No-hair theorems for non-canonical self-gravitating static multiple scalar fields

TL;DR

This paper establishes no-hair theorems for non-canonical scalar fields in static, spherically symmetric spacetimes, showing that black holes and horizonless objects cannot support non-trivial scalar configurations under certain conditions.

Contribution

It introduces new no-hair theorems for non-canonical scalar fields and derives a novel divergence identity to support these results.

Findings

Black hole solutions are limited to Schwarzschild with constant scalar fields.

No static, horizonless solutions with non-trivial scalar fields exist under the assumptions.

Reflecting compact objects cannot support non-trivial scalar fields in their exterior regions.

Abstract

We prove under certain assumptions no-hair theorems for non-canonical self-gravitating static multiple scalar fields in spherically symmetric spacetimes. It is shown that the only static, spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. We also prove that there are no static, horizonless, asymptotically flat, spherically symmetric solutions with static scalar fields and a regular center. The last theorem shows that the static, asymptotically flat, spherically symmetric reflecting compact objects with Neumann boundary conditions can not support a non-trivial self-gravitating non-canonical (and canonical) multi-scalar map in their exterior spacetime regions. In order to prove the no-hair theorems we derive a new divergence identity.