No-Go Theorem for Horizon-Shielded Self-Tuning Singularities

TL;DR

This paper proves a no-go theorem showing that shielding a singularity with a horizon in self-tuning solutions to the cosmological constant problem is impossible under certain energy conditions, unless spatial curvature is introduced.

Contribution

It establishes a general no-go theorem for horizon shielding in self-tuning brane models, valid across various field contents and modifications, with exceptions involving spatial curvature.

Findings

Shielding singularities with horizons is generally impossible without violating energy conditions.

The no-go theorem applies regardless of field types, symmetries, or higher derivative terms.

Introducing spatial curvature can evade the no-go theorem, allowing horizon shielding.

Abstract

We derive a simple no-go theorem relating to self-tuning solutions to the cosmological constant for observers on a brane, which rely on a singularity in an extra dimension. The theorem shows that it is impossible to shield the singularity from the brane by a horizon, unless the positive energy condition (rho+p >= 0) is violated in the bulk or on the brane. The result holds regardless of the kinds of fields which are introduced in the bulk or on the brane, whether Z_2 symmetry is imposed at the brane, or whether higher derivative terms of the Gauss-Bonnet form are added to the gravitational part of the action. However, the no-go theorem can be evaded if the three-brane has spatial curvature. We discuss explicit realizations of such solutions which have both self-tuning and a horizon shielding the singularity.