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I am trying to understand several particle-antiparticle concepts and there are questions that are not answered in any literature:

  1. Hawking's radiation: what happens if classic particle of particle-antiparticle pair falls into black hole and the antiparticle stays out? This actually makes the black hole to grow, but the antiparticle does not annihilate and so the vacuum debt stays unpaid? That's okay?

  2. Hawking's radiation: if the antiparticle falls into black hole and annihilate, it should produce corresponding energy ($E=mc^2$). But as this energy is equal to matter and cannot leave the black hole, how is it possible, that the black hole actually loses weight? If it pays the "vacuum debt" – how does the vacuum know to take this portion of energy from this part of black hole?

  3. How is it possible that antiparticles tend to fall more often then classic particles so that the black holes lose weight?

  4. Which particle-antiparticles are willing to annihilate together? Obviously not all of them as there are mesons which are composed of particle-antiparticles pairs. It looks as if they had to be completely equal?

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Particle antiparticle potential/hypothetical pairs exist in vacuum as a mathematical description, necessary for calculations of interactions between elementary particles. These mathematically annihilate and reappear within the heisenberg uncertainty principle.In the Hawking radiation case the virtual pairs at the event horizon have a probability one of the pair, particle or anti, to fall in the black hole and the other to leave . The energy for the interaction is supplied by the black hole, i.e. the energy of the leaving particle.

Hawking's radiation: what happens if classic particle of particle-antiparticle pair falls into black hole and the antiparticle stays out? This actually makes the black hole to grow, but the antiparticle does not annihilate and so the vacuum debt stays unpaid? That's okay?

No, the black hole gives up gravitational energy to create a real pair , the one that falls in gives up its energy but the one escaping particle/antiparticle will diminish by the amount of the energy it carries away, the mass of the black hole.

Hawking's radiation: if the antiparticle falls into black hole and annihilate, it should produce corresponding energy (E=mc^2). But as this energy is equal to matter and cannot leave the blackhole, how is it possible, that the black hole actaully loses weight? If it pays the "vacuum debt" – how does the vacuum know to take this portion of energy from this part of black hole?

See above. It is the gravitational field of the black hole that interacts with the virtual pair and transfers energy.

Which particle-antiparticles are willing to annihilate together? Obviously not all of them as there are mesons which are composed of particle-antiparticles pairs. It looks as if they had to be completely equal?

An antiparticle has all the quantum numbers of the omonymous particle except of opposite sign. So it is annihilation of quantum numbers that releases the energy contained the masses of the particle/antiparticle.

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