1, pressure gradients slow down the contraction and lead to the formation of a virialized, turbulent core. Weak magnetic fields are strongly tangled and efficiently amplified via the small-scale turbulent dynamo on timescales corresponding to the eddy-turnover time at the viscous scale. For Gamma < 1, on the other hand, pressure support is not sufficient for the formation of such a core. Gravitational contraction proceeds much more rapidly and the flow develops very strong shocks, creating a network of intersecting sheets and extended filaments. The resulting magnetic field lines are very coherent and exhibit a considerable degree of order. Nevertheless, even under these conditions we still find exponential growth of the magnetic energy density in the kinematic regime.

Abstract:
Gravitational collapse of FRW brane world embedded in a conformaly flat bulk is considered for matter cloud consists of dark matter and dark energy with equation of state $p=\epsilon \rho$ $(\epsilon<-{1/3})$. The effect of dark matter and dark energy is being considered first separately and then a combination of them both with and without interaction. In some cases the collapse leads to black hole in some other cases naked singularity appears.

Abstract:
We construct analogue black hole solutions in the braneworld scenario. The quantum fluctuations of condensate gravitons propagating around a $4+n$-dimensional gravitational potential are found yielding a metric similar to higher dimensional Schwarzschild black hole line-element. Black hole analogue solutions in Randall-Sundrum and Dvali-Gabadadze-Porrati brane world models are also constructed. The properties of such black hole analogues are discussed.

Abstract:
We construct analogue black hole solutions in the braneworld scenario. The quantum fluctuations of condensate gravitons propagating around a $4+n$-dimensional gravitational potential are found yielding a metric similar to higher dimensional Schwarzschild black hole line-element. Black hole analogue solutions in Randall-Sundrum and Dvali-Gabadadze-Porrati brane world models are also constructed. The properties of such black hole analogues are discussed.

Abstract:
We consider cosmological inflation driven by the rolling tachyon in the context of the braneworld scenario. We show that sufficient inflation consistent with the observational constraints can be achieved for well defined upper limits on the five-dimensional mass scale, string mass scale and the string coupling for the bosonic string.