标题： 规避德里克定理的弯曲空间：静态亚稳态球形域壁 显示英文标题

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

摘要： 一位作者\cite{Perivolaropoulos:2018cgr}最近的分析指出，德里克定理在弯曲空间中可以被规避。在这里，我们通过展示在广泛的度规类中存在静态亚稳态解来扩展这一分析，这些度规类包括定义为 $ds^2= f(r) dt^2 - f(r)^{-1} dr^2 - r^2 (d\theta^2 +\sin^2\theta d\phi^2)$ 的施瓦西-林德勒-反德西特时空（格鲁米勒度规）（$f(r)=1-\frac{2Gm}{r}+2br-\frac{\Lambda}{3} r^2$ ($\Lambda<0\; b<0$)）。 这种度规作为球对称真空解，在一类标量张量理论\cite{Grumiller:2010bz} 以及在魏尔共形引力\cite{Mannheim:1988dj} 中普遍出现。它也出现在广义相对论（GR）中，在存在宇宙常数和适当的球对称完美流体的情况下。我们证明了这种度规支持一个静态的球对称亚稳态孤子标量场解，这对应于一个球形域壁。我们数值推导出静态解，并确定了度规参数范围$m, b, \Lambda$，在这个范围内球形壁是亚稳态的。我们的结果得到了标量场能量泛函的边界条件最小化以及标量场演化的数值模拟的支持。 亚稳态解可以很好地近似为 $\phi(r) = Tanh\left[q (r-r_0)\right]$，其中 $r_0$ 是依赖于度规参数的亚稳态壁的半径，$q$ 决定了壁的宽度。 我们还发现了薄球形壁解的引力效应及其对背景度规的反作用，这使得其形成成为可能。 我们证明这种反作用并不会阻碍解的亚稳定性，尽管它可能会改变对应于亚稳定性的参数范围。 显示英文摘要

摘要： 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.