Black Holes and Generalized Scalar Field

TL;DR

This paper investigates the existence of scalar hair with non-canonical kinetic terms around static, spherically symmetric black holes, concluding that certain string-inspired tachyon fields do not support such black hole solutions.

Contribution

It provides a general framework for analyzing scalar hair with non-canonical kinetic terms and applies it to specific models, showing the non-existence of solutions for tachyon fields with positive potentials.

Findings

No static black hole solutions with tachyon scalar hair and positive potential.

Develops a general equation for scalar hair with non-canonical kinetic terms.

Analyzes specific examples of kinetic functions $F(X)$.

Abstract

We study the possibility of occurrence of scalar hair with a non-canonical kinetic term for a static, spherically symmetric asymptotically flat black hole spacetime. We first obtain a general equation for this purpose and then consider various examples for the kinetic term $F(X)$ with $X=-{1\over{2}}\partial^{\mu}\phi\partial_{\mu}\phi$. Our study shows that for a tachyon field with a positive potential, which naturally arises in open string theory, asymptotically flat a static black hole solution does not exist.