Shadow of the Scalar Hairy Black Hole with Inverted Higgs Potential

TL;DR

This paper investigates the optical appearance and shadow of a hairy black hole with an inverted Higgs potential, revealing how scalar hair influences observable features and constraining model parameters with astrophysical data.

Contribution

It introduces a detailed ray-tracing analysis of hairy black holes with scalar hair, showing how their shadows differ from Schwarzschild black holes and constraining parameters using real observations.

Findings

The shadow size increases with scalar horizon value $\,\phi_H$.

The brightness of rings remains nearly unaffected by scalar hair.

Constraints on the parameter $\,\Lambda$ are derived from M87 and Sgr A* observations.

Abstract

We study the imaging of a hairy black hole (HBH) in the Einstein-Klein-Gordon theory, where Einstein gravity is minimally coupled to a scalar potential $V(\phi)=-\Lambda \phi^4 + \mu \phi^2$ with $\Lambda$ and $\mu$ are constants. As a consequence, a nontrivial scalar field at the event horizon $\phi_H$ allows the HBH to evade the no-hair theorem, bifurcate from the Schwarzschild black hole by acquiring some new properties, which can affect the shadow of the HBH received by a distant observer. The framework of ray-tracing is adopted to investigate the optical appearance of the HBH, thus the trajectories of light rays around the HBH can be classified into three emissions: direct, lensed and photon ring. Employing three models of optically and geometrically thin accretion disk, we compare the differences between the Schwarzschild black hole and HBH with same horizon radius in a specific model, and find that the size of the shadow and accretion disk increases as $\phi_H$ increases, but the brightness of the rings remain nearly unaffected, this implies our HBH can potentially mimic the Schwarzschild black hole if we vary the horizon radius of the HBH. Finally, we also constraint the parameter $\Lambda$ from the observations of supermassive black holes in the galactic center of M87 and Sgr A$^{*}$, which could offer new insights for imaging of black holes and astrophysical observations.