AR-2019-2020

Charged compact star model in Einstein-Maxwell- Gauss-Bonnet gravity In this work, we present a model of a static charged anisotropic fluid sphere in the Einstein-Maxwell- Gauss-Bonnet (EMGB) theory of gravitation. We utilize the Krori-Barua (KB) ansatz together with a linear equation of state of the form p r = βρ − γ to generate exact solutions of the EMGB field equa- tions describing compact objects. The model ob- tained here is found to satisfy the elementary phys- ical requirements necessary for a physically realiz- able stellar object. We demonstrate that contribu- tions from the Gauss-Bonnet terms have a non-zero impact on the density, pressure and anisotropy pro- files. The vanishing of the electromagnetic field at the centre of the stellar configuration leads to a relation between the equation of state parameter and the Gauss-Bonnet term. Our model reveals a direct connection between the nature of the matter configuration and higher dimensional effects. This work has been done in collaboration with Megan Govender. Naseer Iqbal Bhat Thermodynamics and phase transitions in galaxy clustering The phenomenon of galaxy clustering has been studied from the perspective of the gravitational phase transition, which is somewhat different from a phase transition in material science. There is ev- idence that the phase transition describing galaxy clustering in an expanding universe is a first or- der phase transition exhibiting a mixed phase. As such, the Clausius Clapeyron equation is relevant for studying such a system. In this work, we de- rive a general analogue of the Clausius Clapeyron equation that applies not only towards the coexis- tence curve in pressure-temperature space, but to a more general parameter space. The key finding is that a cusp exists at the critical point in this mixed phase when viewed in this more general pa- rameter space. We extend this formalism to derive an equation for the curvature of the phase coex- istence curve in pressure-temperature space and a more general parameter space. We also verify pre- vious findings of hysteresis in the system via an independent free energy analysis. This work has been done in collaboration with Nasser Demir. Ritabrata Biswas Search for missing links between two extreme wind speed profiles: Dark energy accretion and adiabatic fluid accretion In recent past, the progresses in accretion studies onto relativistically gravitating central objects like a Schwarzschild singularity reveal that the accre- tion flow must be transonic. For such cases, the radial inward speed gradient can be written as a numerator by denominator form, among which the later vanishes somewhere in between infinite dis- tance from the attracter to the event horizon of the same. For sustainability of a physical solution, the numerator should vanish at the same radial dis- tance where denominator does vanish. From this point, we obtain a second degree first order differ- ential equation of radial inward speed and hence, we obtain two branches of flow, namely accretion and wind. For adiabatic accretion case, the wind curve is formed to be more or less parallel to the radial distance axis as we move far from the cen- tral object. For dark energy accretion, this curve is parallel to the radial velocity axis. Here we face a question: Why there is no fluid speed profiles in between these two extremities? While searching the reasons, we follow that dark energy, if treated as an accreting object, should stay around the cen- tral compact star and hence, will contaminate the metric which propertises the compact star. In this research work, we have proposed a model with a ro- tating black hole embedded in quintessence, where quintessence equation of state and spin parame- ters of the black hole are regulatory factors of the model. The resulting accretion and wind curves are studied. The effect of negative pressure of dark energy is found to get catalyzed by the entry of the spin of the black hole. We tally our results with observations of accretion or outflow phenomenon near to different quasars. This work has been done in collaboration with Parthajit Roy. Threshold drop in accretion density if dark energy is accreting onto a supermassive black hole Recent studies of galactic cores tell us that super- massive black holes are hosted at each of these cores. We got some evidences even. Besides, dark energy is expected to be distributed all over in our universe. Dark matter halo, on the other hand, could be found around the galactic regions. Though the natures of spans of them are not clearly