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Over the last decade or so, we have been developing the possible existence of highly magnetized white dwarfs with analytical stellar structure models. While the primary aim was to explain the nature of the peculiar overluminous type Ia supernovae, later on, these magnetized stars were found to have even wider ranging implications including those for white dwarf pulsars, soft gamma-ray repeaters and anomalous X-ray pulsars, as well as gravitational radiation. In particular, we have explored in detail the mass-radius relations for these magnetized stars and showed that they can be significantly different from the Chandrasekhar predictions which essentially leads to a new super-Chandrasekhar mass-limit. Recently, using the stellar evolution code STARS, we have successfully modelled their formation and cooling evolution directly from the magnetized main sequence progenitor stars. Here we briefly discuss all these findings and conclude with their current status in the scientific community., Comment: 13 pages including 7 figures; based on the talk given in the 16th Marcel Grossmann Meeting (MG16) held during July 5-10, 2021; to appear in the proceeding of MG16

We sketch a possible evolutionary scenario by which a highly magnetized super-Chandrasekhar white dwarf could be formed by accretion on to a commonly observed magnetized white dwarf. This is an exploratory study, when the physics in cataclysmic variables (CVs) is very rich and complex. Based on this, we also explore the possibility that the white dwarf pulsar AR Sco acquired its high spin and magnetic field due to repeated episodes of accretion and spin-down. We show that strong magnetic field dramatically decreases luminosity of highly magnetized white dwarf (B-WD), letting them below the current detection limit. The repetition of this cycle can eventually lead to a B-WD, recently postulated to be the reason for over-luminous type Ia supernovae. A spinning B-WD could also be an ideal source for continuous gravitational radiation and soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs). SGRs/AXPs are generally believed to be highly magnetized, but observationally not confirmed yet, neutron stars. Invoking B-WDs does not require the magnetic field to be as high as for neutron star based model, however reproducing other observed properties intact., Comment: 6 pages including 2 figures and 1 table; based on the talk given in the 15th Marcel Grossmann Meeting (MG15), Rome, July 1-7, 2018, in session WD2; to appear in the proceedings of MG15

A modified non-linear time series analysis technique, which computes the correlation dimension $D_2$, is used to analyze the X-ray light curves of the black hole system GRS 1915+105 in all twelve temporal classes. For four of these temporal classes $D_2 $ saturates to $\approx 4-5$ which indicates that the underlying dynamical mechanism is a low dimensional chaotic system. Of the other eight classes, three show stochastic behavior while five show deviation from randomness. The light curves for four classes which depict chaotic behavior have the smallest ratio of the expected Poisson noise to the variability ($ < 0.05$) while those for the three classes which depict stochastic behavior is the highest ($ > 0.2$). This suggests that the temporal behavior of the black hole system is governed by a low dimensional chaotic system, whose nature is detectable only when the Poisson fluctuations are much smaller than the variability., Comment: Accepted for publication in Astrophysical Journal

During inflation primordial quantum fluctuations of the spacetime metric become classical and there is a spontaneous CPT violation by the spin connection coupling terms of the metric with fermions. The energy levels of the left and the right chirality neutrinos is split which gives rise to a net lepton asymmetry at equilibrium. A net baryon asymmetry of the same magnitude can be generated from this lepton asymmetry either by a GUT, $B-L$ symmetry or by electroweak sphaleron processes which preserve $B+L$ symmetry. If the amplitude of the primordial tensor perturbations is of the order of $10^{-6}$ (as is expected from inflation models) and the lepton/baryon number violating processes freeze out at the GUT era $T_d \sim 10^{16} Gev$ then a baryon number asymmetry of the correct magnitude $10^{-10}$ can be generated., Comment: 9 pages Latex file

Spin 1/2 particles in geodesic trajectories experience no gravitational potential but they still have non-zero couplings to the curvature tensor. The effect of space time curvature on fermions can be parameterized by a vector and a pseudo-vector potential. These apparent CPT violating terms can be measured with satellite based spin-polarized torsion balance and clock comparison experiments. The Earth's curvature effect is of the order of 10^{-37} Gev which is not far from the present bounds of ~10^{-29} Gev on such CPT violating couplings., Comment: Latex file 9 pages. Version to appear in Phys. Rev. D

We compute the nucleosynthesis of materials inside advective disks around black holes. We show that composition of incoming matter can change significantly depending on the accretion rate and accretion disks. These works are improvements on the earlier works in thick accretion disks of Chakrabarti, Jin & Arnett (1987) in presence of advection in the flow., Comment: Latex pages including figures. Kluwer Style files included. Appearing in `Observational Evidence for Black Holes in the Universe', ed. Sandip K. Chakrabarti, Kluwer Academic Publishers (DORDRECHT: Holland)