Photon emission from the ISCO of a rotating black hole in Asymptotic Safety

Abstract

We study the isotropic emission of photons from the innermost stable circular orbit (ISCO) of a subextremal rotating black hole (BH) in asymptotic safety (AS). We calculate both the photon escape probability (PEP) and the maximum observable blueshift (MOB) of photons to reach infinity, and compare with the corresponding results for photon emission from the ISCO of a classical Kerr BH. In AS, quantum gravity effects reduce the radius of the ISCO, therefore quantum gravity effects should reduce the PEP and MOB of photons from emitters moving on the ISCO. We show that this is not the case and that, when rotating BHs with high spin are considered and the quantum parameter (which encodes the quantum gravity effects) increases towards its critical value, which is different for different spin values, the PEP and MOB also increase despite the reduction in ISCO radius. Our results on the PEP show explicitly how quantum gravity effects start to dominate over the classical background at the level of the ISCO. We also discuss the relation between these quantum gravity modifications and particular features of the shadow of a rotating BH in AS.

Figures (8)

• Figure 1: Left panel: the function $\Delta(r)$ as a function of the radial coordinate for $a^{\star}=0.7$ and $\xi=\xi_{\rm CR}\simeq 0.282$ (blue), $\xi=0.150$ (red), and for $\xi=0$ which corresponds to the classical BH (black dashed). Right panel: plots of the parameters $\tilde{\xi}_{c+}$ (green) and $\tilde{\xi}_{c-}$ (red) as functions of the spin parameter $a$. The green region is the parameter space for allowed BH solutions.
• Figure 2: The impact parameter $\chi^{\rm cl}_{\rm SPO}(r,0)$ for a Kerr BH (black dashed) and $\chi^{\rm q}_{\rm SPO}(r,\xi=0.07)$ for a RGI BH (red) for $a=0.9$ The vertical red and black dashed lines mark the positions of the couples of radial coordinates that are relevant to describe the photon escape. The horizontal blue line shows the relation between a fixed value of $\chi^{\rm cl,q}_{\rm SPO}$ and the radii $r^{\rm cl,q}_i$ ($i=1,2$) of the SPO
• Figure 3: Plots of the effective potentials $\eta^{\rm cl,q}_1$ and $\eta^{\rm cl,q}_2$ for $a=0.9$. The black dashed curves are for the classical Kerr BH, while the red curves are for the RGI BH with $\xi=0.07<\xi_{\rm CR}\simeq 0.099$. The impact parameter $\chi$ has been set to $\chi=10$ (left panel) and $\chi=25$ (right panel).
• Figure 4: Parameterization of the orbiter sky by the local angles ($\alpha,\beta)$.
• Figure 5: Escape cone for a photon emitted from a source moving on the ISCO of a subextremal BH with spin parameter $a=0.9$. The upper panel is for a Kerr BH, the middle panel is for a RGI BH with the source moving on the classical ISCO, and the bottom panel is for a RGI BH with the orbiter moving along the ISCO calculated from the AS theory. The escape cone corresponds to the region bounded by the curves in the $(\alpha,\beta)$ plane that contains the coordinate origin.