Black holes in a gravitational uncertainty principle with backreaction

Inspired by Padmanabhan’s work about beyond-Heisenberg uncertainty principle for the uncertainties in the position and momentum stemming from the Schrödinger equation for a gravitational potential, we will work out some predictions in the strong field regime. We will comment on a literature uncertainty principle for a test particle subject to the gravitational field of a black hole, enlightening its dependence on the Planck constant and on the quantum energy level, neither on the Newton gravitational constant nor on the speed of light. We will show that our formalism reduces to the Extended Uncertainty Principle in an appropriate limiting scenario. We will assess quantitative and conceptual differences with respect to the Generalized Uncertainty Principle in the context of isolated black holes by interpreting the test body as the probe used in the measurement process and whose energy leads to a spoiling of the mass of the system. We will compare and contrast our framework with the Asymptotically Safe Gravity paradigm. We will investigate the phenomena of accretion and evaporation for our quantum-corrected black hole geometry, also identifying the characteristics of the most appropriate probe for testing the mass–temperature relation of the analogue Hawking radiation. Thus, we will scrutinize the role played by the measurement process in the quantitative estimates of gravitational physics parameters.