https://doi.org/10.1140/epjc/s10052-023-11360-x
Regular Article - Theoretical Physics
A critique on some aspects of GUP effective metric
1
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 180 Siwangting Road, 225002, Yangzhou, Jiangsu, China
2
Shanghai Frontier Science Center for Gravitational Wave Detection, School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, Shanghai, China
Received:
9
November
2022
Accepted:
24
February
2023
Published online:
11
March
2023
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.
© The Author(s) 2023
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