From Fake Supergravity to Superstars

TL;DR

This paper applies fake supergravity to 5D asymptotically AdS spacetimes with scalar and gauge fields, deriving solutions including superstars and analyzing their holographic properties.

Contribution

It develops a fake supergravity framework with a specific superpotential form for charged solutions in AdS, extending previous methods to include gauge fields and boundary conditions.

Findings

Derived first order equations for charged solutions

Found solutions including superstars with horizons

Computed holographic parameters of the solutions

Abstract

The fake supergravity method is applied to 5-dimensional asymptotically AdS spacetimes containing gravity coupled to a real scalar and an abelian gauge field. The motivation is to obtain bulk solutions with R x S^3 symmetry in order to explore the AdS/CFT correspondence when the boundary gauge theory is on R x S^3. A fake supergravity action, invariant under local supersymmetry through linear order in fermion fields, is obtained. The gauge field makes things more restrictive than in previous applications of fake supergravity which allowed quite general scalar potentials. Here the superpotential must take the form W(\phi) ~ exp(-k\phi) + c exp(2\phi/(3k)), and the only freedom is the choice of the constant k. The fermion transformation rules of fake supergravity lead to fake Killing spinor equations. From their integrability conditions, we obtain first order differential equations which we solve analytically to find singular electrically charged solutions of the Lagrangian field equations. A Schwarzschild mass term can be added to produce a horizon which shields the singularity. The solutions, which include "superstars", turn out to be known in the literature. We compute their holographic parameters.