Are nonsingular black holes with super-Planckian hair ruled out by S2 star data?

Abstract

We propose a novel nonsingular black-hole spacetime representing a strong deformation of the Schwarzschild solution with mass $M$ by an additional hair $\ell$, which may be hierarchically larger than the Planck scale. Our black-hole model presents a de Sitter core and $\mathcal{O}({\ell }^2/r^2)$ slow-decaying corrections to the Schwarzschild solution. Our black-hole solutions are thermodynamically preferred when $0.2\lesssim \ell /GM\lesssim 0.3$ and are characterized by strong deviations in the orbits of test particles from the Schwarzschild case. In particular, we find corrections to the perihelion precession angle scaling linearly with $\ell$. We test our model using the available data for the orbits of the S2 star around ${\text{SgrA}}^{\ast }$. These data strongly constrain the value of the hair $\ell$, casting an upper bound on it of $\sim 0.47GM$, but do not rule out the possible existence of regular black holes with super-Planckian hair.

6 pages, 2 figures, 1 table. Revised version: Addendum and some references have been added

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