What Causes Hypervelocity Stars to Eject from Black Holes?

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Hypervelocity stars may be ejected from black holes due to their high speeds, surpassing the black hole's mass. The discussion compares the event horizon to water flowing from a faucet, suggesting that intense gravitational forces could push stars out, similar to pressure forcing a pimple to pop. The idea of space-time as a skin-like layer is explored, but it is clarified that gravity warps four-dimensional space rather than a two-dimensional membrane. Overall, the mechanics of hypervelocity stars' ejection involve complex interactions of mass and energy within the warped fabric of space-time. Understanding these dynamics remains a challenging yet intriguing area of astrophysics.
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I'm not very good with words so if this seems redundant or not very well put together, know that i tried...

I recently heard about white holes through an example of water from a faucet. The event horizon was a the ring of water that appears in the sink while the water is running. In the "even horizon" the water was moving fast enough to not allow water to move in the opposite direction. With this in mind, i realized that hyper-velocity stars are most likely capable of being shot out of a black hole because they're moving at a speed faster then the black holes mass. (very rough explanation) Anyway, Hyper-velocity stars generally appear to be coming from black holes surrounding a massive black hole, since space time is flat and these black holes are all absorbing so much energy, could a hvs be forced out by the intense build up of all the mass under the distorted space time? (Like a pimple?) Or is it being shot out like in a situation involving two objects pressing against each other until one slips, tilts, ect, and the second is shot out with a speed equivalent to the pressure?

[just a thought, is it wrong to assume space time is like a layer of skin? Since a black hole is so heavy it makes sense to picture them as sinking inward and holding the energy in a region just below the surface of space, like an infected pore. I could be WAY wrong here and in this case i can under stand why none of this would make much sense.]
 
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Well firstly, gravity doesn't bend two dimensional space which is how you are visualizing it (Curvature on a membrane). Gravity is the warping of four dimensional space which is much more difficult to visualize.
 
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