Evading Derrick's theorem in curved space: Static metastable spherical domain wall

Understand

A recent analysis by one of the authors\cite{Perivolaropoulos:2018cgr} has pointed out that Derrick's theorem can be evaded in curved space.

• Here we extend that analysis by demonstrating the existence of a static metastable solution in a wide class of metrics that include a Schwarzschild-Rindler-AntideSitter spacetime (Grumiller metric) defined as $ds^2= f(r) dt^2 - f(r)^{-1} dr^2 - r^2 (d\theta^2 +\sin^2\theta d\phi^2)$ with $f(r)=1-\frac{2Gm}{r}+2br-\frac{\Lambda}{3} r^2$ ($\Lambda<0\; b<0$).
• This metric emerges generically as a spherically symmetric vacuum solution in a class of scalar-tensor theories\cite{Grumiller:2010bz} as well as in Weyl conformal gravity\cite{Mannheim:1988dj}.
• It also emerges in General Relativity (GR) in the presence of a cosmological constant and a proper spherically symmetric perfect fluid.