Constraining the spin parameter of near-extremal black holes using LISA

TL;DR

This paper presents a model showing that LISA can measure the spin of near-extremal black holes with unprecedented precision, leveraging the unique gravitational wave signatures of such objects.

Contribution

The paper introduces a waveform model and analysis demonstrating that LISA can precisely measure near-extremal black hole spins, surpassing previous limits and utilizing geodesic properties for high accuracy.

Findings

LISA can measure black hole spins near 1 with 3-4 orders of magnitude better precision than moderate spins.

High precision is due to the spin dependence of the radial inspiral, dominated by geodesic properties.

LISA could identify black holes with spins up to 1-10^{-9}, exceeding the Thorne limit.

Abstract

We describe a model that generates first order adiabatic EMRI waveforms for quasi-circular equatorial inspirals of compact objects into rapidly rotating (near-extremal) black holes. Using our model, we show that LISA could measure the spin parameter of near-extremal black holes (for $a \gtrsim 0.9999$) with extraordinary precision, $\sim$ 3-4 orders of magnitude better than for moderate spins, $a \sim 0.9$. Such spin measurements would be one of the tightest measurements of an astrophysical parameter within a gravitational wave context. Our results are primarily based off a Fisher matrix analysis, but are verified using both frequentest and Bayesian techniques. We present analytical arguments that explain these high spin precision measurements. The high precision arises from the spin dependence of the radial inspiral evolution, which is dominated by geodesic properties of the secondary orbit, rather than radiation reaction. High precision measurements are only possible if we observe the exponential damping of the signal that is characteristic of the near-horizon regime of near-extremal inspirals. Our results demonstrate that, if such black holes exist, LISA would be able to successfully identify rapidly rotating black holes up to $a = 1-10^{-9}$ , far past the Thorne limit of $a = 0.998$.