2004/09/13 | S黑洞光线塌陷[Schwarzschild Black Hole--Radial Infall]
类别(Ω〖物理〗) | 评论(0) | 阅读(38) | 发表于 13:53
From the static isotropic metric for general relativity,
(1)

where
(2)

(3)



(4)

For radial infall, J = 0 and
(5)

For a particle starting at rest at R = r,
(6)

(7)

(8)

(9)

Switch to non-dimensionalized coordinates with , then

(10)

where the constant has been chosen such that . Now introduce the "cycloid parameter" defined by
(11)

giving
(12)

(13)

(14)

so combining (9) and (8) gives


]
(15)

(16)

Now,
(17)

Here and

so

Plugging these in
(18)

Note that
(19)


so


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