PV criticality of Achucarro–Ortiz black hole in the presence of higher-order quantum and GUP corrections

In this paper, we study the quantum-corrected and generalizedf uncertinty principle (GUP)-corrected thermodynamics of the [Formula: see text]-dimensional charged-rotating Achucarro–Ortiz (AO) black hole. The corrected parameters include temperature, entropy, and heat capacity which help to investigate the instability phases of the Achucarro–Ortiz black hole. We show that this black hole with small mass possesses unstable regions. However, we reveal that those instabilities can be removed by the GUP corrections. Finally, we also compute the maximum temperature that can be reached by the Achucarro–Ortiz black hole. We show that corrected temperatures by different methods we used are identical at the small mass limit, hence GUP correction at small mass limit is a quantum gravity correction. Interestingly, we show by graphical analysis that leading-order quantum-corrected temperature of the Achucarro–Ortiz black hole behaves similar to the GUP-corrected temperature of uncharged Achucarro–Ortiz black hole.

A new length scale, and modified Einstein–Cartan–Dirac equations for a point mass

We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale [Formula: see text], dubbed the Compton–Schwarzschild length, to which the Compton wavelength and Schwarzschild radius are small mass and large mass approximations, respectively. Here, we write down the field equations which follow from this action. We argue that the large mass limit yields Einstein equations, provided we assume the wave function collapse and localization for large masses. The small mass limit yields the Dirac equation. We explain why the Kerr–Newman black hole has the same gyromagnetic ratio as the Dirac electron, both being twice the classical value. The small mass limit also provides compelling reasons for introducing torsion, which is sourced by the spin density of the Dirac field. There is thus a symmetry between torsion and gravity: torsion couples to quantum objects through Planck’s constant [Formula: see text] (but not [Formula: see text]) and is important in the microscopic limit. Whereas gravity couples to classical matter, as usual, through Newton’s gravitational constant [Formula: see text] (but not [Formula: see text]), and is important in the macroscopic limit. We construct the Einstein–Cartan–Dirac equations which include the length [Formula: see text]. We find a potentially significant change in the coupling constant of the torsion driven cubic nonlinear self-interaction term in the Dirac–Hehl–Datta equation. We speculate on the possibility that gravity is not a fundamental interaction, but emerges as a consequence of wave function collapse, and that the gravitational constant maybe expressible in terms of Planck’s constant and the parameters of dynamical collapse models.