Constraining fractionality using some observational tests

Abstract

Recently, a fractional version of the Schwarzschild-Tangherlini black hole with a fractal horizon has been introduced. Motivated by the key role of the Schwarzschild solution in gravitational and astrophysical studies, some consequences of this fractional-fractal generalization of the Schwarzschild black hole have been investigated. In this line, the corresponding i) Shapiro and Sagnac time delays, ii) shadow, iii) orbital precession, and iv) gravitational lensing are studied and confronted with observational data. MCMC analysis also unveils i) the potential of this metric in dealing with the solar-system tests and ii) the necessity of studying fractional spacetimes and objects.

Figures (7)

• Figure 1: The photon path (from $P$ to $E$).
• Figure 2: Approximate relationship between the impact parameter, $D$ (black hole distance), and $\Theta$.
• Figure 3: In the presence of an object, the null geodesics are bent, and correspondingly, the observer $B$ can see the object $A$ but in another position, i.e., a straight path extension with a deflection angle $\alpha$.
• Figure 4: One-dimensional marginalized posterior distribution of the fractional dimension $D$ obtained from perihelion precession data.
• Figure 5: One-dimensional marginalized posterior distribution of the fractional dimension $D$ obtained from deflection angle data.