Probing beyond-vacuum general relativistic effects with extreme mass-ratio inspirals

TL;DR

This paper develops a cohesive framework to test gravity with EMRIs in beyond-vacuum settings by combining dark matter environmental effects with scalar Gauss–Bonnet gravity. It uses a two-timescale, fixed-frequency perturbative approach to compute leading-order corrections to energy fluxes and waveforms, incorporating both dynamical friction and scalar radiation. The study finds that dark matter spikes can imprint sizable phase dephasing, and scalar charges in sGB gravity yield detectable deviations in LISA data, with parameter correlations quantified via Fisher-matrix forecasts. The results provide a path to disentangle environmental imprints from beyond-GR signatures, enabling robust constraints on new physics with LISA observations.

Abstract

We examine extreme mass-ratio inspirals (EMRIs) as probes of beyond-vacuum general relativistic effects, accounting for both astrophysical environments and scalar Gauss-Bonnet (sGB) gravity. In beyond-vacuum scenarios, the evolution of an EMRI immersed in a cold dark matter environment modifies the gravitational wave flux and introduces additional dissipative effects such as dynamical friction. In parallel, in the beyond-general relativistic settings such as in sGB gravity, the inspiraling object carries an effective scalar charge and emits scalar radiation. Both environmental and modified-gravity effects modify the flux-balance law, thereby inducing changes in the EMRI dynamics. Using a two-timescale analysis within the fixed-frequency formalism, we compute leading-order corrections to the energy fluxes for quasi-circular, equatorial orbits in static, spherically symmetric spacetimes and construct the corresponding gravitational waveforms, which are used to quantify the accumulated gravitational wave dephasing and waveform mismatch relative to the vacuum general relativistic case. We further perform the Fisher Information Matrix analysis to estimate parameter correlations and the ability of future space-based detectors such as the Laser Interferometer Space Antenna (LISA) to disentangle environmental and modified gravity effects. Our results show that both dark matter and scalar field effects can leave measurable imprints on EMRI waveforms and that a consistent beyond-vacuum treatment is essential for robust tests of gravity.

Figures (9)

• Figure 1: The plot of the $\delta m(r)$ (left panel) and $\delta f(r)$ (right panel) as the functions of $r$. In each of these plots the red curve represents the Hernquist spike profile whereas the blue curve represents the NFW spike profile. The mass of the spike profile is taken to be $\textup{M}_{\textrm{halo}}=10^4\textup{M}_{\textrm{BH}}$ with $\textup{M}_{\textrm{halo}}/a_0=10^{-3}$ and the cut off radius $r_c=100 \textup{M}_{\textrm{halo}} a_0/\textup{M}_{\textrm{BH}}$. The fitting parameters $\{\mathfrak{a},\mathfrak{b},\mathfrak{c}\}$ are the same as \ref{['tab:Fitting_Parameters']}.
• Figure 2: The energy fluxes as functions of the orbital radius $r_{\Omega}/\textup{M}_{\textrm{BH}}$ is presented. Left panel: The absolute value of the ratio between the dark-matter-induced correction to the gravitational wave flux, $\dot{\textup{E}}_{\textrm{GW}}^{(1,1)}$, and the vacuum gravitational wave flux, $\dot{\textup{E}}_{\textrm{GW}}^{(1,0)}$, as a function of $r_\Omega/\textup{M}_{\textrm{BH}}$ for the Hernquist and NFW profiles is presented. The numerical parameters used in this flux calculation are the same as those listed in \ref{['tab:Fitting_Parameters']}. Right panel: the absolute value of the ratio between the scalar radiation flux, $\dot{\textup{E}}_{\textrm{SW}}^{(1,0)}$, and the gravitational wave flux, $\dot{\textup{E}}_{\textrm{GW}}^{(1,0)}$, in sGB theory for different values of the scalar charge, shown as a function of $r_\Omega/\textup{M}_{\textrm{BH}}$.
• Figure 3: The logarithm of dephasing for different environmental configurations as a function of observation time is plotted, which considers four comparison cases: the sGB theory and the standard GR case in the top-left panel, the Hernquist-type (top-right panel) or NFW-type (bottom-left panel) dark matter model and sGB theory, the vacuum and two dark matter models of Hernquist-type/NFW-type in the bottom-right panel. The scalar charges in sGB theory are set to $q_s=\{0.01,0.05,0.08,0.1,0.3,0.5\}$.
• Figure 4: Comparison of the plus polarization $h_{+}$ of EMRI waveforms between the standard GR and dark matter environments, setting scalar charge $q_s= 0.01$. The time-domain waveforms display four cases: signal from Schwarzschild spacetime, including scalar radiation in vacuum and beyond-vacuum of dark matter environments. The three panels consider different stages in the time-domain, namely initial time (left panel), the evolutions of two weeks (middle panel) and three months (right panel). Inclusion of dark matter environments can yield phase shifts and amplitude modulations relative to the GR case, highlighting the impact of the environments on the waveform morphology.
• Figure 5: Mismatch as a function of the length scale $a_0$ and halo mass $\textup{M}_{\textrm{halo}}$ for the Hernquist (left panel) and NFW (right panel) dark matter profiles. The secondary is initialized at $r_{\Omega} = 10\textup{M}_{\textrm{BH}}$ and evolved adiabatically down to the Schwarzschild ISCO. The black dashed line marks the threshold mismatch $\mathcal{M} = 10^{-3}$, above which the two waveforms are expected to be distinguishable by LISA detector.