Towards the use of the most massive black hole candidates in active galactic nuclei to test the Kerr paradigm

The supermassive objects in galactic nuclei are thought to be the Kerr black holes predicted by general relativity, although a definite proof of their actual nature is still lacking. The most massive objects in AGN ($M\sim {10}^9$ $M_{\odot }$) seem to have a high radiative efficiency ($\eta \sim 0.4$) and a moderate mass accretion rate ($L_{\mathrm{bol}}/L_{\mathrm{Edd}}\sim 0.3$). The high radiative efficiency could suggest they are very rapidly rotating black holes. The moderate luminosity could indicate that their accretion disk is geometrically thin. If so, these objects could be excellent candidates to test the Kerr black hole hypothesis. An accurate measurement of the radiative efficiency of an individual AGN may probe the geometry of the space-time around the black hole candidate with a precision comparable to the one achievable with future space-based gravitational-wave detectors like LISA. A robust evidence of the existence of a black hole candidate with $\eta >0.32$ and accreting from a thin disk may be interpreted as an indication of new physics. For the time being, there are several issues to address before using AGN to test the Kerr paradigm, but the approach seems to be promising and capable of providing interesting results before the advent of gravitational wave astronomy.

Figure 1

Kerr space-time. Left panel: maximum radiative efficiency in the NT model, angular frequency at the ISCO radius, and ISCO radius (divided by 10) in Boyer-Lindquist coordinates as a function of the spin parameter. Units $M=1$. Right panel: Evolution of the spin parameter for an initially nonrotating BH of mass $M_0$. See text for details.

Figure 2

JP space-time with deformation parameter ${ϵ}_3$ and ${ϵ}_i=0$ for $i\ne 3$. Contour plots of the radiative efficiency $\eta =1-E_{\mathrm{ISCO}}$: $\eta =0.30$ (red solid curve), 0.32 (blue dotted curve), 0.34 (red solid curve), 0.36 (blue dotted curve), 0.38 (red solid curve), 0.40 (blue dotted curve). The black solid curve is the equilibrium spin parameter $a_{*}^{\mathrm{eq}}$ as inferred from Eq. (2.2) and represents the maximum value for the spin parameter of the supermassive BH candidates. This means that the region with $a_{*}>a_{*}^{\mathrm{eq}}$ is not allowed. The right panel is simply the enlargement of the area inside the orange box in the left panel.

Figure 3

JP space-time with deformation parameter ${ϵ}_3$ and ${ϵ}_i=0$ for $i\ne 3$. Left panel: contour plot of the angular frequency at the ISCO radius: ${\Omega }_{\mathrm{ISCO}}/M=0.32$ (red solid curve), 0.34 (blue dotted curve), 0.36 (red solid curve), 0.38 (blue dotted curve), 0.40 (red solid curve), 0.42 (blue dotted curve). Right panel: contour plot of the ISCO radius in Boyer-Lindquist coordinates: $r_{\mathrm{ISCO}}/M=2.00$ (red solid curve), 1.75 (blue dotted curve), 1.50 (red solid curve), 1.25 (blue dotted curve). The black solid curve is the equilibrium spin parameter $a_{*}^{\mathrm{eq}}$ as inferred from Eq. (2.2).

Figure 4

As in Fig. 2, for the JP space-time with deformation parameter ${ϵ}_4$ and ${ϵ}_i=0$ for $i\ne 4$ (left panel) and for the one with deformation parameter ${ϵ}_5$ and ${ϵ}_i=0$ for $i\ne 5$ (right panel).

Figure 5

As in Fig. 2 for the MN space-time with deformation parameter $\tilde{q}$. The compact object is oblate (prolate) when $\tilde{q}>-1$ ($\tilde{q}<-1$), but it is more oblate (prolate) than a Kerr BH with the same value of the spin parameter for $\tilde{q}>0$ ($\tilde{q}<0$).

Figure 6

As in Fig. 3 for the MN space-time with deformation parameter $\tilde{q}$.