Mohsen Fathi and colleagues explored the ergosphere, photon region structure and the shadow of a rotating charged Weyl black hole (RCWBH) that was generated in the context of Weyl gravity. They showed that, this black hole is very sensitive to electric charge and the spin parameter. In addition, its shadow changes from being oblate to being sharp, by increasing in the spin parameter. Their study recently appeared in the *Journal Galaxies*.

Recently, conformal (Weyl) gravity, which is described by a pure Weyl squared action, has attracted a considerable amount of interest as an alternative theory to Einstein gravity. From the equation of motion and the symmetry of conformal gravity, any conformal class of the Einstein solution arises naturally as a solution to the conformal gravity. In particular, subject to the Neumann boundary condition, conformal gravity can single out Einstein’s solution. Moreover, unlike Einstein’s gravity, conformal gravity has been shown to be perturbatively renormalizable in four dimensions, leading to many interesting alternative approaches to quantum gravity.

Another appealing aspect of conformal gravity comes from cosmology. Although Einstein’s gravity can describe the physics within the scale of the Solar system perfectly, there are still many unsolved puzzles when applied to a larger scale, such as the inconsistency with the observation of galactic rotation curves and accelerating universe. Consequently, unknown entities namely “dark matter and dark energy”, have to be introduced in order to fix the inconsistency problems. Thus, one may wonder whether it is possible to modify the nature of gravity to explain the physics at a larger scale, while maintaining the correct behaviors at the scale of the Solar system. Since conformal gravity admits more solutions than Einstein’s gravity, it can produce the effective potential consistent with the observed phenomenon, making it a compelling modified gravity theory.

Now, Mohsen Fathi and colleagues discussed the optical properties of RCWBH and its shadow, in the context of Weyl gravity.

They first demonstrated that, black hole is very sensitive to electric charge and the spin parameter. Meaning, any changes in the electric charge and spin parameter can bring large variations in the black hole’s ergosphere.

Later, they discussed the optical properties of the black hole, by using the first order light-like geodesic equations. It has been shown that the photon region is the ultimate limit of black hole’s optical visibility and, in fact, confines the black hole’s shadow.

In addition, in order to demonstrate the shadows of the RCWBH, they calculated the Cartesian celestial coordinates. It has been shown that the boundary of the shadow, to be both oblate and sharp toward the origin of the celestial coordinates, and, for a given charge parameter, an increase in the spin parameter shrinks the shadow, horizontally and vertically.

Finally, the evolution of the photon region and the shadow of the RCWBH depends rigorously on the presence of an electric charge. Based on this fact, they applied the calculations corresponding to the vertical angular diameter of the shadow, to obtain an estimation for the electric charge of M87*, if it was supposed to be a RCWBH. Their results indicated that this black hole will have about 10^{36} free protons to fulfill its electric charge deposit, which is about 10¯^{21} times the total protons of the Sun. This, in the realm of charged black holes, makes sense, because a black hole is not supposed to have active nuclear fusion.

“Thus, our investigation may help to understand the optical evolution of charged black hole spacetimes, which are inferred from alternative theories of gravity, as well as providing information about the impacts of the electromagnetic constituents of such spacetimes. For future investigations, we can consider the motion of mass-less and massive test particles around the RCWBH and can investigate the relevant gravito-electromagnetic effects. These tasks are left for future studies.”

— concluded authors of the study

**Funding**: M. Fathi has been supported by the Agencia Nacional de Investigación y Desarrollo (ANID) through DOCTORADO Grants No. 2019-21190382, and No. 2021-242210002. J.R. Villanueva was partially supported by Centro de Astrofísica de Valparaíso (CAV).

*For more: *

*Fathi, M.; Olivares, M.; Villanueva, J.R. Ergosphere, Photon Region Structure, and the Shadow of a Rotating Charged Weyl Black Hole. Galaxies 2021, 9, 43. **https://doi.org/10.3390/galaxies9020043*

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