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I am doing great, thank you for asking! I also want to thank Anthony and Andy for answering my question! I have tried to calculate the Schwarzschild radius before, but I had some trouble doing it. From what I was doing, I wanted to calculate the gravity of a black hole at the event horizon (I'm also assuming that the gravity of all black holes at their event horizons has the same value) with the assumption that that gravitational strength would be enough to stop time (from an outsider's perspective). I assumed that time would "stop" at the event horizon because, as an object approaches the event horizon, an outside observer perceives it in similar ways to if the object was approaching the speed of light (ex. time slows for the object to almost stopping nearing the horizon, its acceleration "slows", it never actually crosses the horizon... all factors that would also be attributed to that object if it was approaching the speed of light).

Anyway, I'm having trouble with the idea that an outside observer would only see time for the object stop at the singularity (at infinite gravity), when in fact time slows to almost stopping as it gets closer and closer to the event horizon, where gravity is still finite (that's why I assumed it "stops" at the horizon from the perspective of an outside observer). As I was doing some more research, I came upon some information that would describe how far an object would move back in time if it was moving faster than light (using special relativity). I was wondering if I could use the same idea and apply the information to general relativity (using the formulas for general relativity, of course), in order to mathematically calculate the required gravitational strength to stop/reverse time (just like the info in the attachment calculated the required speed to reverse time). On what I read, the author uses the Lorentz transformation to calculate how far back in time an object would go if it moved at a speed greater than the speed of light (from the perspective of an outside observer). Is there a counterpart of the Lorentz transformation in general relativity that I could use in order to calculate the gravity needed to stop/reverse time? If not, what could I use to do such a calculation?

Once again, I would just like to thank you guys for all your help regarding this subject. I only have a limited (but growing!) knowledge of relativity, and your answers have been very important in helping me gain a deeper understanding of how this theory works. Thank you!

Best Regards,
Question Date: 2011-06-10
Answer 1:

I was wrong about the singularity and the outside observer; what you read is correct; I am sorry about that (my knowledge of relativity is also very limited, and you're rapidly pushing the envelope of what I know!). I am fairly certain that time does genuinely stop at the singularity, though, which would imply that an observer already inside of the event horizon would see another object further inside of the black hole slow to a stop as it reaches the singularity. But I am humbled already - believe what you read.

I do know that gravity is not the same between different black holes at the event horizon. Gravitational potential is the same for all black holes at the event horizon, but remember that gravitational potential also scales with the size of the gravity well. Consider the Earth and the Sun, for instance - there is a distance from the Sun where the gravitational acceleration toward the center of the Sun is the same as that of the Earth, but the potential there is much lower than on the surface of the Earth, because it takes a whole lot more energy to drag the object out to infinity than it does to launch it over the Earth's surface. Work after all is the integral of force over distance, and because the Sun is so much more massive than the Earth, it exerts its gravitational influence over a much greater distance than the Earth does, and consequently has a deeper potential well for any given gravitational acceleration. Black holes are the same way: the more massive the black hole, the weaker gravity actually is at the event horizon itself.

However, as I said, don't think in terms of reversing time. Imaginary and negative are two very different things.

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