The metric due to the gravitational field of a spherical mass is described by the schwarzschild metric(adsbygoogle = window.adsbygoogle || []).push({});

ds^{2}= c^{2}(1 - R/r) dt^{2}- (1 - R/r)^{-1}dr^{2}- r^{2}d[tex]\Omega[/tex]^{2}

Where [tex]\Omega[/tex] is the solid angle, and R is the schwarzschild radius.

What are the physical meanings of the coordinates t and r? My understanding is that r is simply the radial distance and t is the proper time of a STATIONARY observer at infinity.

If two events are separated by dt, dr, d[tex]\Omega[/tex], how would they seem to a stationary observer at some arbitrary distance r_{0}? What is dr' and dt' (measured in the stationary frame of the observer) in terms of dr and dt? How about for a non-stationary observer?

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# Physical meanings of universal coordinates in schwarzschild metric

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