球对称引力场通过广义相对论经典检验的新度规
New metrics of a spherically symmetric gravitational field passing classical tests of General Relativity
摘要：
得到了球坐标系下球对称引力场和角动量保持所有对称性的度量的一般形式。这样的度量可以具有$g_{01}(r)\neq 0$。牛顿极限唯一地定义了$g_{00}(r)$。如果度规的时间径向部分的行列式为$-1$，则在这种度规下的测地运动精确地再现了行星轨道的岁差、双星的近星点推进、光的偏转和{Shapiro时间延迟}。在这个模型中，光的径向往返的总时间与史瓦西模型相同，但它允许光线以不同的速度传播到大质量物体或从大质量物体传播。通过测量这些速度可以获得$g_{01}(r) $的值。所有这些度规都满足爱因斯坦的场方程
英文摘要：
A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines $g_{00}(r)$. Geodesic motion under such metric exactly reproduces the precession of a planetary orbit, periastron advance of a binary, deflection of light and {Shapiro time delay} if the determinant of the time-radial parts of the metric is $-1$. In this model, the total time for a radial round trip of light is as in the Schwarzschild model, but it allows for light rays to have different speeds propagating toward or from the massive object. The value of $g_{01}(r) $ could be obtained by measuring these speeds. All of these metrics do satisfy Einstein's field equations
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