Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Heretofore, only {\it configurations} of negative mass had been found \cite{Belletete:2013nqa,Mbarek:2014ppa}, the analysis did not address stability or dynamics. In this paper, we analyze both of these criteria. We demonstrate the existence of {\it stable}, static, negative mass bubbles in an asymptotically de Sitter space-time. The bubbles are solutions of the Einstein equations and correspond to an interior region of space-time containing a specific mass distribution, separated by a thin wall from the exact, negative mass Schwarzschild-de Sitter space-time in the exterior. We apply the Israel junction conditions at the wall. For the case of an interior corresponding simply to de Sitter space-time with a different cosmological constant from the outside space-time, separated by a thin wall with energy density that is independent of the radius, we find static but unstable solutions which satisfy the dominant energy condition everywhere. The bubbles can collapse through spherically symmetric configurations to the exact, singular, negative mass Schwarzschild-de Sitter solution. Interestingly, this provides a counter-example of the cosmic censorship hypothesis. Alternatively, the junction conditions can be used to give rise to an interior mass distribution that depends on the potential for the radius of the wall. We show that for no choice of the potential, for positive energy density on the wall that is independent of the radius, can we get a solution that is non-singular at the origin. However, if we allow the energy density on the wall to depend on the radius of the bubble, we can find {\it stable}, static, non-singular solutions of negative mass which everywhere satisfy the dominant energy condition.

中文翻译：

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德西特时空中稳定的薄壁负质量气泡

只要相应的能量-动量张量满足主导能量条件，负质量就具有完美的物理意义。迄今为止，只发现了负质量的 {\it 配置} \cite{Belletete:2013nqa,Mbarek:2014ppa}，该分析没有解决稳定性或动力学问题。在本文中，我们分析了这两个标准。我们证明了在渐近德西特时空中存在 {\it stable}、静态、负质量气泡。气泡是爱因斯坦方程的解，对应于包含特定质量分布的时空内部区域，由薄壁与外部精确的负质量 Schwarzschild-de Sitter 时空隔开。我们在墙上应用以色列连接条件。对于简单对应于德西特时空的内部情况，其宇宙常数与外部时空不同，由能量密度与半径无关的薄壁隔开，我们找到静态但不稳定的解，满足无处不在的主导能量条件。气泡可以通过球对称配置坍塌成精确的、奇异的、负质量 Schwarzschild-de Sitter 解。有趣的是，这提供了宇宙审查假说的反例。或者，连接条件可用于产生取决于壁半径的势能的内部质量分布。我们表明，对于电位没有选择，对于与半径无关的壁上的正能量密度，我们能得到一个在原点非奇异的解吗？然而，如果我们允许壁上的能量密度取决于气泡的半径，我们可以找到 {\it stable} 的负质量的静态非奇异解，它处处满足主导能量条件。