[jeffreyH (OP)]

If we had say a micro black hole near the earths surface would the earths gravitational field completely cancel the field of the black hole so that its gravity no longer trapped the mass behind an horizon?

[Bill S]

Does the Earth's gravity contain energy?  If so, wouldn't the BH accrete that energy, and grow?

[evan_au]

If we had say a micro black hole near the earths surface

If a micro black hole came in from outside our solar system, it would most likely have enough velocity to pass right through the Earth and out the other side, picking up a few atoms along the way (depending on exactly how "micro" it was).

Some science fiction authors have imagined the impact of a micro black hole trapped in the Earth's core, gradually consuming it from the inside, faster and faster...

would the earths gravitational field completely cancel the field of the black hole so that its gravity no longer trapped the mass behind an horizon?

When a black hole is approached by another black hole close enough that they are about to touch, the shape of their event horizons are distorted from the usual ellipsoid shape for a moment. But in no case does the matter inside the event horizon come outside the event horizon.

Since Earth's gravitational field is incredibly weak compared to the strength of a micro-black hole's gravitational field at the event horizon, I suggest that Earth's gravitational field will not noticeably distort the shape of the event horizon of a micro black hole. And it would not cause matter inside the micro black hole to appear outside the micro black hole.

no longer trapped the mass behind an horizon?

Hawking radiation predicts that micro black holes should effectively lose some of their mass via quantum effects, even when alone in deep space. This would cause them to eventually evaporate.
See: https://en.wikipedia.org/wiki/Hawking_radiation

[wolfekeeper]

If you think about it in terms of potential energy, I think that the earth's gravity can only make the event horizon bigger.

[Bill S]

Does the Earth's gravity contain energy?  If so, wouldn't the BH accrete that energy, and grow?

If you think about it in terms of potential energy, I think that the earth's gravity can only make the event horizon bigger.

Are we thinking along the same lines, or do you have something different (possibly more technical) in mind?

[opportunity]

Aristotle once said said nature abhors a vacuum.

If we're considering the idea of micro black holes, is there any evidence for micro black holes on a cosmic level, somewhere in space around which is just dust and debris?

Say a micro black hole formed in the Kuiper belt, somehow, through a resonance (and I'm being hypothetical here) of gamma bursts from wherever, what would happen?

We could suggest that the sun has within it a micro black hole that is still resolving, and thus could say that of all the stars. We could even suggest the big bang represented a type of great expansion of mass and energy and then collapse creating what is evident.

Once again, this is just a hypothesis, I wouldn't even really call it plausible. Yet, we only know what works by what doesn't.

The question of an external gravity source altering the mechanics of as small-scale black hole would need an equation to demonstrate any type of black hole is a runaway event independent of external gravitational influences.

[jeffreyH (OP)]

Imagine we have achieved the astronomical engineering feat of trapping a black hole in the void at the centre of a vary large mass. Consider what would happen if this system were to exactly cancel the potential at all points on the surface of the event horizon. So that an object could sit still at that position.

[jeffreyH (OP)]

Is the above scenario impossible?

[opportunity]

That depends on the equation we're willing to accept, right? Or some other theory.

[wolfekeeper]

Does the Earth's gravity contain energy?  If so, wouldn't the BH accrete that energy, and grow?

If you think about it in terms of potential energy, I think that the earth's gravity can only make the event horizon bigger.

Are we thinking along the same lines, or do you have something different (possibly more technical) in mind?

If you approximate it as a Newtonian gravity (not totally accurate, but may be illuminating), then the gravitational potential energy at any point is just the sum of the potential energy of the sources of gravity. If the gravitation potential is such that light can no longer escape then you're within the event horizon. SInce gravitational potential energy is always negative, then the event horizon can only grow in area/volume, and cannot be cancelled out.