Energy Bounds in Designer Gravity

TL;DR

This paper analyzes energy bounds in asymptotically anti-de Sitter gravity coupled with tachyonic scalar fields, establishing conditions under which the gravitational energy is bounded below in designer gravity theories.

Contribution

It provides a general proof that Hamiltonian generators are finite in these theories and derives explicit energy bounds based on boundary conditions and scalar potential properties.

Findings

Hamiltonian generators are finite and well-defined.

Derived lower bounds on gravitational energy under specific conditions.

Confirmed the form of generators includes scalar field contributions.

Abstract

We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound in d greater than or equal to 4 spacetime dimensions. The boundary conditions in these ``designer gravity'' theories are defined in terms of an arbitrary function W. We give a general argument that the Hamiltonian generators of asymptotic symmetries for such systems will be finite, and proceed to construct these generators using the covariant phase space method. The direct calculation confirms that the generators are finite and shows that they take the form of the pure gravity result plus additional contributions from the scalar fields. By comparing the generators to the spinor charge, we derive a lower bound on the gravitational energy when i) W has a global minimum, ii) the Breitenlohner-Freedman bound is not saturated, and iii) the scalar potential V admits a certain type of "superpotential."