Schwarzschild

Monday, 11 January 2010

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Posted by Schwarzschild at 21:02

Schwarzschild: Techno/Electro In Schwarzschild coordinates, the Schwarzschild metric has the form: c^2 {d \tau}^{2} = \left(1 - \frac{r_s}{r} \right) c^2 dt^2 - \frac{dr^2}{1-\frac{r_s}{r}} - r^2 \left(d\theta^2 + \sin^2\theta \, d\varphi^2\right) where τ is the proper time (time measured by a clock moving with the particle) in seconds, c is the speed of light in meters per second, t is the time coordinate (measured by a stationary clock at infinity) in seconds, r is the radial coordinate (circumference of a circle centered on the star divided by 2π) in meters, θ is the colatitude (angle from North) in radians, φ is the longitude in radians, and rs is the Schwarzschild radius (in meters) of the massive body, which is related to its mass M by r_{s} = \frac{2GM}{c^{2}} where G is the gravitational constant.[1]

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