We have proposed a new Analogue Gravity example - a spinning (or Kerr) Black Hole in an extended fluid model. It applies to electron dynamics in Condensed Matter lattice systems in the hydrodynamic limit. We construct the acoustic metric for sonic fluctuations following Unruh's prescription.  The Kerr Black Hole analogy has been put in a robust setting by revealing explicitly the presence of horizon and ergo-region for a specific background fluid velocity profile.

2) Cosmological features of Barrow Holographic Dark Energy (BHDE) are studied in the context of DGP brane, RS II brane-world, and the cyclic universe. It is found that BHDE parameter $\Delta$, despite its theoretically constrained range of values, is significant in describing the evolution of the universe. The viability of the models is also probed with observed Hubble data.
 
3) Gamma-ray production from the decay of \pi^0 mesons deriving from proton-proton interactions in case of accretion around a rotating black hole has been considered. The temperature profile of the accreting material has been calculated for accretion on the Kerr metric. The emissivity due to gamma-ray production through the reaction p+p -----> p+p+ \pi^{0} (2\gamma), computed using the pp reaction rate, has been incorporated in the dimensionless temperature and bulk velocity gradient through the first law of thermodynamics. We have presented some early results that show the effects of hadronic interaction on the flow profile.