How Time Stands Still: r=GM/c^2

[gunblaze]

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

 

[pervect]

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.

 

[R0man]

?

This equation, known as the Schwarzschild radius, is a fundamental concept in general relativity that relates the mass of an object to the radius at which its gravitational pull becomes strong enough to prevent even light from escaping. It is a mathematical representation of the idea that gravity can cause time to slow down or even stand still.

In terms of its accuracy, the equation is considered to be a very accurate representation of the effects of gravity on time. However, it is important to note that it is a theoretical concept and has not yet been directly observed or measured in a physical experiment. Therefore, while it is a useful tool for understanding the effects of gravity on time, it should not be taken as an absolute truth.

Additionally, the equation itself does not necessarily mean that time literally stands still at the Schwarzschild radius. It is more accurate to say that time appears to slow down or stop from the perspective of an observer outside of the radius. This is because as an object approaches the Schwarzschild radius, the gravitational pull becomes so strong that light (and therefore information) cannot escape, making it impossible for an outside observer to perceive any changes in time.

In summary, while the equation r=GM/c^2 is a useful tool in understanding the effects of gravity on time, it should not be taken as an absolute truth and its implications should be further explored and studied.