A Critique on Some Aspects of GUP Effective Metric

Abstract

The generalized uncertainty principle (GUP) is a gravitational correction of Heisenberg's uncertainty principle, which allows us to probe some features of quantum gravity even without the full theory. We are used to working with metric tensors in general relativity; they are convenient to have available when we wish to calculate physical quantities like Hawking temperature and black hole shadow. Various authors have tried to incorporate GUP into an effective metric that allows such calculations. In this note, I point out that some of these results are not correct due to working with series truncation rather than the full GUP-corrected expressions. Perhaps more importantly, we rely too much on heuristic arguments and lack a guiding principle in constructing the correct effective metric.

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• Radial Oscillations and Dynamical Instability Analysis for Linear-Quadratic GUP-modified White Dwarfs
• GUP Effective Metric Without GUP: Implications for the Sign of GUP Parameter and Quantum Bounce
• Tidal effects based on GUP-induced effective metric
• Statistical Entropy Based on the Generalized-Uncertainty-Principle-Induced Effective Metric
• Phenomenology of Schwarzschild-like Black Holes with a Generalized Compton Wavelength
• Minimal Proper Time and Deterministic Microstates: Emergent Quantum Fields and Relativistic Spacetime