What is the Time Dilation Relationship Near a Black Hole's Event Horizon?

In summary: CoxIn summary, time dilation is a relationship between a time interval at a remote location and a time interval at infinity. The equation calculates the ratio between a time interval at radius r and a time interval at infinity. The Schwarzschild radius is at r=2GM/c^2.
  • #1
Samuel A. (Sam) Cox
3
0
Hi:

A couple of people on this forum have this formula reduced to a software program.

As an object nears a black hole, and is remotely observed, it appears to slow and hang suspended over the event horizon...time slows in any gravitational field with respect to a remote and less affected location.

One second of time at the remote observation location is equivalent to what amount of time for an object poised at say 10 to the minus 36th Cm above the event horizon of a black hole? Consider the object going into the black hole to be a point mass with no radius of its own...I'm only interested in the time dilation relationship; remote observing an object at 10 to the minus 36th Cm above the event horizon of a black hole.

Thanks, Sam Cox
 
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  • #2
The equation was already shown in the thread "What is time dilation". Fill in for [tex]r=2GM/c^2+10^{-34}[/tex]
Mortimer said:
Expression for time dilation in a gravity field:

[tex]\frac{\Delta t_r}{\Delta t_{\infty}}=\sqrt{1-\frac{2GM}{rc^2}[/tex]

The equation calculates the ratio between a time interval at radius r and a time interval at infinity. G is the gravity constant, M the mass.
The Schwarzschild radius is at [tex]r=2GM/c^2[/tex]
 
  • #3
Hi Mortimer, 10:44EDT Monday 4/25/05

That was quick. Yes, I've already read the threads and noticed your name. I mentioned software, because I really could use a set of information...10 to the minus 30,31,32,33,34,35,36,37,38 CM

In case you are curious, for about 5 years I've been conceptualizing a GR/QM/SRT dual universe in 7 foundational dimensions, complete with inverse mapping, in the presumption that the dualism of GR and the Schwarzschild Mirror Geometry may not be mathematically vestigial.

This request for a set of data on time dilation close to the event horizon relates to the remote cross-reading of an inversely mapped universe on 4D event horizon surfaces via photonic entanglement.

The geometric model, a modified Schwarzschild Mirror Geometry with a Planck Realm at the center beautifully explains the anomalous gravitational acceleration of the Pioneer 10 and 11 spacecraft . You might be interested in seeing the math on that...

Right now I'm gathering a set of data which will (presumably) show that when the universe is cross-read remotely...one inversely mapped side to the other via phortonic entanglement- almost on the Planck Realm event horizon, the time dilation will be at some reasonable (and interesting) point exactly equal to the radius of the observed universe...the metric equivalent of 13.6 Billion Light Years.

In this scenario, space and time in the universe is created by the way we observe it at a certain place in scale...

Thanks again...Sam
 

What is gravitational time dilation?

Gravitational time dilation is a phenomenon predicted by Einstein's theory of general relativity, where time passes at different rates in different regions of space due to the presence of a strong gravitational field.

How does gravitational time dilation work?

According to general relativity, gravity is the result of the curvature of spacetime caused by massive objects. This curvature causes time to pass more slowly in regions with stronger gravitational fields, such as near massive objects like planets or stars.

What is the equation for calculating gravitational time dilation?

The equation for gravitational time dilation is t0 = tf * sqrt(1 - (2GM/rc2)), where t0 is the time measured in a weaker gravitational field, tf is the time measured in a stronger gravitational field, G is the gravitational constant, M is the mass of the massive object, r is the distance from the object, and c is the speed of light.

How does gravitational time dilation affect the measurement of time?

Gravitational time dilation means that time will pass more slowly for an observer near a massive object compared to an observer farther away. This effect has been observed in experiments using atomic clocks, where clocks closer to Earth's surface run slower than those at higher altitudes.

Are there any practical applications of gravitational time dilation?

One practical application of gravitational time dilation is in GPS technology. The satellites that make up the GPS system have atomic clocks on board, and these clocks experience time dilation due to the weaker gravitational field in orbit. Without accounting for this effect, the GPS system would not work accurately.

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