Hierarchical constraints on gravitational waves from horizonless compact objects

TL;DR

The paper addresses testing Kerr-like predictions for black-hole remnants by constraining near-horizon deviations that would arise in horizonless compact objects. It models such deviations with a near-horizon boundary at $r_{NH}=r_+(1+\epsilon)$ and analyzes the resulting long-lived QNMs characterized by frequency $f$, damping time $\tau$, and amplitude $A$ via Bayesian inference on LIGO/Virgo data, including hierarchical stacking across events. The main finding is a hierarchical bound of $\log_{10} \epsilon = -30.9$ and a coordinate-distance bound of $\log_{10} \Delta r = -25.6$, improving on single-event limits and approaching Planck-scale sensitivity. The results constrain several horizonless models and demonstrate how multi-event Bayesian stacking can significantly tighten constraints on near-horizon physics, with implications for quantum-gravity-inspired modifications.

Abstract

We use the data of several promising gravitational wave observations to obtain increasingly stringent bounds on near-horizon deviations of their sources from the Kerr geometry. A range of horizonless compact objects proposed as alternatives to black holes of general relativity would possess a modified gravitational wave emission after the merger. Modelling these objects by introducing reflection of gravitational waves near the horizon, we can measure deviations from Kerr in terms of a single additional parameter, the location of the reflection. We quote bounds on deviations for 5 events in addition to previous results obtained for GW150914. Additionally, we improve upon previous results by hierarchically combining information from all analysed events, yielding a bound on deviations of less than $2.5 \times 10^{-26}$ meters above the horizon.

Figures (5)

• Figure 1: Posteriors of $\log_{10} \epsilon$ obtained from post-merger analysis of the listed events. The corresponding 90% credible upper bounds are marked by dashed lines. The combined posterior is marked by the solid black contour and shaded region. The dashed grey shaded region shows the uniform prior of $\log_{10} \epsilon$.
• Figure 2: The one-sided 90% credible upper bound of $\log_{10} \epsilon$ obtained by combining data from multiple events as a function of the number of events included. The fit is given by $y=7.55x^{-1.33}-31.45$ and the curve asymptotes to $y=-31.43$.
• Figure 3: Posteriors of $\log_{10} \Delta r$ obtained from post-merger analysis of the listed events. $\Delta r$ is measured in meters. The corresponding 90% credible upper bounds are marked by dashed lines. The combined posterior is marked by the black contour and shaded region.
• Figure 4: The one-sided 90% credible upper bound of $\log_{10} \Delta r$ obtained by combining data from multiple events as a function of the number of events included. The fit is given by $y=7.35x^{-1.43}-26.02$ and the curve asymptotes to $y=-26.01$.
• Figure 5: The priors on coordinate distance, $\log_{10} \Delta r$. The top panels show a zoom-in of the lower and upper bounds of the priors. Individual priors are shaded, while the combined prior is shown by the black contour. The priors are approximately uniform, deviating from this only at the boundaries of the allowed range.