A rotating GUP black hole: metric, shadow, and bounds on quantum parameters

Abstract

Recently, for the first time, a metric of a static spherically symmetric generalized uncertainty inspired quantum black hole was derived. We apply the modified Newman-Janis algorithm to this metric and derive its rotating counterpart. We show that this metric has all the correct limits, while due to Newman-Janis side effects, the singularity which was resolved in the static case, is introduced back into the model. However, the slowly-rotating limit of this black hole is singularity-free. Furthermore, we show that the presence of quantum parameters modifies the location of the horizons, temperature, and entropy of the black hole, and allows the existence of naked singularities even if the ratio of the spin parameter to mass of the black hole is less than unity. Finally, by computing the shadow parameters of this black hole and comparing them with data from the Event Horizon Telescope for both M87* and Sgr A*, we set bounds on one of the quantum parameters of the model, and show that there is a limit on the angular momentum of M87* if this model is valid.

Figures (6)

• Figure 1: Plot of rotating GUP metric components in Schwarzschild coordinates with the given values of parameters on the top of the plot.
• Figure 2: Plot of the horizon function, $\Omega(r)$, for several values of the spin parameter $a$, with the given value of parameters on the top of the plot.
• Figure 3: Plot which shows the radial positions of inner (dashed colored lines) and outer (solid colored lines) horizons for an $M = 1$ black hole, as a function of the spin parameter $a$ for different values of the quantum parameter $Q_b$. Coloured points indicate the radii at which the inner and outer horizons merge to form one horizon, yielding an extremal black hole.
• Figure 4: Shadow contours in celestial coordinates for three values of the spin parameter, $\frac{a}{M}=0$ (black lines), $\frac{a}{M}=0.8$ (red lines) and $\frac{a}{M}=0.95$ (blue lines). Solid lines correspond to the shadow for this rotating GUP black hole with quantum parameters $\frac{Q_{b}}{M^{2}}=0.1=\frac{Q_{c}}{M^{6}}$, dashed lines correspond to the respective Kerr black hole $\left(\frac{Q_{b}}{M^{2}}=0=\frac{Q_{c}}{M^{6}}\right)$. The black hole mass is $M=1$ and the inclination angle is $\theta_{0}=\frac{\pi}{2}$.
• Figure 5: Angular shadow diameter $d_{{\rm sh}}$ (left plot) and Schwarzschild shadow deviation $\delta$ (right plot) for a range of quantum parameter $Q_{b}$ values and spin parameter $a$ values for the Sgr A* black hole, which has a mass, distance and inclination angle as given in the text. The solid black lines indicate the lower bounds on the values of $d_{{\rm sh}}$ and $\delta$, respectively, for Sgr A* as measured from EHT observations. The white region shows the values of $Q_{b}$ and $a$ for which the black hole has no horizons.