论文标题
渐近广告空间的数值库奇演变，没有对称性
Numerical Cauchy evolution of asymptotically AdS spacetimes with no symmetries
论文作者
论文摘要
在本论文中，我提出了第一个能够在溶液上没有对称性要求下对反射边界条件进行渐近广告空间的Cauchy演变。该方案基于爱因斯坦方程的广义谐波公式。删除所有对称假设的主要困难可以用找到与ADS边界条件一致的一组广义谐波源函数来表达。我详细介绍了处方，以获取以完全通用性达到稳定进化的一组源函数。该处方会导致第一个长时间稳定的3+1个仿真四个维空间的模拟，而笛卡尔坐标为负宇宙常数。我显示了重力塌陷的结果，没有对称假设，随后的响声响起，散装中的静态黑洞，这与边界上均匀状态的进化相对应。此外，据认为，在Kerr-Ads时空中，该方案非常适合研究黑洞超级的研究 - 散射旋转黑洞的波的放大。该陈述得到了扰动Kerr-Ads的初步模拟的结果。
In this thesis, I present the first numerical scheme able to perform Cauchy evolutions of asymptotically AdS spacetimes with reflective boundary conditions under no symmetry requirements on the solution. The scheme is based on the generalised harmonic formulation of the Einstein equations. The main difficulty in removing all symmetry assumptions can be phrased in terms of finding a set of generalised harmonic source functions that are consistent with the AdS boundary conditions. I detail a prescription to obtain the set of source functions that achieves stable evolution in full generality. This prescription leads to the first long-time stable 3+1 simulations of four dimensional spacetimes with a negative cosmological constant in Cartesian coordinates. I show results of gravitational collapse with no symmetry assumptions, and the subsequent ringdown to a static black hole in the bulk, which corresponds to evolution towards a homogeneous state on the boundary. Furthermore, it is argued that this scheme is well-suited for the study of black hole superradiance -- the amplification of waves scattering off a rotating black hole -- in Kerr-AdS spacetime. This statement is supported by the results of a preliminary simulation of perturbed Kerr-AdS.
