标题： Taub-NUT瞬子作为Kerr的自对偶模拟 显示英文标题

标题： Taub-NUT Instanton as the Self-dual Analog of Kerr

摘要： 最近有人猜想，一种特定的真空Kerr-Schild时空，可以视为Kerr度规的自对偶类似物，等价于自对偶Taub-NUT瞬子。 我们通过将Cartan-Karlhede算法应用于每个度规，并证明对于合适的空四重矢选择，该算法会为两者产生相同的不变量和线性各向同性群，从而确立它们的等价性。 虽然众所周知，Taub-NUT解及其自对偶版本具有双重Kerr-Schild形式，但最近才观察到自对偶Taub-NUT瞬子具有单个Kerr-Schild形式。 我们比较的两个度规可以被视为具有洛伦兹(1,3)符号的复数度规，或具有克莱因(2,2)符号的实数度规；在这里我们采用后一种观点。 当空四重矢由两对复共轭空矢组成而非四个实独立空矢时，会出现显著的简化。 作为额外收获，我们的工作提供了首次使用这种类型空四重矢应用Cartan-Karlhede算法的例子。 显示英文摘要

摘要： It was recently conjectured that a certain vacuum Kerr-Schild spacetime, which may be regarded as a self-dual analog of the Kerr metric, is equivalent to the self-dual Taub-NUT instanton. We confirm this conjecture by applying the Cartan-Karlhede algorithm to each metric and showing that for suitable choices of null tetrad, the algorithm leads to the same invariants and linear isotropy groups for both, establishing their equivalence. While it is well-known that the Taub-NUT solution and its self-dual version admit a double Kerr-Schild form, the observation that the self-dual Taub-NUT instanton admits a single Kerr-Schild form has only been made very recently. The two metrics we compare may be regarded as either complex metrics with Lorentzian (1,3) signature or real metrics with Kleinian (2,2) signature; here we take the latter view. Significant simplifications occur when the null tetrads are chosen to consist of two pairs of complex conjugate null vectors rather than four real independent ones. As a bonus, our work provides the first example of applying the Cartan-Karlhede algorithm using a null tetrad of this type.