The GUP and quantum Raychaudhuri equation

Understand

In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalized uncertainty principle, with the corrections from the quantum Raychaudhuri equation.

• The reason for this comparison is to connect the deformation parameters $\beta_0$ and $ \alpha_0$ with $\eta$ which is the parameter that characterizes the quantum Raychaudhuri equation.
• The derived relation between the parameters appears to depend on the relative scale of the system (black hole), which could be read as a beta function equation for the quadratic deformation parameter $\beta_0$.
• This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime.