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Posted by Bruce on March 5, 2002 08:11:23 UTC

describe the interchange in the t-coordinate and r-coordinate for r < 2M (keep in mind that the r-coordinate is the reduced circumference [circumference / 2pi]). The curvature factor (1-2M/r) in the Schwarzchild metric becomes negative. In consequence, the signs reverse between the radial part and the time part of the metricm making the dt^2 term negative and the dr^2 term positive. Space and time themselves do not interchange roles: Coordinates do: The t-coordinate changes in character from a timelike coordinate to a spacelike coordinate and the r-coordinate changes in character from a spacelike coordinate to a timelike one. What does this mean to say that inside the Schwarzchild radius the r-coordinate changes in character from a spacelike coordinate to a timelike coordinate? It means our free float frame moves to ever smaller r with all the inevitability that we oprdinarily associate with the passage of time.

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