Can we speed up the evaporation of black holes manually by accelerating it? If we throw an object to pass near a black hole, to bypass it, it will change the speed of the black hole, just like gravitational assist for a space probe. Does an accelerating black hole evaporate faster because:


*

*When object accelerates, mass increases

*When mass increases, gravity increases

*When gravity increases, the black hole collects virtual particles more rapidly
Is above true?
 A: Actually, the larger a black hole's mass, the slower it emits Hawking radiation. So, if you add mass to a black hole, you slow down its evaporation. In any case, passing an object by a (probably vastly more massive) black hole won't change its velocity much, and will have a minuscule effect on its mass.
A: No,usually we can not speed up the evaporation of black holes manually by accelerating it under normal circumstances,but we can of course write a letter to our dead ancestors to speed it up
A: Isn't this just like the twin paradox? The twin that undergoes acceleration is the one that ages the slowest. So if you want to speed up the evaporation of black holes (from your viewpoint), you should accelerate yourself. 
Maybe black holes work differently, but offhand I don't see why they should. 
A: Black holes emit radiation through what is essentially a modified case of the Casimir Effect. That is what we know as Hawking Radiation. Most black holes would only emit in the microwave band, which is why a stellar black hole will outlive most of the matter in the universe. It also must be taken into consideration that they are already moving very quickly, as everything else is when taking the CMB as the frame of reference. All of that said, just due to the orders of magnitude we're dealing with, there is likely no way to effect the speed of evaporation due to hawking radiation. Black holes actually do emit more radiation as they gain mass, just as a smaller proportion of overall mass, because you are evaporating something with a bare minimum of one solar mass (smaller ones have never been observed in any way, though they could exist) with low-energy photons. 
The pedantic answer, however, which is clearly what you're after, is yes. If you hucked the entire solar system at one for a tight gravitational slingshot, you might speed up the entire 10^80 year process of black hole evaporation by a couple of femtoseconds. 
A: The question related to speeding up evaporation of Black Holes manually has no basis ever in the science of Physics of the universe. The General Theory of Relativity had predicted the presence of Black Holes as regions in space, in which space-time distorted in such a way that nothing, not even light can escape.
However, the characteristics of these Black Holes are subjected to evaporation,  destruction of the inner parts of information, and depletion of radiation that caused confusion in the world of physics,  reference to the Theory of Quantum Mechanics. The Laws of Quantum Mechanics are clear and straight forward and state:
   a) Black Holes cannot evaporate.
   b) Radiation of Black Holes never stops.
   c) Black Holes have an infinite life, in other words are eternal.
As a conclusion, the chaos between the Theory of Relativity and the Theory of Quantum Mechanics started forty years ago and still going on, that created a dilemma of having Black Hole  information paradox and Black Hole radiation.
