Stationary Configurations Imply Shift Symmetry: No Bondi Accretion for Quintessence / k-Essence

TL;DR

The paper demonstrates that stationary scalar field configurations require shift symmetry, leading to the conclusion that k-Essence and Quintessence cannot sustain steady Bondi accretion onto black holes, with implications for their field redefinitions.

Contribution

It establishes the necessity of shift symmetry for stationary configurations in scalar fields and shows the impossibility of steady accretion for k-Essence and Quintessence.

Findings

Stationary configurations imply shift symmetry in scalar fields.

k-Essence and Quintessence cannot have exact steady Bondi accretion.

Stationary fields are linear in Killing time under shift symmetry.

Abstract

In this paper we show that, for general scalar fields, stationary configurations are possible for shift symmetric theories only. This symmetry with respect to constant translations in field space should either be manifest in the original field variables or reveal itself after an appropriate field redefinition. In particular this result implies that neither k-Essence nor Quintessence can have exact steady state / Bondi accretion onto Black Holes. We also discuss the role of field redefinitions in k-Essence theories. Here we study the transformation properties of observables and other variables in k-Essence and emphasize which of them are covariant under field redefinitions. Finally we find that stationary field configurations are necessarily linear in Killing time, provided that shift symmetry is realized in terms of these field variables.