No-scalar hair conjecture in asymptotic de-Sitter spacetime

TL;DR

This paper investigates the no-hair conjecture in asymptotic de-Sitter spacetime, demonstrating that scalar fields with convex or double well potentials do not support regular black hole solutions, with some exceptions found numerically.

Contribution

It provides a numerical analysis of scalar field solutions in de-Sitter spacetime, confirming the no-hair conjecture for convex and double well potentials and exploring new unstable solutions.

Findings

No regular black hole solutions for massless or convex potential scalar fields.

Existence of scalar field solutions with double well potential depends on parameters.

Unstable boson star-like solutions are found in the zero horizon radius limit.

Abstract

We discuss the no-hair conjecture in the presence of a cosmological constant. For the firststep the real scalar field is considered as the matter field and the spacetime is assumed to be static spherically symmetric. If the scalar field is massless or has a convex potential such as a mass term, it is proved that there is no regular black hole solution. For a general positive potential, we search for black hole solutions which support the scalar field with a double well potential, and find them by numerical calculations. The existence of such solutions depends on the values of the vacuum expectation value and the self-coupling constant of the scalar field. When we take the zero horizon radius limit, the solution becomes a boson star like solution which we found before. However new solutions are found to be unstable against the linear perturbation. As a result we can conclude that the no-scalar hair conjecture holds in the case of scalar fields with a convex or double well potential.