On cosmological properties of black-hole hair in linearly coupled scalar-Gauss-Bonnet theory

TL;DR

This paper studies the behavior of scalar hair around black holes in de Sitter space within a specific scalar-Gauss-Bonnet theory, revealing superhorizon growth and energy flux characteristics.

Contribution

It demonstrates that scalar hair exhibits superhorizon growth due to scalar field dynamics in de Sitter space, independent of black hole specifics, and discusses implications for static solution construction.

Findings

Scalar hair grows on superhorizon scales in de Sitter spacetime.

Growth is due to scalar field dynamics, not black hole properties.

Scalar hair carries a steady outward energy flux.

Abstract

We investigate the superhorizon behavior of scalar hair sourced by black holes in de Sitter spacetime in the linearly coupled shift-symmetric scalar-Gauss-Bonnet theory. Working in the test-field regime, we show that this hair exhibits both temporal and spatial growth on superhorizon scales. This growth is not a special consequence of the black hole, but instead follows from the dynamics of a minimally coupled massless scalar field in expanding de Sitter spacetime. Moreover, it is not even specific to black holes, but also arises for a point scalar charge in de Sitter, indicating that a scalarized black hole acts effectively as a localized subhorizon source of scalar perturbations. Backreaction, when important, first arises on subhorizon scales and does not by itself eliminate the superhorizon profile. The time-dependent scalar hair also carries a steady outward energy flux, which frames the test-field regime as a transient, and helps explain the difficulties encountered in attempts to construct self-consistent static solutions.