Universality of the Blandford-Znajek emission in stationary and axisymmetric spacetimes

Abstract

The Blandford-Znajek (BZ) mechanism is widely recognised as the most compelling process to extract rotational energy from an accreting black hole and power the emission of relativistic jets. We explore the universality of this process for generic black-hole spacetimes within the Konoplya-Rezzolla-Zhidenko formalism and find that the lowest-order contribution to the BZ power is invariant across different black-hole spacetimes. We also show that at the next-leading-order, different black-hole spacetimes will lead to different BZ luminosities. As a result, while slowly rotating black holes cannot be distinguished via measurements of their jet power, rapidly rotating ones have the potential of providing information on the strong-field properties of the spacetime when independent measurements of the BZ luminosity and of the black-hole angular velocity are available.

Figures (7)

• Figure 1: Top panel: Admissibility region for the KRZ parameter $\varrho$ for different values of the BH spin $a_*$ and of the $a_1$ parameter. As summarised in Eq. \ref{['eq:KRZconstraints']}, for any fixed value of $a_*$, $\varrho$ is allowed to range between a maximum value $\varrho^{_{\rm max}}$ and a minimum value $a_1^{_{\rm min}}$. The plots on the right represent the values of $\varrho^{_{\rm extr}}$ attained at $a_*=1$. Bottom panel: the same as in the top one but for the KRZ parameter $a_1$ for different values of $a_*$ and $\varrho$. The plots on the right represent the values of $a_1^{_{\rm extr}}$ attained at $a_*=1$.
• Figure 2: Range of variation of the BH angular velocity $\Omega_h$ as a function of the BH spin $a_*$ in the space allowed by changes in the KRZ parameter $\varrho$. Shown with a black solid line is the well-known nonlinear relation for a Kerr BH, i.e., for $\varrho=0$. The line distinguishes the possible solutions in a super-Kerr regime (above the solid line) and in a sub-Kerr one (below the solid line). Shown with different colours are regions with constant values of the KRZ parameter $a_1$ that enters in setting the range for $\varrho$ (see top panel of Fig. \ref{['fig:param']}). Finally, reported with a red and blue dotted line are representative sub/super-Kerr relations $\Omega_h = \Omega_h(a_*)$ for selected values of the parameter $\varrho$ such that $\varrho=\varrho^{_{\rm max}}$ for $a_*^{_{\rm max}}=0.95$.
• Figure 3: Variation of the relative spacetime deviation $\Delta_\%$ computed from the Kretschmann scalar at $a_*=1$ as a function of three KRZ parameters. Black, red and blue lines refer to variations introduced by changes in $\varrho$, $a_1$, and $b_1$, respectively.
• Figure 4: Variation of the BZ luminosity in a generic KRZ spacetime $(P_{_{\rm BZ}})_{_{\rm KRZ}}$ [Eq. \ref{['eq:BZKRZ']}], when normalised by the power extracted by an extreme Kerr BH $(P_{_{\rm BZ}})^{_{\rm max}}$ [Eqs. \ref{['eq:BZ2']} and \ref{['eq:f_GR']}], shown as a function of the (dimensionless) BH angular velocity $2M\,\Omega_h$. Reported with a black solid line is the power in a Kerr spacetime, while solid red and blue lines highlight two representative choices of the parameters $\varrho$ and $a_1$ that lead to super-Kerr and sub-Kerr behaviours, respectively. For these spacetimes, the relative variations in the Kretschmann scalar are $\Delta_\% \approx 41\%$ (super-Kerr) and $\Delta_\% \approx- 41\%$ (sub-Kerr). The curves are truncated at the maximum value of $\Omega_h$ consistent with the constraints on the KRZ parameters and the red-shaded are refers to solutions not allowed in GR. Note that although slowly rotating BHs can hardly be distinguished, significant changes appear for $\Omega_h \gtrsim 0.3/M$.
• Figure 5: Colormap showing the relative deviation between the BZ power emitted from a KRZ BH and that from a Kerr BH, $\Delta P_{_{\rm BZ}}$ shown as a function of the BH spin $a_*$ and of the fractional spacetime deviation from Kerr $\Delta_\%(\varrho,a_1)$. The latter depends on the KRZ parameters $\varrho$ and $a_1$ ($b_1=0$), and is presented for $a_1=0.1$ (top panel) and for $a_1=-0.1$ (bottom panel). The solid red and blue lines represent curves of constant $\varrho$ associated to a super-Kerr BH ($\varrho=0.03$) and to a sub-Kerr one ($\varrho=-0.06$), matching the representative cases shown in Fig. \ref{['fig:BZ']}.