Shad Ali

This report is divided into three main parts: 1. The first two chapters discuss the emission of Short GRB (SGRB) from binary mergers surrounded by a strong magnetic field. By introducing our model, we investigated the physics of the emission of SGRBs from rotating and charged rotating BHs. A rapidly spinning, strongly magnetized neutron star (millisecond magnetar) is the primary source of strong magnetic fields ranging from $10^{13}~\rm to ~ 10^{16} G$. The decay of the magnetic field could power electromagnetic radiation, especially X-rays and gamma rays from NSs or NS-BH mergers as their primary sources. Considering the merger of compact bodies (NS-NS or NS-BH or BH-BH), we can obtain interesting results. 2. In the next two chapters, we reviewed the BH interiors to understand the nature of black hole interior information and evaporation from its initial to final phases via entropy variation. The evolution relation obtained from two types of entropy gives diverse understandings of the evaporation of BHs under Hawking radiation. 3. The fifth Chapter is related to BH configuration (information) entropy and the thermodynamic phase transition of $f(R)$ BH. Here, we consider a d$-$dimensional black hole (BH) in $f(R)$ gravity and analyze the effect of modified gravity on critical point parameters, the difference in number densities, and configuration entropy during the BH phase transition phenomenon. These results were also compared with charged AdS BH, the holographic dual of van der Waal's fluid, and hence the BH in modified gravity.