Spacetime of rotating black holes surrounded by massive scalar charges

TL;DR

This paper develops spectral methods to accurately model the spacetime of rotating black holes with massive scalar fields, enabling precise predictions of horizon properties and facilitating new tests of fundamental physics through gravitational-wave and electromagnetic observations.

Contribution

It introduces a spectral approach to construct rotating black hole spacetimes with massive scalar charges and computes leading-order horizon modifications for various scalar couplings.

Findings

Achieves residual errors below 10^{-5} for scalar fields with short Compton wavelengths.

Provides leading-order shifts in surface gravity and horizon angular velocity.

Enables potential new tests of scalar fields via gravitational-wave and electromagnetic signals.

Abstract

Massive scalar charges are ubiquitous in extensions to General Relativity and the Standard Model in particle physics. We describe spectral methods which can accurately construct the spacetime of rotating black holes with dimensionless spin up to $a \leq 0.8$ surrounded by massive scalar fields nonminimally coupled to spacetime curvature. We consider axi dilaton, dynamical Chern Simons, and scalar Gauss Bonnet couplings, and obtain leading order solutions for both the scalar field and the associated metric modifications. Our method accurately resolves massive scalar fields with Compton wavelengths as short as 5 times the black hole mass, achieving residual errors $\lesssim 10^{-5}$, and yields the corresponding leading order spacetime modifications with residual errors $\lesssim 10^{-3}$. Using the constructed spacetimes, we computes the leading-order shifts in the surface gravity and the angular velocity of the event horizon, important information for computing the quasinormal modes. These results pave the way to incorporate massive scalar charges into electromagnetic observations and gravitational-wave detections of black holes, potentially enabling new probes of fundamental scalar degrees of freedom.