Probing vector hair of black holes with extreme mass ratio inspirals

TL;DR

This paper explores how gravitational wave observations from extreme mass ratio inspirals can detect or constrain vector hair on black holes predicted by bumblebee gravity, surpassing current observational limits.

Contribution

It demonstrates that space-based gravitational wave detectors can significantly improve constraints on black hole vector hair in bumblebee gravity models.

Findings

One-year EMRI observations can probe vector charge as small as 10^{-3}.

Gravitational wave detection offers three orders of magnitude tighter constraints than EHT.

Black hole metric deviations due to vector hair are detectable with upcoming GW observatories.

Abstract

The bumblebee gravity model, with a vector field nonminimally coupled to gravity, is a natural extension of the Einstein-Maxwell theory. In this theory, a black hole can carry a vector hair, making the metric deviate from the Schwarzschild metric. To investigate the detectability of the vector hair, we consider an Extreme Mass Ratio Inspiral (EMRI) system, where a stellar-mass black hole inspiraling into a supermassive black hole. We find that, with a one-year observation of an EMRI by a space-based gravitational-wave detector, we can probe the vector charge as small as $Q\sim 10^{-3}$ in the bumblebee gravity model, which is about three orders of magnitude tighter comparing to current EHT observations.