Evading Derrick's theorem in curved space: Static metastable spherical
  domain wall
  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. We demonstrate that this metric supports a static
spherically symmetric metastable soliton scalar field solution that corresponds
to a spherical domain wall. We derive the static solution numerically and
identify a range of parameters $m, b, \Lambda$ of the metric for which the
spherical wall is metastable. Our result is supported by both a minimization of
the scalar field energy functional with proper boundary conditions and by a
numerical simulation of the scalar field evolution. The metastable solution is
very well approximated as $\phi(r) = Tanh\left[q (r-r_0)\right]$ where $r_0$ is
the radius of the metastable wall that depends on the parameters of the metric
and $q$ determines the width of the wall. We also find the gravitational
effects of the thin spherical wall solution and its backreaction on the
background metric that allows its formation. We show that this backreaction
does not hinder the metastability of the solution even though it can change the
range of parameters that correspond to metastability.
