Gravitational Time Dilation at Event Horizon

In summary, the gravitational time dilation formula, which takes into account the effects of gravity on time, shows that as an observer gets closer to a massive object, their time dilation factor increases. However, this formula assumes that the observer is stationary, which is not possible at the event horizon. Therefore, an observer cannot experience infinite time dilation at the event horizon. Additionally, inside the event horizon, time dilation does not work at all due to the lack of a stationary frame of reference.
  • #1
mjordan2nd
177
1
According to Wikipedia, the gravitational time dilation formula is given by

[tex]t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}} = t_f \sqrt{1 - \frac{r_0}{r}}[/tex]

where

t0 is the proper time between events A and B for a slow-ticking observer within the gravitational field,

tf is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate),

and r is the radial coordinate of the observer.

Does this mean that if we get arbitrarily close to the event horizon we can make our time dilation factor increase arbitrarily without bound? Does this also mean that for an observer on the event horizon time never passes?
 
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  • #2
This is like asking if time would stand still when traveling at the speed of light. The formula you cite for gravitational time dilation assumes that the observer is stationary and there is simply no way for an observer to be stationary at the event horizon.
 
  • #3
What about getting arbitrarily close to the event horizon? Would there be a point in space where, say, only ten years have passed since the creation of the black hole though the black hole looks billions of years old from Earth? What about on the other side of the event horizon? How does gravitational time dilation work there?
 
  • #4
mjordan2nd said:
What about getting arbitrarily close to the event horizon? Would there be a point in space where, say, only ten years have passed since the creation of the black hole though the black hole looks billions of years old from Earth?
Yes. You cannot be stationary at the event horizon, but if you're willing to accept an arbitrarily large acceleration you can hover arbitrarily close to the event horizon and your time dilation relative to an observer at infinity will also be arbitrarily latrge.

What about on the other side of the event horizon? How does gravitational time dilation work there?
It doesn't work at all. There are no such thing as "stationary" inside the event horizon, so we have the same problem with defining time dilation as we have at the event horizon, and a further problem in that there is no possible way to compare the time on the clock inside the horizon with the time outside the horizon.
 

What is gravitational time dilation at event horizon?

Gravitational time dilation at event horizon is a phenomenon in which time appears to slow down near the event horizon of a black hole due to the intense gravitational pull. This means that time appears to pass slower for an observer closer to the black hole compared to an observer further away.

What causes gravitational time dilation at event horizon?

Gravitational time dilation at event horizon is caused by the strong gravitational pull of a black hole. The closer an object is to the black hole, the stronger the gravitational force, which results in a slower passage of time. This is due to the distortion of spacetime near the event horizon.

How does gravitational time dilation at event horizon affect objects and light?

Gravitational time dilation at event horizon affects both objects and light. Objects closer to the black hole will experience slower time compared to objects further away. Light passing through the intense gravitational field of a black hole will also appear to slow down, making it difficult for an outside observer to see what is happening near the event horizon.

Can gravitational time dilation at event horizon be observed?

Gravitational time dilation at event horizon can be observed indirectly through various experiments and observations. For example, the time dilation effect has been observed in the orbits of stars near the supermassive black hole at the center of our galaxy. However, it is not possible for an observer to directly observe the time dilation effect at the event horizon of a black hole.

Does gravitational time dilation at event horizon have any practical applications?

Gravitational time dilation at event horizon has several practical applications, such as in GPS systems. The satellites in the GPS system experience slower time due to their higher altitude, which is affected by the Earth's gravitational pull. Without accounting for this time dilation effect, GPS calculations would be inaccurate.

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