Relativistic Stars and the Schwarzschild Solution
Relativistic Stars and the Schwarzschild Solution
Relativistic Stars and the Schwarzschild Solution
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Stellar Metric<br />
<strong>Schwarzschild</strong> Coordinates<br />
• choose a radial coordinate r (not a “radius”!) as<br />
R 2 (r‘) = r 2 � measures <strong>the</strong> area of a 2-sphere<br />
• this choice is called geometrical coordinates or<br />
<strong>Schwarzschild</strong> coordinates (t, r, θ, φ)<br />
• now <strong>the</strong> angle dependence is written as<br />
r 2 (sin 2 ө dφ 2 + dө 2 )<br />
• for a curve with t =cnst, r= cnst, in <strong>the</strong> equatorial<br />
plane ө = π/2 <strong>and</strong> parameter φ = 0 … 2π<br />
ds 2 = r 2 dφ 2