Calculating Gravitational Time Dilation in black hole/Future Time Travel

[aaron35510]

First of all, (following Einstein's theory of Gravitational Time Dilation (I'll just call it GTD,)) objects (such as us) age slower near strong gravitational fields than in empty space. The higher the local distortion of spacetime due to gravity, the more slowly time passes. So according to GTD, we should pretty much not age at all if were able to survive in a black hole.

is the formula for GTD, so in that case, a black hole has INFINITE mass (m=infinity), which means that the formula is (original time outside/ infinity.) Therefore, if let's say the time OUTSIDE of the black hole was 50 years, then the time you spent INSIDE the black hole (dilated time) was an infinite amount of time? That doesn't make sense.

 

[JesseM]

First of all, (following Einstein's theory of Gravitational Time Dilation (I'll just call it GTD,)) objects (such as us) age slower near strong gravitational fields than in empty space. The higher the local distortion of spacetime due to gravity, the more slowly time passes. So according to GTD, we should pretty much not age at all if were able to survive in a black hole.

is the formula for GTD, so in that case, a black hole has INFINITE mass (m=infinity), which means that the formula is (original time outside/ infinity.) Therefore, if let's say the time OUTSIDE of the black hole was 50 years, then the time you spent INSIDE the black hole (dilated time) was an infinite amount of time? That doesn't make sense.

You're talking as though that formula compares time "inside" a black hole with time "outside", but that isn't true. Rather, it compares the rate of a clock at hovering radius R from the gravitating object (which could be a black hole), with the rate of a clock at infinite distance from the gravitating object (or large enough so that gravitational time dilation is negligible). The event horizon of a black hole, which divides "inside" from "outside", is the Schwarzschild radius of R = 2GM/c^2. And the formula really only seems to work for a choice of R that's larger than 2GM/c^2 (i.e. for a radius that puts you 'outside' the black hole)--if you plug in a value of R smaller than that, you get an imaginary number!

Also, are you imagining that all black holes have infinite mass, or do you just want to imagine we are dealing with a hypothetical black hole that does? Black holes don't have infinite mass, though the singularity at the center has infinite density. And if you try to imagine one with infinite mass, then since the formula only works for values of R larger than 2GM/c^2, your radius would have to be larger than infinity for the formula to apply, which doesn't make sense.

 

[aaron35510]

You're talking as though that formula compares time "inside" a black hole with time "outside", but that isn't true. Rather, it compares the rate of a clock at hovering radius R from the gravitating object (which could be a black hole), with the rate of a clock at infinite distance from the gravitating object (or large enough so that gravitational time dilation is negligible).

if what i stated is not true, then please tell me what "T" stands for and what "T_0" stands for

but then aren't black holes created when a star's mass becomes infinitely big so that it collapses on itself and creates a rip in spacetime? Anyways, if the mass of a black hole is NOT infinity, then the equation makes a lot more sense.

 

[A.T.]

if what i stated is not true, then please tell me what "T" stands for and what "T_0" stands for

Explained here:
http://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere

but then aren't black holes created when a star's mass becomes infinitely big

Mass doesn't have to change at all to form a black hole. You are confusing mass and density.

 

[JesseM]

if what i stated is not true, then please tell me what "T" stands for and what "T_0" stands for

T0 would be the tick of a clock at infinite distance from the gravitating object, T would be tick of a clock at radius R > 2GM/c^2 from the object (and for a non black hole R should also be larger than or equal to the radius of the object's object's surface). T is larger than T0 because the tick of the clock closer to the object takes longer.

but then aren't black holes created when a star's mass becomes infinitely big so that it collapses on itself and creates a rip in spacetime?

No, as I said it's the density that goes to infinity, which also causes the curvature of spacetime in the immediate vicinity of the matter (at R=0) to go to infinity, but the mass stays the same as that of the original star.

 

[granpa]

from the point of view of an accelerating rocket there is a sort of black hole somewhere behind it. a point in space where time stands still and nothing not even light from that place can ever reach the rocket.

beyond that point time would seem to run backwards to people on the rocket (if they could detect it)