By adopting a theory-agnostic approach and considering a recently proposed Kerr-like black hole model, Chen and Yang investigated the structure and properties of accretion disk around a rotating black hole without reflection symmetry. They showed that, in the absence of reflection symmetry, the accretion disk is curved surface in shape. Furthermore, they found that the parameter ϵ would shrink the size of the innermost stable circular orbits (ISCO), and enhance the efficiency of the black hole in converting rest-mass energy to radiation during accretion. Their study recently appeared in Arxiv.

Rotating black holes without equatorial reflection symmetry i.e. Z2 symmetry, can naturally arise in effective low-energy theories of fundamental quantum gravity, in particular, when parity-violating interactions are introduced. Due to the complexity of the theories, the rotating black hole solutions do not have analytic expressions and they can only be studied using numerical or perturbative approaches.

Now, Chen and Yang adopted a theory-agnostic approach and considered a relatively simple Kerr-like black hole model to investigate the astrophysical implications of Z2 asymmetry.

“The Kerr-like metric we considered is relatively simple in that its geodesic equations are designed to be completely separable. Therefore, the metric can be a good approximation of those complicated solutions in effective theories and can be very useful in studying the astrophysical implications of reflection asymmetry in a phenomenological manner.”

At first, they investigated the properties of accretion disk around the Kerr-like black hole and found that, in the absence of reflection symmetry, the accretion disk is curved surface in shape, rather than a flat disk lying on the equatorial plane.

They also explored the astrophysical implications of Z2 asymmetry on the accretion disk properties around a Kerr-like black hole. In particular, they found that, in a toy model with a specific choice of the deviation function, the parameter ϵ would shrink the size of the innermost stable circular orbits (ISCO), and enhance the efficiency of the black hole in converting rest-mass energy to radiation during accretion.

Finally, they investigated the gravitational redshift effect and computed the g-factor associated with the emission coming from the ISCO in the Kerr-like spacetime. They suggested that the spin measurements based on the redshift g-factor observations should be analyzed with great care and assuming the Kerr hypothesis, such measurements could overestimate the true spin value of the black hole if the black hole is actually the Kerr-like one with a large deviation parameter |ϵ| (at a level of ∼ 16% if |ϵ| ∼ 17).

“There are other important observables of the accretion disk that we have not explored in this study, such as the disk temperature and luminosity. In the cases in which the spacetime possesses equatorial reflection symmetry, one can adopt the thin-disk model and the calculations of these observables can be quite straightforward. However, in the absence of reflection symmetry, the disk is a curved surface and one has to rebuild the corresponding curved thin-disk model. This is beyond the scope of the present paper. In addition, it will be interesting to investigate the detailed motions of particles after they cross the ISCO and enter the plunging phase. All the above explorations would give further insights into the fundamental differences between Kerr and Kerr-like black holes, and possibly their observable signatures. We will leave these interesting topics to future works.”, they conclude.

**Reference***: Che-Yu Chen, Hsiang-Yi Karen Yang, “Curved accretion disks around rotating black holes without reflection symmetry”, Arxiv, pp. 1-20, 2021. https://arxiv.org/abs/2109.00564*

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