# Can a tachyon escape a black hole?

1. Nov 20, 2008

### liamgibbs

Assuming a tachyon exists, can one escape a black hole?

Now, at the singularity of a black hole, gravity is infinite, right?* Since gravity is infinite, would it not suck in everything, even superluminal particles? On the flipside, since gravity can't exceed the speed of light, is it able to suck in anything travelling faster than light?

At the very least, the event horizon for a tachyon would be closer to the singularity than one for light and all else, I'm assuming. But then an event horizon for a tachyon couldn't exist if gravity can't catch it.

Then again, am I off my rocker?

* I'm under the assumption that gravity is actually infinite. But one thing I could never understand is if we think it's infinite since we apply both quantum mechanics and relativity to a singularity (and applying both at the same time gives an infinite answer)... or if it actually is infinite.

2. Nov 20, 2008

### gamma-ray-burst

well it's been a while since i read about this stuff, but i'd say that the main problem with singularities was actually the fact that we had to say that there was "infinite" stuff going on down there. one of the points of string theory is to say that there is no infinitely small dimension, so you don't have to have an infinite density.

anyway.

also the escape velocity of a black hole depends on its mass and size.
so, we'd have to know at what speed your tachyon can travel.
i don't know, it could travel at 1.5 the speed of light and the escape velocity could be 1.66 speed of light.

get my point?

3. Nov 21, 2008

### Fredrik

Staff Emeritus
Yes. All time-like curves (world lines of particles with mass >0) inside the event horizon end up at the singularity within a finite proper time, but tachyons (by definition) move on space-like geodesics, so that statement doesn't apply to them.

It's more accurate to talk about what happens in the limit where the distance from the singularity goes to zero. The curvature (i.e. "gravity") is one of the things that go to infinity in that limit.

If you e.g. push the Sun "a little to the left", the effect caused by the change would propagate at the speed of light, but when you're talking about a black hole that has existed a long time, the speed of gravitational waves isn't relevant since nothing is changing.

It's general relativity (a classical theory) that says that the curvature goes to infinity in the limit where the distance from the singularity goes to zero, but no one expects GR to be valid in that limit. It will break down sooner or later, and at the scale where that happens, another theory is needed. The new theory would probably be a quantum theory of gravity (and probably other stuff as well). There's no reason to assume that there would even be a singularity in this new theory.