The Kerr spacetime is perhaps the most astrophysically important of the currently known exact solutions to the Einstein field equations. Whenever spacetimes can be put in unit-lapse form it becomes possible to identify some very straightforward timelike geodesics, (the "rain" geodesics), making the physical interpretation of these spacetimes particularly clean and elegant. The most well-known of these unit-lapse formulations is the Painleve-Gullstrand form of the Schwarzschild spacetime, though there is also a Painleve-Gullstrand form of the Lense-Thirring (slow rotation) spacetime. More radically there are also two known unit-lapse forms of the Kerr spacetime -- the Doran and Natario metrics -- though these are not precisely in Painleve-Gullstrand form. Herein we shall seek to explicate the most general unit-lapse form of the Kerr spacetime. While at one level this is "merely" a choice of coordinates, it is a strategically and tactically useful choice of coordinates, thereby making the technically challenging but astrophysically crucial Kerr spacetime somewhat easier to deal with.

中文翻译：

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克尔时空的单位推移版本

克尔时空可能是目前已知的爱因斯坦场方程精确解中最重要的天体物理学。每当可以将时空置于单位推移形式时，就可以识别一些非常简单的类时测地线（“雨”测地线），从而使这些时空的物理解释特别干净和优雅。这些单位延时公式中最著名的是 Schwarzschild 时空的 Painleve-Gullstrand 形式，尽管也有 Lense-Thirring（慢速旋转）时空的 Painleve-Gullstrand 形式。更根本的是，还有两种已知的克尔时空单位延迟形式——Doran 和 Natario 度量——尽管这些并不完全是 Painleve-Gullstrand 形式。在这里，我们将试图解释克尔时空的最一般的单位推移形式。虽然在一个层面上，这“仅仅是”坐标的选择，但它是战略和战术上有用的坐标选择，从而使在技术上具有挑战性但在天体物理学上至关重要的克尔时空更容易处理。