infinite time dilation?

[petrushka.googol]

As per the relativistic equation when v approaches c time dilation approaches infinity.

But theoretically how far could this go? If time is dilated close to infinity it will cross the age of the universe. (relative to the big bang). Then what would happen at the event horizon of a black hole where the gravitational shear forces are sufficient to produce such an event?

Please advise.

Edited January 25, 2014 by petrushka.googol

[Endercreeper01]

As per the relativistic equation when v approaches c time dilation approaches infinity.

 

When [latex]v[/latex] approaches [latex]c[/latex], time dilation does not approach infinity.

In special relativity, proper time and coordinate time are related by

[latex]\tau = \int_0^t \sqrt{1-\frac{v^2}{c^2}} \ dt[/latex]

This does not approach infinity, but 0. As [latex]v[/latex] gets larger, [latex]\sqrt{1-\frac{v^2}{c^2}}[/latex] gets smaller. Therefore, [latex]\tau [/latex] becomes smaller as [latex]v[/latex] approaches c.

 

What would happen at the event horizon of a black hole where the gravitational shear forces are sufficient to produce such an event?

This is again the same problem.

Time dilation for a black hole is given by

[latex]\tau = \int_0^t \sqrt{g_{00}} \ dt[/latex]

For a Schwarzschild black hole,

[latex]g_{00}=1-\frac{R_s}{r}[/latex]

Where

[latex]R_s=\frac{2GM}{rc^2}[/latex]

so

[latex]\tau = \int_0^t \sqrt{1-\frac{R_s}{r}} \ dt[/latex]

Because [latex]\sqrt{1-\frac{R_s}{r}}[/latex] does not approach infinity as [latex]r[/latex] approaches [latex]R_s[/latex].

This means that [latex]\tau[/latex] does not approach infinity.

To answer your question, time would keep dilating more and more as [latex]r[/latex] approaches [latex]R_s[/latex]. An object will never actually reach the event horizon, as time would keep dilating more and more as it approaches the event horizon.

Edited January 25, 2014 by Endercreeper01

[phyti]

I think p.googol is considering the dilated (stretched) interval, not the proper (local) time.

I.e. the tick is never completed.

[Endercreeper01]

I think p.googol is considering the dilated (stretched) interval, not the proper (local) time.

 

The coordinate time never changes. One second in coordinate time will be one second in coordinate time regardless of proper time.

[davidivad]

As per the relativistic equation when v approaches c time dilation approaches infinity.

But theoretically how far could this go? If time is dilated close to infinity it will cross the age of the universe. (relative to the big bang). Then what would happen at the event horizon of a black hole where the gravitational shear forces are sufficient to produce such an event?

Please advise.

what will happen at the singularity?

[swansont]

When [latex]v[/latex] approaches [latex]c[/latex], time dilation does not approach infinity.

 

 

The "amount" of dilation is often equated with the value of gamma

[MigL]

Endercreeper01, you are getting the same malady as Decraig, but you can still be saved.

 

"An object will never actually reach the event horizon," ???

 

The mathematics is all well and good but you have to consider the physicality of the results. Sometimes they don't make sense.

 

Consider sending a probe towards the event horizon of a black hole. The probe sends a signal back to us ( at a safe distance ), using pulses of light. It is not just the interval between pulses which dilates as the EH is approached, the timebase of the EM wave also dilates so that the frequency approaches zero and the wavelength approaches infinity as the EH is approached. In effect there is no more signal reaching us, not even reflected light from the probe.

To us, distant observers, the probe does not stop at the EH, rather it disappears and sends no more information to us. Now if an astronaut was riding the probe, he would certainly see himself crossing the EH and proceeding to the ( possible ) singularity. Now other than the fact that the astronaut is an idiot, I would say his point of view is the more physical, since we will never detect ( by any means you can possibly imagine ), anything 'frozen' at the event horizon.

Edited January 25, 2014 by MigL

[J.C.MacSwell]

As per the relativistic equation when v approaches c time dilation approaches infinity.

But theoretically how far could this go? If time is dilated close to infinity it will cross the age of the universe. (relative to the big bang). Then what would happen at the event horizon of a black hole where the gravitational shear forces are sufficient to produce such an event?

Please advise.

Not sure what this means. Time dilation is rate of time passage going forward, not something affecting history.

 

Anything happening at the event horizon must be consistent in all frames.

Edited January 26, 2014 by J.C.MacSwell

[petrushka.googol]

What I was thinking is that the time shear (if we could call it that) would be so appreciable near a black hole that every "passing second" would be more difficult to reach than the previous one. Which implies that one would never really reach the event horizon in toto. It would be a near miss or something similar. I guess.

[Endercreeper01]

 

 

Consider sending a probe towards the event horizon of a black hole. The probe sends a signal back to us ( at a safe distance ), using pulses of light. It is not just the interval between pulses which dilates as the EH is approached, the timebase of the EM wave also dilates so that the frequency approaches zero and the wavelength approaches infinity as the EH is approached. In effect there is no more signal reaching us, not even reflected light from the probe.

To us, distant observers, the probe does not stop at the EH, rather it disappears and sends no more information to us. Now if an astronaut was riding the probe, he would certainly see himself crossing the EH and proceeding to the ( possible ) singularity. Now other than the fact that the astronaut is an idiot, I would say his point of view is the more physical, since we will never detect ( by any means you can possibly imagine ), anything 'frozen' at the event horizon.

I mean that it won't reach the event horizon with respect to a distant observer. Relative to the infalling object, it will go beyond the event horizon. But, it will not see anything, as any light in the event horizon will be drawn towards the singularity.

 

What I was thinking is that the time shear (if we could call it that) would be so appreciable near a black hole that every "passing second" would be more difficult to reach than the previous one. Which implies that one would never really reach the event horizon in toto. It would be a near miss or something similar. I guess.

Time dilates only with respect to a distant observer. The particle approaching the event horizon will experience no time dilation with respect to itself.

[Delta1212]

Is it possible that the black hole would evaporate before you reached the singularity?

[Endercreeper01]

Relative to the object falling, it would reach the singularity long before the black hole evaporates.

With respect to a distant observer, it is different. The observer will see the particle go slower and slower, until it appears to be frozen at the event horizon. However, because the black hole is evaporating, it will be moving very slowly with the event horizon shrinking. It will keep happening like this until the black hole evaporates. This seems to be a paradox, as the object would already have evaporated. The object will most likely evaporate at the event horizon.