AR_final file_2018-19

well- known ordinary calculus is being used exten- sively in many fields, particularly in understand- ing stochastic process and fractal dynamics. In this work, we apply the techniques of fractional calculus to study some specific modifications of the geometry of submanifolds. Our generalisation is applied to extend the Israel formalism, which is used to glue together two spacetimes across a timelike, spacelike or a null hypersurface. In this context, we show that the fractional extrapolation leads to some striking new results. More precisely, we demonstrate that in contrast to the original Is- rael formalism, where many spacetimes can only be joined together through an intermediate thin hy- persurface admitting effective matter fields violat- ing standard energy conditions, the fractional gen- eralisation allows these spacetimes to be smoothly sewed together without any such requirements on the stress tensor of the matter fields. We dis- cuss the ramifications of these results for spacetime structure and the possible implications for gravita- tional physics. This work has been done in collab- oration with Ankit Anand. Ritaban Chatterjee The accretion disk-jet connection in blazars The power spectral density (PSD) of the X-ray emission variability from the accretion disk-corona region of black hole X-ray binaries and active galac- tic nuclei has a broken power-law shape with a char- acteristic break timescale T B . If the disk and the jet are connected, the jet variability may also con- tain a characteristic timescale related to that of the disk-corona. Recent observations of the blazar Mrk 421 have confirmed the broken power-law shape of the PSD of its jet X-ray variability. We model the time variability of a blazar, in which emitting particles are assumed to be accelerated by suc- cessive shock waves flowing down the jet with a varying inter-shock timescale ( T IS ). We investi- gate the possible relation between the characteris- tic timescales in the disk and jet variability based on the above model, along with mathematically and physically simulated disk variability. We find that both the PSD of the jet and disk variability may have a broken power-law shape, but the break timescales are not related in general, except only in systems with a small range of BH mass. The break in the jet and disk PSD are connected to the interval between large amplitude outbursts in the jet ( T IS ) and to the viscous timescale in the disk, respectively. In frequency bands where mul- tiple emission processes are involved or emission is from lower energy particles, the break in the PSD may not be prominent enough for detection. This work has been done in collaboration with Sagnick Mukherjee and Kaustav Mitra. Probing the jets of blazars using the temporal sym- metry of their multi-wavelength outbursts We analyze X-ray light curves of the blazar Mrk 421 obtained from the Soft X-ray Imaging Telescope and the Large Area X-Ray Proportional Counter instrument onboard the Indian space telescope As- troSat and archival observations from Swift . We show that the X-ray power spectral density (PSD) is a piece-wise power-law with a break, i.e., the in- dex becomes more negative below a characteristic “break-timescale”. Galactic black hole X-ray bi- naries and Seyfert galaxies exhibit a similar char- acteristic timescale in their X-ray variability that is proportional to their respective black hole mass. X-rays in these objects are produced in the accre- tion disk or corona. Hence, such a timescale is be- lieved to be linked to the properties of the accretion flow. Any relation observed between events in the accretion disk and those in the jet can be used to characterize the disk-jet connection. However, ev- idence of such link have been scarce and indirect. Mrk 421 is a BL Lac object, which has a prominent jet pointed towards us and a weak disk emission, and it is assumed that most of its X-rays are gen- erated in the jet. Hence, existence of the break in its X-ray PSD may indicate that changes in the ac- cretion disk, which may be the source of the break timescale are translating into the jet, where the X- rays are produced. This work has been done in collaboration with Namrata Roy, Manasvita Joshi, and Aritra Ghosh. Suchetana Chatterjee X-ray surface brightness profiles of optically se- lected active galactic nuclei: Comparison with X- ray AGNs We use data from the All Wavelength Extended Groth Strip International Survey to construct stacked X-ray maps of optically bright active galac- tic nuclei (AGNs), and an associated control sam- ple of galaxies at high redshift (z ∼ 0.6). From our analysis of the surface brightness profiles obtained ( 180 )