Hairy black holes via gravitational decoupling: light rings, absorption and spectral lines

TL;DR

This work uses gravitational decoupling to generate three families of hairy black holes under SEC, DEC, and WEC and analyzes their interaction with massless scalar waves. The hair introduces new parameters that modify the scattering potential, enabling outside-the-horizon wells and, in some cases, stable light rings; these features give rise to quasibound states and spectral lines in the absorption spectrum, including Breit-Wigner resonances in the transmission coefficient. Across the studied configurations, the absorption cross section approaches the horizon area at low frequencies and exhibits sinc-like oscillations around the geometric cross section at high frequencies, in agreement with universal results. The observed spectral lines and resonances connect to the spacetime’s light-ring structure and offer a potential observational avenue to test no-hair theorems and to distinguish hairy BHs from standard GR solutions.

Abstract

We investigate the absorption of massless scalar waves by three distinct hairy black hole solutions obtained through the gravitational decoupling method, considering the weak, the strong or the dominant energy conditions. Remarkably, in certain configurations of hairy black holes associated with the fulfillment of the weak energy condition, quasibound states may appear, resulting in Breit-Wigner-like resonances in their absorption profile. These quasibound states (and consequently the spectral lines in the absorption spectrum) can be related to stable light rings in the spacetime, a structure often associated with horizonless exotic compact objects, such as wormholes. We investigate how the gravitational decoupling method introduces novel light ring structures in hairy black holes and influences the absorption spectra through its deformation parameters. Our numerical results show excellent agreement with well-known approximations.

Figures (12)

• Figure 1: Regions of the parameter space where the effective potential develops a local minimum outside the event horizon. The top panel corresponds to the SEC solution, while the bottom panel shows the WEC solution. The color coding indicates whether the corresponding energy condition is satisfied throughout the region exterior to the event horizon, helping to visualize possible violations in specific domains.
• Figure 2: Region of the parameter space of the WEC (satisfied everywhere outside the event horizon) solution in which the effective potential presents a well.
• Figure 3: WEC hairy BH configuration with monotonically increasing redshift function outside the horizon and stable light ring structure ($\jmath/M = 0.534,~\beta/M = 0.325$). The top panel shows the redshift function, while the middle panel shows its derivative, making explicit the monotonicity of $f(r)$. The bottom panel shows the occurrence of a local minimum, even though $f(r)$ is strictly increasing.
• Figure 4: Scattering potential as functions of the radial coordinate (in units of the event horizon radius, $r_\text{h}$), all with $\alpha = 1$ (or $\alpha/M = 0.5$ in the WEC case). The top, middle, and bottom panels correspond to the DEC, SEC and WEC BH configurations, respectively. In all cases, the Schwarzschild scattering potential is included for comparison.
• Figure 5: Potential well for chosen configurations of the SEC (top panel) and WEC (middle and bottom panel) solutions for $l=\{0,1,2\}$, as a function of $r$, in units of $r_{h}$.