论文标题
关于超跨度无空间的不稳定性
On the instability of ultracompact horizonless spacetimes
论文作者
论文摘要
最近的结果激发了报道没有稳定的光环的无水平对象的不稳定，我们重新审视了此类结构的线性稳定性。特别是，我们考虑了一个外部的kerr时空，在表面上截断了无质量标量的条件。当表面在重力电势中充分深处时，该时空具有巨大的环境和光环。我们确定，当时空是在与麦格尔奇相关的机制中足够紧凑的时线性，模式不变的。特别是，这种不稳定性具有关联的零模型。在大的多个多极数字上，零模式存在的关键表面位置恰好是沿赤道的Ergosurface的位置。我们表明，当表面不在麦格雷奇之外时，这种模式不存在，并且任何推定的线性不稳定性机制都作用于时标$τ\ gtrsim 10^5 m $，其中$ m $是黑洞质量。因此，我们的结果表明，即使存在旋转和灯环，至少某些类别的物体在没有登台的情况下是线性稳定的。
Motivated by recent results reporting the instability of horizonless objects with stable light rings, we revisit the linearized stability of such structures. In particular, we consider an exterior Kerr spacetime truncated at a surface where Dirichlet conditions on a massless scalar are imposed.This spacetime has ergoregions and light rings when the surface is placed sufficiently deep in the gravitational potential. We establish that the spacetime is linearly, mode-unstable when it is sufficiently compact, in a mechanism associated with the ergoregion. In particular, such instability has associated zero-modes. At large multipole number the critical surface location for zero modes to exist is precisely the location of the ergosurface along the equator. We show that such modes don't exist when the surface is outside the ergoregion, and that any putative linear instability mechanism acts on timescales $τ\gtrsim 10^5 M$, where $M$ is the black hole mass. Our results indicate therefore that at least certain classes of objects are linearly stable in the absence of ergoregions, even if rotation and light rings are present.
