标题： 球对称性作为无约束超抛物演化的一个测试案例 显示英文标题

标题： Spherical symmetry as a test case for unconstrained hyperboloidal evolution

摘要： 我们考虑数值相对论中的双曲初始值问题，其动机是希望通过包含未来null无限的数值网格来演化辐射的致密天体，如黑洞双星。 无约束演化方案有望实现最佳效率，但在null无限处难以正则化，因为在该处紧化后的爱因斯坦方程在形式上是奇异的。 在本工作中，我们处理了球对称情况，这已经提出了非平凡的问题，并构成了重要的第一步。 我们已经使用广义BSSN和Z4方程与标量场耦合进行了稳定的数值演化。 关键要素是找到一个适当的度规函数演化方程，并调整约束阻尼项以处理null无限。 显示英文摘要

摘要： We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution schemes promise optimal efficiency, but are difficult to regularize at null infinity, where the compactified Einstein equations are formally singular. In this work we treat the spherically symmetry case, which already poses nontrivial problems and constitutes an important first step. We have carried out stable numerical evolutions with the generalized BSSN and Z4 equations coupled to a scalar field. The crucial ingredients have been to find an appropriate evolution equation for the lapse function and to adapt constraint damping terms to handle null infinity.