Affine quantization of black holes: Thermodynamics, singularity removal, and displaced horizons

In this work we investigate the thermodynamical properties and modified dynamics of black hole solutions in the semiclassical regime of affine coherent state quantization. Using the weak correspondence principle we build a semiclassical effective action that we use to study thermodynamics in the canonical ensemble and to compare classical analytical solutions with the corresponding semiclassical ones. We determine a strong compatibility of these affine black holes with the thermodynamical properties of the classical counterparts, with only minor restrictions on the free parameters of the models. Furthermore we obtain that black hole singularities are removed by quantum effects, resulting also in a modified extension of the horizon, in agreement with the sign of entropy corrections.

Figure 1

Regions of the $ab$ parameter plane with regions of thermodynamical instability and non-physical solutions.

Figure 2

Comparison of classical (continuous line) and semiclassical (dashed line) solutions for the Schwarzschild BH model, for parameters $\gamma =10^{-10}$, $M=1$, $B=1/2$, $r_0=10^3$.

Figure 3

Comparison of classical (continuous line) and semiclassical (dashed line) solutions for the Jackiw-Teitelboim BH model, for parameters $\gamma =10^{-4}$, $M=40$, $B=1$, $r_0=10^3$.

Figure 4

Comparison of classical (continuous line) and semiclassical (dashed line) solutions for the Witten BH model, for parameters $\gamma =10^{-5}$, $M=1$, $B=4$, $r_0=10$.

Figure 5

Comparison of classical (continuous line) and semiclassical (dashed line) solutions for Liouville gravity, for parameters $\gamma =10^{-5}$, $M=4$, $a=1$, $\alpha =-1/2$, $b=-1$, $r_0=100$.

Figure 6

Comparison of classical (continuous line) and semiclassical (dashed line) solutions for the Schwarzschild-(A)dS model, for parameters $\ell =1$, $G_4=1/2$ $M=1$ and $\gamma =10^{-10}$.