Testing conformal gravity using the supermassive black hole NGC 4258

Abstract

In this paper, we perform a Bayesian statistical fit to estimate the free parameters of a nonsingular black hole in conformal gravity by employing megamaser astrophysical data of the supermassive black hole hosted at the center of the active galactic nucleus of NGC 4258. This estimation has been carried out by taking into account a general relativistic approach, which makes use of the positions on the sky of the photon sources and the frequency shift observations from the water megamaser system in circular motion around the black hole. Within the framework of conformal gravity, a way to eliminate the singularity at r = 0 from the Schwarzschild spacetime is by introducing a conformal factor characterized by a length scale parameter l and an integer parameter N. Therefore, the spacetime geometry depends on the mass of the black hole, and the conformal gravity parameters l and N. In this work, we estimate the mass-to-distance ratio M/D and the length scale ratio l/D with fixed values of the integer parameter N = 1, 2, considering the geodesics of conformally/non-conformally coupled massive particles. This method leads to posterior Gaussian distributions for all parameters, thus yielding a most probable value for the parameter l for both conformally/non-conformally coupled particles, in contrast to previous constraints based on X-ray astrophysical data, where an upper bound for the parameter l has been established. Furthermore, we obtain new physical properties regarding the existence of the ISCO radius for this nonsingular spacetime in the case of non-conformally coupled particles.

Figures (5)

• Figure 1: Posterior distribution of the conformal gravity fit for NCC particles (upper left/right panel corresponds to $N=1$/$N=2$) and CC particles (lower left/right panel corresponds to $N=1$/$N=2$). Note that contour levels amount to $1\sigma$ and $2\sigma$ confidence regions.
• Figure 2: Plot of the ISCO Eq. \ref{['rISCOeq']} for $N=1$/$N=2$ (top/bottom), in units where $M=1$. Here it is shown that for small values of $l$, the $r_{ISCO}$ approaches the Schwarzschild $r_{ISCO}$ ($r=6$), and for larger values of $l$, the $ISCO$ curves does not intersect the horizontal axis.
• Figure 3: Plots of the total redshift/blueshift for conformally and non-conformally coupled particles as a function of $l$ for fixed values of $r_{e} = 1$ pc, $M=1$ and we display only the case $N=1$ for ilustrative purposes. It can be observed that the NCC frequency shift decays faster, and therefore, it takes greater values of $l$ for CC to reach the same values.
• Figure 4: Plots of the angular momentum $L$ expression in Eq. \ref{['AngularMomentum']} for $N=1$ in units where $M=1$, as a function of $l$ (top) and as a function the radius of the emitter $r_e$ (bottom).
• Figure 5: Plots of the angular momentum $L$ expression from Eq. \ref{['AngularMomentum']} for $N=1$/$N=2$ (left panel/right panel), in units where $M=1$, as a function of $l$ and the radius of the emitter $r_e$.