Is It Possible to Escape a Black Hole Using Charge?

[Narcissus]

I am not a physicist but with a very big passion for the subject. I might not be able to solve your equations but i love the mind games associated with BH. Having said that, let me move on to my observation:
A kerr BH has two event horizons- The outer event horizon marks the boundary within which an observer cannot resist being dragged around the black hole with space-time. The inner event horizon marks the boundary from within which an observer cannot escape. Now the ergosphere existing between these event horizons is the main issue here.

If I have a body inside the ergosphere (assuming that it is not crushed etc etc...), theoretically it should be possible to get out of the black hole if it possesses the right amount of charge correct? Now again, if the body possesses the right quantity of charge would it not be possible to exist in a steady state (not moving relative to the event horizons).

Also once the charge moves towards the outer event horizon, then it should lose charge. Suppose we are able to impart sufficient charge to this body, can't we have a situation in which the body will indefinitely oscillate in the event horizon?

If I got my basics wrong, I am here to learn :-)

---Narcissus.

 

[mathman]

The basic problem with your description is that it emphasizes charge, which has very little to do with black hole physics. Gravity is the principal force involved. General relativity is the theory describing what happens.

 

[DW]

I am not a physicist but with a very big passion for the subject. I might not be able to solve your equations but i love the mind games associated with BH. Having said that, let me move on to my observation:
A kerr BH has two event horizons- The outer event horizon marks the boundary within which an observer cannot resist being dragged around the black hole with space-time. The inner event horizon marks the boundary from within which an observer cannot escape. Now the ergosphere existing between these event horizons is the main issue here.

Actually, the static limit is the outer edge of the ergosphere in which everything must rotate with the hole. The outer horizon is spherical. The static limit is an obloid spheroid that is larger than the outer horizon. They just touch at the north and south polar axis.

If I have a body inside the ergosphere (assuming that it is not crushed etc etc...), theoretically it should be possible to get out of the black hole if it possesses the right amount of charge correct?

A hole with any charge or rotation is described by a spacetime geometry with multiple exterior regions some of which are accessible from within the horizons and some of which are not. If one is under the static limit and outside the outer horizon one is still in our external region and can escape as he never left it.

Now again, if the body possesses the right quantity of charge would it not be possible to exist in a steady state (not moving relative to the event horizons).

Also once the charge moves towards the outer event horizon, then it should lose charge. Suppose we are able to impart sufficient charge to this body, can't we have a situation in which the body will indefinitely oscillate in the event horizon?

If I got my basics wrong, I am here to learn :-)

---Narcissus.

There are timelike geodesics for which something in free fall neither escapes to an external region, nor intersects the physical singularities for the Kerr-Newman geometry. The charged particle doesn't loose charge though if that is what you mean.

 

[Narcissus]

Actually, the static limit is the outer edge of the ergosphere in which everything must rotate with the hole. The outer horizon is spherical. The static limit is an obloid spheroid that is larger than the outer horizon. They just touch at the north and south polar axis.

The static limit, I presume is the inner horizon? If this were true wouldn't it be completely contained within the outer horizon? In general space-time it could be bigger than the outer horizon, but I think SR precludes the inner horizon from extending outside the sphere in space!. I am on some very edgy ground here, so do correct me if my understanding is wrong.

A hole with any charge or rotation is described by a spacetime geometry with multiple exterior regions some of which are accessible from within the horizons and some of which are not. If one is under the static limit and outside the outer horizon one is still in our external region and can escape as he never left it.

But my point is what if a particle with a charge has actually got into the outer horizon (which is i believe possible if it is not a schwarzchild BH )Then would it still be able to leave the horizon because of its charge? Because the singularity ring might repulse it.

There are timelike geodesics for which something in free fall neither escapes to an external region, nor intersects the physical singularities for the Kerr-Newman geometry. The charged particle doesn't loose charge though if that is what you mean.

I am not sure I understand this part though.
One more thing I would like to clarify is whether it is possible to achieve some kind of equilibrium within the ergosphere? (Assuming the inner horizon is contained within the outer and our charged particle is in this ergosphere?)

 

[DW]

The static limit, I presume is the inner horizon?

No. The static limit is outside of the outer horizon. The ergosphere is outside the outer horizon. The place where things must rotate with the hole extends outside the outer horizon.

In general space-time it could be bigger than the outer horizon, but I think SR precludes the inner horizon from extending outside the sphere in space!.

The static limit is not the inner horizon. The inner horizon is a sphere within the outer horizon. The outer horizon is a sphere within the static limit. The static limit is an obloid spheroid outside of the outer horizon that just touches the outer horizon at the poles.

But my point is what if a particle with a charge has actually got into the outer horizon (which is i believe possible if it is not a schwarzchild BH )Then would it still be able to leave the horizon because of its charge?

Whether the particle has charge does not matter. Whether the black hole has charge or spin is what matters. Anything can escape into certain of the exterior regions of a charged or rotating black hole.

I am not sure I understand this part though.
One more thing I would like to clarify is whether it is possible to achieve some kind of equilibrium within the ergosphere? (Assuming the inner horizon is contained within the outer and our charged particle is in this ergosphere?)

The ergosphere is outside of the horizons. It is inside the static limit. The static limit is not a horizon.

 

[Narcissus]

Thanks DW. Got what static limit is.