  Since its first introduction, the Schwarzschild metric has been written in
various coordinate systems. This has been done primarily to understand the
nature of the coordinate singularity at the event horizon. However, very often,
the mathematics of a coordinate system does not provide a clear physical
interpretation. In Schwarzschild's original work, the origin of the radial
coordinate was at the event horizon. Hence, there was no black hole. The
generally accepted current definition of the radial coordinate has an origin
beyond the horizon. This necessitates the discussion of black holes. Here, some
well-known and some not-so-well-known coordinate systems will be visited in
search of a physical interpretation. It will be noted that they all agree at
large radial distances. However, the location of the origin of the radial
coordinate can be different for different systems. Some "natural" coordinate
systems can exclude the entirety of the interior of a black hole from the
physical manifold. Such coordinate systems maybe physically more acceptable as
they avoid the issue of the metric signature change across the horizon.
Mathematically, the metric signature alone can distinguish time from space
coordinates. Hence, coordinate systems that include the interior of the black
hole need to switch the physical meanings of time and one of the space
coordinates.
