Dolan Sam R, Kavanagh Chris, Wardell Barry
Consortium for Fundamental Physics, School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom.
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany.
Phys Rev Lett. 2022 Apr 15;128(15):151101. doi: 10.1103/PhysRevLett.128.151101.
Perturbations of Kerr spacetime are typically studied with the Teukolsky formalism, in which a pair of gauge invariant components of the perturbed Weyl tensor are expressed in terms of separable modes that satisfy ordinary differential equations. However, for certain applications it is desirable to construct the full metric perturbation in the Lorenz gauge, in which the linearized Einstein field equations take a manifestly hyperbolic form. Here we obtain a set of Lorenz-gauge solutions to the linearized vacuum field equations on Kerr-Newman-Unti-Tamburino spacetimes in terms of homogeneous solutions to the spin-2, spin-1, and spin-0 Teukolsky equations. We also derive Lorenz-gauge completion pieces representing mass and angular momentum perturbations of Kerr spacetime.
克尔时空的微扰通常用特克尔什基形式体系来研究，在该体系中，微扰外尔张量的一对规范不变分量用满足常微分方程的可分离模式来表示。然而，对于某些应用而言，希望在洛伦兹规范下构建完整的度规微扰，在这种规范下，线性化的爱因斯坦场方程具有明显的双曲形式。在此，我们根据自旋 - 2、自旋 - 1 和自旋 - 0 特克尔什基方程的齐次解，得到了克尔 - 纽曼 - 昂蒂 - 坦布里诺时空上线性化真空场方程的一组洛伦兹规范解。我们还推导了表示克尔时空质量和角动量微扰的洛伦兹规范完备项。
