论文标题
渐近全局广告的库奇演变没有对称性
Cauchy Evolution of Asymptotically Global AdS Spacetimes with No Symmetries
论文作者
论文摘要
我们提出了基于爱因斯坦方程的广义谐波形式的数值方案，提出了渐近全球广告空间的首次原理证明，没有施加对称性。在此方案中，可以根据找到一组与ADS边界条件一致的广义谐波源函数来删除所有对称假设的主要困难。在四个时空维度中，我们详细介绍了一组明确的源函数，这些源功能以完整的一般性实现了进化。类似的处方还应导致较高的时空维度，与物质场的各种耦合以及在Poincare贴片上的稳定进化。我们使用此方案使用该方案，以使用由无质量标量场来源的初始数据获得四个维空间的第一个长期稳定3+1模拟，具有负宇宙常数。我们提出了引力崩溃的初步结果，没有对称假设，随后的准正常模式响应到了大块中的静态黑洞，这对应于边界上均匀状态的进化。
We present the first proof-of-principle Cauchy evolutions of asymptotically global AdS spacetimes with no imposed symmetries, employing a numerical scheme based on the generalized harmonic form of the Einstein equations. In this scheme, the main difficulty in removing all symmetry assumptions can be phrased in terms of finding a set of generalized harmonic source functions that are consistent with AdS boundary conditions. In four spacetime dimensions, we detail an explicit set of source functions that achieves evolution in full generality. A similar prescription should also lead to stable evolution in higher spacetime dimensions, various couplings with matter fields, and on the Poincare patch. We apply this scheme to obtain the first long-time stable 3+1 simulations of four dimensional spacetimes with a negative cosmological constant, using initial data sourced by a massless scalar field. We present preliminary results of gravitational collapse with no symmetry assumptions, and the subsequent quasi-normal mode ringdown to a static black hole in the bulk, which corresponds to evolution towards a homogeneous state on the boundary.
