On Existence of Self-Tuning Solutions in Static Braneworlds without Singularities

TL;DR

This paper investigates the conditions for self-tuning solutions in static braneworld models, demonstrating that certain energy conditions cannot be simultaneously satisfied, and provides examples including Lifshitz scaling backgrounds.

Contribution

It proves the incompatibility of energy conditions in static regular braneworlds with broken Lorentz invariance and offers explicit solutions like Lifshitz backgrounds.

Findings

NEC and positive energy density cannot both hold in static regular backgrounds

Examples of solutions with Lifshitz scaling are provided

Certain energy conditions are incompatible in these models

Abstract

A static self-tuning SO(3)xZ_2 symmetric and translation invariant braneworld setup with flat brane is considered. We discuss the null energy conditions (NEC) for matter on the brane and in the bulk and prove that for the static regular background with broken Lorentz invariance the NEC and positiveness of the total energy density on the brane and NEC in the bulk cannot be satisfied simultaneously. Then we give some examples and elaborate some special cases. For instance, we provide a macroscopic solution for a background with Lifshitz scaling.