Proca in an Expanding Universe

TL;DR

This paper investigates how a positive cosmological constant affects superradiant instabilities of massive vector fields around rotating black holes, revealing a transition from growth to decay in the presence of dark energy.

Contribution

It extends previous superradiance studies by incorporating a cosmological constant and using numerical relativity to show the transition from instability to decay.

Findings

Instability growth turns into decay with positive cosmological constant.

Numerical evolution with GRBoondi demonstrates new phenomenology.

Results suggest potential for future studies on gravitational emission decay.

Abstract

The superradiant growth of massive vector fields in rotating black hole spacetimes has garnered significant attention in recent literature. However, the majority of these studies overlook the influence of a cosmological constant, which likely constitutes the primary energy content of our universe. In this paper, we extend recent research by incorporating a cosmological constant into the Einstein+Proca system and numerically evolving the resulting equations of motion. Utilizing the newly released GRBoondi numerical relativity code, designed specifically for the numerical evolution of (generalized) Proca fields, we discover that parameters causing a growing instability in the $\Lambda = 0$ scenario transition to a decaying state when $\Lambda > 0$. This results in a more intriguing phenomenology. These simulations pave the way for future full Einstein+Proca simulations to explore the secular decay of the resultant cloud from gravitational emission.