# How true is this ?

## Main Question or Discussion Point

How true is this equation in determining that time stands still at a point when $$r=GM/c^2$$

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pervect
Staff Emeritus
gunblaze said:
How true is this equation in determining that time stands still at a point when $$r=GM/c^2$$
I assume that this formula refers to time standing still at the event horizon of a Schwarzschild black hole (which is at r=2GM/c^2).

The formula is mathematically correct, but doesn't have any physical significance. It reflects what is called a "coordinate singularity" near the event horizon of a black hole.

A good anology is this - suppose you are at the north pole of the Earth. The direction "East" is not well defined. However, there is nothing physically special about the north pole of the Earth, an observer standing there would see nothing geometrically unusual.

Similarly, there is nothing geometrically unusual about the event horizon of a black hole. However, Schwarzschild coordinates are not well behaved in that neighborhood, much as the concept of "east" is not well behaved at the North pole.