In classical mechanics, to raise from some height [itex]h_{0}[/itex] to infinity over a gravitational body, takes a certain amount of energy, the energy associated with escape velocity, let's just call it [itex]ε[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

[itex]ε = \lim_{t\rightarrow +\infty} \int_{h_{0}}^t ƒ(h)dh[/itex]

Likewise, it's time-reversible, so dropping something from stationary at an infinite distance, then when it reaches [itex]h_{0}[/itex], because of potential energy becoming kinetic, it will have that same amount of energy in kinetic.

So, if the energy required to escape from the event horizon is infinite, then what keeps something falling into a black hole from achieving an infinite amount of energy as it reaches the event horizon, thus contributing an infinite amount of mass to the black hole?

I guess time-reversal doesn't really apply in the same way here, since a time-reversal would mean reversing the direction of gravity as well (since its a curve in spacetime), creating a white hole. But I'm still wondering how it can be that something can require an infinite amount of energy to escape from a certain [itex]h_{0}[/itex], yet not achieve an infinite energy when dropping from higher up down to [itex]h_{0}[/itex]. So different equations would be used to describe something falling as opposed to something attempting to rise out of the gravity well?

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# Material Behavior at the Event Horizon

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