In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in (n + 2)-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we have shown that the nature of singularities (naked singularity or black hole) completely depend on the parameters. Choices of various parameters are shown in tabular form. In Gauss-Bonnet gravity theory, it can be concluded that the possibility of naked singularity increases with increase in dimensions. In dimensionally continued Lovelock gravity, the naked singularity is possible for odd dimensions for several values of parameters. In pure Lovelock gravity, only black hole forms due to the gravitational collapse for any values of parameters. It has been shown that when accretion is taking place on a collapsing object, it is highly unlikely to get a black hole. Finally on considering the phantom era in the expanding P. Rudra · U. Debnath ( ) universe it is observed that there is no possibility of formation of a black hole if we are in the Gauss-Bonnet gravity considering the accreting procedure upon a collapsing object.

In this work we investigate the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by brane cosmology. Here DGP and the RSII brane models have been considered separately. Dark energy in the form of modified Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is considered in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy models. Graphs and phase diagrams are drawn to study the variations of these parameters. It is also seen that the background dynamics of modified Chaplygin gas is completely consistent with the notion of an accelerated expansion in the late universe. Finally, it has been shown that the universe in both the models follows the power law form of expansion around the critical point, which is consistent with the known results.

We investigate the Joule-Thomson expansion for five-dimensional Einstein-Maxwell-Gauss-Bonnet-AdS black holes. Here, we derive the expressions for the Joule-Thomson coefficient μ in two different approaches and show that both of these approaches are consistent with each other. Further, we analyze both inversion and isenthalpic curves in the t-P plane. Then we determine the cooling-heating regions. Finally, we compute the ratio between minimum inversion temperature T min i and critical temperature Tc for the said black holes and show that this ratio has two values unlike the charged AdS black holes and van der Waals' fluids as we achieve two critical temperatures from two equations. We also show graphically as well as by computing the critical points that the Gauss-Bonnet coupling constant α can have only positive values if the black hole is small.

In black hole physics, the second law of thermodynamics is generally valid whether the black hole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of black hole dynamics extends to the non-negativity of the sum of the entropy of the matter and the horizon, known as generalized second law of thermodynamics(GSLT). Here, we have assumed the universe to be bounded by the event-horizon where Bekenstein entropy-area relation and Hawkingtemperature are not applicable. Thus considering entropy to be an arbitrary function of the area of the event-horizon, we have tried to find the nature of the entropy-function for the validity of the GSLT both in quintessence-era and in phantom-era. Finally, some graphical representation of the entropy-function has been presented.In black hole physics, semi-classical description shows that just like a black body , black hole emits thermal radiation (known as Hawking radiation) and it completes the missing link between a black hole and a thermodynamical system. The temperature (known as the Hawking temperature) and the entropy (known as Bekenstein entropy) are proportional to the surface gravity at the horizon and area of the horizon [1, 2] respectively (i.e. related to the geometry of the horizon). Also this temperature , entropy and mass of the black hole satisfy the first law of thermodynamics [3]. As a result , physicists start speculating about the relationship between the black hole thermodynamics and Einstein's field equations (describing the geometry of space time). It is Jacobson [4] who first derived Einstein field equations from the first law of thermodynamics: δQ = T dS for all local Rindler causal horizons with δQ and T as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. Then Padmanabhan [5] was able to formulate the first law of thermodynamics on the horizon, starting from Einstein equations for a general static spherically symmetric space time. The following nice equivalence Laws of thermodynamics ⇔ Analogous laws of black hole dynamics(Semi classical analysis)⇔ Einstein f ield equations(gravity theory) (classical treatment) perhaps shows the strongest evidence for a fundamental connection between quantum physics and gravity.Subsequently, this identity between Einstein equations and thermodynamical laws has been applied in the cosmological context considering universe as a thermodynamical system bounded by the apparent horizon (R A ). Using the Hawking temperature T A = 1 2πRA and Bekenstein entropy S A = πR 2 A G at the apparent horizon, the first law of thermodynamics (on the apparent horizon) is shown to be equivalent to Friedmann equations [6] and the generalized second law of thermodynamics (GSLT) is obeyed at the horizon. Also in higher dimensional space time the relation was established for gravity with Gauss-Bonnet term and for the Lovelock gravity theory ([7],[8], [9]).But difficulty arises if we consider universe to be bounded by event horizon. First of all, in the us...

We study the accretion of modified Chaplygin gas upon different types of black hole. Modified Chaplygin gas is one of the best candidates for a combined model of dark matter and dark energy. In addition, from a field theoretical point of view the modified Chaplygin gas model is equivalent to that of a scalar field having a self-interacting potential. We formulate the equations related to both spherical accretion and disc accretion, and respective winds. The corresponding numerical solutions of the flow, particularly of velocity, are presented and are analyzed. We show that the accretion-wind system of modified Chaplygin gas dramatically alters the wind solutions, producing faster winds, upon changes in physical parameters, while accretion solutions qualitatively remain unaffected. This implies that modified Chaplygin gas is more prone to produce outflow which is the natural consequence of the dark energy into the system.