Greybody factors in scalar-tensor gravity and beyond

TL;DR

This work investigates greybody factors and quasinormal modes for scalarized black holes in beyond Horndeski gravity through two complementary routes: test-field propagation on fixed scalarized backgrounds and full backreaction analyses in axial perturbations. It analyzes a parity-symmetric beyond-Horndeski solution with analytic metric functions and two scalar-tensor submodels (shift-symmetric Horndeski and EsGB), revealing how the effective potential can develop multiple extrema, wells, and barriers that qualitatively reshape greybody factors and QNMs. The study finds that increasing hair-sourcing parameters generally suppresses or nonmonotonically modulates greybody factors and shifts QNM frequencies toward larger real parts and smaller damping, with pronounced effects in axial perturbations. Overall, these results highlight observable probes for distinguishing scalarized black holes in modified gravity from GR and guide future explorations of Hawking radiation spectra and gravitational-wave signatures in such theories.

Abstract

In the framework of the beyond Horndeski action, we consider three subtheories that support scalarised black-hole solutions, and look for modified characteristics compared to GR. We first study the propagation of massless scalar and vector test fields in the fixed background of an analytical spherically symmetric black hole derived in the context of a parity-symmetric beyond Horndeski theory, and show that the profiles of the effective gravitational potentials, greybody factors, absorption cross sections and quasinormal frequencies exhibit distinct modifications as we move away from the GR limit. We then turn our attention to the perturbations of the gravitational field itself and adopt a full-theory analysis that takes into account the backreaction of the scalar field on the metric. Employing as background solutions scalarized black holes arising in the shift-symmetric Horndeski theory and in the quadratic-quartic-scalar-Gauss-Bonnet theory, we compute the greybody factors and quasinormal modes of the axial sector. In both theories, in direct correspondence to the form of the gravitational potential, which features multiple extremal points, we find modified (suppressed or nonmonotonic) greybody curves and altered quasinormal frequencies (smaller oscillating frequencies and larger damping times), especially as the hair-sourcing parameter increases.

Figures (10)

• Figure 1: Dominant mode $(l=s)$ effective potentials for scalar $(s=0)$ and electromagnetic (EM) $(s=1)$ test-field perturbations in the background \ref{['eq:BCKL_metric']}, left panel for $p_1\,M=0.05$ and right panel for $p_1\,M=1$.
• Figure 2: Greybody factors for scalar $(s=0)$ and EM $(s=1)$ test fields, in the background \ref{['eq:BCKL_metric']}, for $M\,p_1=0.05$ (left panel), and $M\,p_1=1$ (right panel). Solid curves correspond to $l=s$, dashed to $l=s+1$ and dot-dashed to $l=s+2$.
• Figure 3: Total absorption cross sections normalized by the surface area of the event horizon, for $M\,p_1=0.05$ (left panel), and $M\,p_1=1$ (right panel), for scalar $(s=0)$ and EM $(s=1)$ test-field perturbations in the background \ref{['eq:BCKL_metric']}. For each total absorption cross section, we have taken into account the partial absorption cross sections with multipole numbers $l \leqslant n+s$, where $n$ is the number of peaks that appear in the figure for each case. The dashed lines correspond to the geometric cross sections as obtained numerically for \ref{['eq:BCKL_metric']}, see also Table \ref{['tab:sigma_g_Ah']}.
• Figure 4: Quasinormal modes for scalar $(s=0)$ and EM $(s=1)$ test-field perturbations in the background \ref{['eq:BCKL_metric']}. Left panel, the real and imaginary parts for $l=s$. Right panel, $l=s,s+1,s+2$, the curves correspond to a continuous scan of the domain $p_1\,M\in[10^{-4},10]$, with the QNMs approaching the Schwarzschild limit values $(p_2=0)$ monotonically for all $p_2\neq0$ as $p_1\,M\gg1$. The color coding is the same in all panels.
• Figure 5: Scalar charge of the hairy solutions in the shift-symmetric theory, versus the hair-sourcing parameter $\alpha$. Each point in the solid line corresponds to a different black hole solution. We also show the seven points we use as reference in our analysis.