Time Travel & Gravitational Time Dilation Function

[Invutil]

If you square both sides of the gravitational time dilation function for non-rotating spherical bodies, do you not get a "time travel function" that allows you to travel back in time with a massive enough body like a black hole?

 

[Nugatory]

If you square both sides of the gravitational time dilation function for non-rotating spherical bodies, do you not get a "time travel function" that allows you to travel back in time with a massive enough body like a black hole?

I don't understand what you mean by a "time travel function", but there's nothing that happens in the neighborhood of a non-rotating spherical black hole that allows you to travel back in time.

 

[Invutil]

I must be not understanding something then. If 0 < 2GM/rc² < 1 or 0 < r0/r < 1, then time in the gravity well is less than time at an arbitrarily far distance from it. For 0<x<1, 0<sqrt(x)<1, when (1-2GM/rc²) < 1 or (1-r0/r) < 1. The greater the mass M, the smaller the distance from center r, the farther the observer is in the past (t0). Might the value inside the square root become negative even, if 2GM/rc² > 1 or r0/r > 1, (at a black hole?) and go to a higher dimension? Does it make sense? Since it's inside a square root, might it become a complex number and still make sense that way? Then, maybe the effect can be repeated to return back to real numbers (going through another black hole, assuming that doesn't totally annihalate whatever is pulled in)? This seems really amazing to me.

 

[PeterDonis]

I must be not understanding something then. If 0 < 2GM/rc2 < 1 or 0 < r0/r < 1, then time in the gravity well is less than time at an arbitrarily far distance from it.

No. For this range of the radial coordinate, you are inside the black hole's horizon, and there are no static observers there--i.e., no observers that "hover" at a constant $r$ (doing this inside the horizon would require moving faster than light). So there's no way to make the comparison of "time" that you are trying to make here.

The greater the mass M, the smaller the distance from center r, the farther the observer is in the past (t0).

t0 doesn't appear anywhere in what you said. What is t0?