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arXiv 1408.4601gr-qc
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修订的Kerr-Schild模型

The Kerr-Schild ansatz revised

Donato Bini, Andrea Geralico, Roy P. Kerr

备注：
11 pages, no figures; published version
发表信息：
IJGMMP 7, 693 (2010)
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摘要：

克尔-席德度规被引入为平坦时空度规和零向量场平方的线性叠加，比如$\boldsymbol{k}$，乘以某个标量函数，比如$H$。Kerr解的基本假设是$\boldsymbol{k}$既测地线又无剪切。本文放宽了这一条件，并通过将Kerr-Schild度规看作闵可夫斯基时空的{ \it精确线性扰动}来修正Kerr-Schild度量.以标量函数$H$为微扰函数，使爱因斯坦场方程按$H$的幂级数逐阶求解.结果表明，由于三阶和二阶方程的存在，该同余式必须是测地线和无剪力的，从而导出了克尔解的另一种推导方法。

英文摘要：

Kerr-Schild metrics have been introduced as a linear superposition of the flat spacetime metric and a squared null vector field, say $\boldsymbol{k}$, multiplied by some scalar function, say $H$. The basic assumption which led to Kerr solution was that $\boldsymbol{k}$ be both geodesic and shearfree. This condition is relaxed here and Kerr-Schild ansatz is revised by treating Kerr-Schild metrics as {\it exact linear perturbations} of Minkowski spacetime. The scalar function $H$ is taken as the perturbing function, so that Einstein's field equations are solved order by order in powers of $H$. It turns out that the congruence must be geodesic and shearfree as a consequence of third and second order equations, leading to an alternative derivation of Kerr solution.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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