Regarding the Schwinger effect and the corresponding thermodynamic properties of near-extremal black holes, we have thoroughly studied very general black hole backgrounds including rotation, electric charge, magnetic charge, andcosmological constants. We have been trying to extend the research to study non-extremal black holes. In these cases, the corresponding dynamic equation is the Heun differential equation with four singular points. The current method cannot handle it. However, we found a mathematical concept which provides a suitable technique for the problem we are studying. Indeed, we already have preliminary results. Moreover, recently we have begun to study the quantum gravity effect, through the renormalization group equation to determine the energy-scale dependent Newton's constant, and then to discuss the quantum improved black hole physics. We found that when this method is applied to a rotating black hole, some contradictions may appear in the black hole thermodynamics. We are clarifying their physical relations and studying the singularity resolving and the Hawking radiation problem.We have also achieved technological breakthroughs in the research of holographic superconductivity. We have studied the vortex formation by applying an external magnetic field, and further analyzed and discussed related physical properties. Moreover, we initially discovered that some non-equilibrium evolution processes in the region away from the critical temperature are similar to experimental observations, and these behaviors cannot be obtained from the Ginzburg-Landau theory. We need to study this problem more precisely, therefore we must improve our numerical simulation technology and analyze more complex systems. We will also continue to study the quasi-local energy (conserved quantity) of gravity, focusing on energy calculations related to gravitational waves.