标题： 广义西克洛斯时空 显示英文标题

标题： Generalized Siklos space-times

摘要： 受广义相对论中超对称方法的启发，我们研究了四维洛伦兹时空，其中存在一个满足类似Killing旋量方程的复狄拉克旋量场，其中Killing常数被提升为复函数。 我们称这种几何结构为广义Siklos时空。 在推导出复空间的若干恒等式后，我们将其专门化到洛伦兹符号，其中我们证明Killing函数必须是实数，并且相应的狄拉克旋量是马约拉纳型（只要时空不是共形平坦的），并且我们得到了度规的局部形式。 我们证明纯引力自由度对应于波，而物质源通过爱因斯坦场方程通常对应于纯辐射和类空完美流体的和。 因此，我们得出结论，当Killing函数在波面上是齐次的时候，得到的是物理上有意义的情况。 显示英文摘要

摘要： Motivated by supersymmetry methods in general relativity, we study four-dimensional Lorentzian space-times with a complex Dirac spinor field satisfying a Killing-spinor-like equation where the Killing constant is promoted to a complex function. We call the resulting geometry a generalized Siklos space-time. After deriving a number of identities for complex spaces, we specialize to Lorentz signature, where we show that the Killing function must be real and that the corresponding Dirac spinor is Majorana (as long as the space-time is not conformally flat), and we obtain the local form of the metric. We show that the purely gravitational degrees of freedom correspond to waves, whereas the matter sources generically correspond, via Einstein's field equations, to a sum of pure radiation and a space-like perfect fluid. Consequently, we conclude that the physically relevant case is obtained when the Killing function is homogeneous on the wave surfaces.