A Self-tuning Exact Solution and the Non-existence of Horizons in 5d Gravity-Scalar System

TL;DR

This paper presents an exact 5d gravity-scalar domain wall solution with naked singularities, demonstrating the non-existence of horizons and discussing the physical implications of these solutions.

Contribution

It provides a self-tuning exact solution with a specific exponential potential coefficient derived from string theory compactification, and proves the non-existence of horizons in such setups.

Findings

Exact thick domain wall solution with naked singularities

Proof of non-existence of horizons in these solutions

Discussion on physical relevance of naked singularities

Abstract

We present an exact thick domain wall solution with naked sigularities to five dimensional gravity coupled with a scalar field with exponential potential. In our solution we found exactly the special coefficient of the exponent as coming from compactification of string theory with cosmological constant. We show that this solution is self-tuning when a 3-brane is included. In searching for solution with horizon we found a similar exact solution with fine-tuned exponent coefficient with an integration constant. Failed to find a solution with horizon we prove the non-existence of horizons. These naked sigularities actually can't be resolved by horizon. We also comment on the physical relevance of this solution.}