  General relativity (GR) is the most successful theory of gravity, with great
observational support on local scales. However, to keep GR valid over cosmic
scales, some phenomena (such as flat galaxy rotation curves and the cosmic
expansion history) require the assumption of exotic dark matter. The radial
acceleration relation (RAR) indicates a tight correlation between dynamical
mass and baryonic mass in galaxies. This suggests that the observations could
be better explained by modified gravity theories without exotic matter.
Modified Newtonian Dynamics (MOND) is an alternative theory that was originally
designed to explain flat galaxy rotation curves by using a new fundamental
constant acceleration $a_0$, the so-called Milgromian parameter. However, this
non-relativistic model is too rigid (with insufficient parameters) to fit the
large diversity of observational phenomena. In contrast, a relativistic
MOND-like gravity naturally emerges from the hyperconical model, which derives
a fictitious acceleration compatible with observations. This study analyses the
compatibility of the hyperconical model with respect to distinct RAR
observations of 10 galaxy clusters obtained from HIFLUGCS and 60 high-quality
SPARC galaxy rotation curves. The results show that a general relation can be
fitted to most cases with only one or two parameters, with an acceptable
$\chi^2$ and $p$-value. These findings suggest a possible way to complete the
proposed modification of GR on cosmic scales.
