Symmetry in Hawking radiation? I have a question concerning how Hawking radiation works.

As I understand, a pair of particle-antiparticle may pop to existence near the event horizon (from a virtual particle).

Then it might happen that the negative particle (antimatter) gets captured by the black hole whereas the positive particle (matter) escapes.

This results in a net loss of the black hole mass. If you repeat this process an astonishing number of times the Black Hole might end up completely evaporating.

Am I right so far? (Even if the explanation is not very mathematical)

My question then is: 

This assumes that when a pair particle-antiparticle is created, a bias towards antiparticles being captured and particles escaping must exist.

Otherwise, the mass of the black hole might fluctuate, but in average for big numbers of pairs, equal percentage of particles and antiparticles would be captured/escape.

So, is there really a bias needed for the black hole to loose mass, or is it something wrong about my understanding of Hawking radiation?

Thanks
This assumes that when a pair particle-antiparticle is created, a bias towards antiparticles being captured and particles escaping must exist.


No such assumption or bias exists.

As far as we know the universe treats anti-particles just like particles with different properties (e.g. charge is opposite compared to the corresponding particle).


  Otherwise, the mass of the black hole might fluctuate, but in average for big numbers of pairs, equal percentage of particles and antiparticles would be captured/escape.


You seem to be implying that anti-matter has negative mass.  All particles (including anti-matter) have either zero mass (like photons) or positive mass (like electrons).

So regardless of whether the anti-particle or particle escapes, the black hole looses mass (more precisely it looses energy).


  So, is there really a bias needed for the black hole to loose mass, or is it something wrong about my understanding of Hawking radiation?


Your understanding of the mass of anti-particles is likely the problem.  They have positive mass, just like particles, because they are particles.