I'm doing my grade 12 ISU and I've taught myself how to work around spherical coordinate systems, however, the schwarzschild metric confuses me.

I'm aware that the two angles represent the azimuthal angle and the angle of inclination (measured from the zenith), rs represents the schwarzschild radius, ts represents the "proper time" (measured in an inertial frame of reference), tm represents the time in motion, or the time measured by a distant observer for an event to occur, which is in a non-intertial frame of reference and of course c stands for the speed of light.

Where the problems begin are the d (distance) in the metric and the radii in the metric. I'm not sure what these stand for. Is the "r" the radial coordinate present in the spherical coordinate systems? To go along with this distance, I have no idea what that stands for to any degree in this metric. The distance to what?

*This is all in relation to black holes, which is what I am doing my project on.*

Thanks in advance!