Abstract
In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters β0 and α0 with η which is the parameter that characterises 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 β0. 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.
Highlights
With β0 to be the dimensionless deforming parameter of generalised uncertainty principle (GUP), or, both linear and quadratic terms [5]
The quadratic deformations were derived from doubly special relativity (DSR), loop quantum gravity, and string theory [4, 6,7,8,9,10], while the linear-quadratic deformations were developed later as a generalisation [5]
The GUP has important implications in cosmology and black hole physics [11]. It has indicated a cyclic non-singular universe [12], black hole remnants and that the deformed black hole thermodynamics derived from GUP appears to coincide with the one obtained from studying black hole entropy in loop quantum gravity and string theory [13]
Summary
With β0 to be the dimensionless deforming parameter of GUP, or, both linear and quadratic terms [5],. P 2 m2p with β0 to be the dimensionless deforming parameter of GUP, or, both linear and quadratic terms [5], It has indicated a cyclic non-singular universe [12], black hole remnants and that the deformed black hole thermodynamics derived from GUP appears to coincide with the one obtained from studying black hole entropy in loop quantum gravity and string theory [13].
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