Non-asymptotically AdS/dS Solutions and Their Higher Dimensional Origins

TL;DR

This paper finds and analyzes exact Einstein-Maxwell-dilaton solutions in arbitrary dimensions, which are not asymptotically AdS/dS but can be uplifted to higher dimensions with different asymptotic behaviors, aiding holographic understanding.

Contribution

It provides new exact solutions in Einstein-Maxwell-dilaton gravity and explores their higher-dimensional origins and holographic implications.

Findings

Solutions can have various horizon types and curvatures.

Some solutions uplift to higher dimensions with different asymptotics.

Insights into holography of non-asymptotically AdS/dS spacetimes.

Abstract

We look for and analyze in some details some exact solutions of Einstein-Maxwell-dilaton gravity with one or two Liouville-type dilaton potential(s) in an arbitrary dimension. Such a theory could be obtained by dimensionally reducing Einstein-Maxwell theory with a cosmological constant to a lower dimension. These (neutral/magnetic/electric charged) solutions can have a (two) black hole horizon(s), cosmological horizon, or a naked singularity. Black hole horizon or cosmological horizon of these solutions can be a hypersurface of positive, zero or negative constant curvature. These exact solutions are neither asymptotically flat, nor asymptotically AdS/dS. But some of them can be uplifted to a higher dimension, and those higher dimensional solutions are either asymptotically flat, or asymptotically AdS/dS with/without a compact constant curvature space. This observation is useful to better understand holographic properties of these non-asymptotically AdS/dS solutions.