On Static Charged Black Holes in Type IIA on a Nearly-Kahler Coset

TL;DR

This paper investigates static, spherically symmetric black hole solutions in a specific four-dimensional supergravity theory derived from massive type IIA string theory compactified on a nearly-Kahler coset, concluding that only uncharged solutions are possible.

Contribution

It demonstrates that charged black hole solutions are forbidden in this setup due to the Stuckelberg deformation caused by the Romans' mass parameter.

Findings

Charged solutions are forbidden in the model.

Only AdS vacua or Schwarzschild-AdS black holes are allowed.

Scalar fields must have vanishing covariant derivatives.

Abstract

We study static, spherically symmetric black hole solutions in four-dimensional N=2 gauged supergravity with one vector multiplet and one hyper-tensor multiplet. This is derived from massive type IIA theory compactified on the nearly-Kahler coset space G2/SU(3). It is well-known that the Romans' mass parameter yields the Stuckelberg-type deformation of the gauge field strengths in the four-dimensional system. This deformation requires that all the (covariant) derivatives of the scalar fields must vanish and the two-form field is closed. It turns out that charged solutions are forbidden. This implies that only AdS vacua or Schwarzschild-AdS black holes are allowed as the static, spherically symmetric solutions.