Scalar Field Dark Matter: behavior around black holes

TL;DR

This paper numerically studies the evolution of massive scalar fields around black holes, revealing rapid dilution of scalar field dark matter near Schwarzschild black holes within a year.

Contribution

It introduces a hyperboloidal slicing method to simulate scalar fields around black holes, providing new insights into scalar dark matter behavior in strong gravity.

Findings

Scalar field energy density decays polynomially over time

Scalar field dilutes by five orders of magnitude in less than a year

Scalar dark matter would be rapidly depleted near black holes

Abstract

We present the numerical evolution of a massive test scalar fields around a Schwarzschild space-time. We proceed by using hyperboloidal slices that approach future null infinity, which is the boundary of scalar fields, and also demand the slices to penetrate the event horizon of the black hole. This approach allows the scalar field to be accreted by the black hole and to escape toward future null infinity. We track the evolution of the energy density of the scalar field, which determines the rate at which the scalar field is being diluted. We find polynomial decay of the energy density of the scalar field, and use it to estimate the rate of dilution of the field in time. Our findings imply that the energy density of the scalar field decreases even five orders of magnitude in time scales smaller than a year. This implies that if a supermassive black hole is the Schwarzschild solution, then scalar field dark matter would be diluted extremely fast