Is it possible that the intense gravity of a black hole converts matter into antimatter? Does this mean that matter or energy that goes inside the black hole is converted to antimatter?
It would be more accurate to say that a black hole eventually turns whatever falls in it into equal quantities of matter and antimatter.
The difference between matter and antimatter is defined by some conserved (or approximately conserved) quantum numbers. For example, matter baryons and quarks have positive baryon number, while antibaryons and antiquarks have negative baryon number. Leptons (e.g., electrons, neutrinos) and their antiparticles have a corresponding lepton number instead.
Semiclassically, a black hole evaporates through Hawking radiation. For astrophysically large black holes, this will be overwhelmingly be in terms of photons, which are their own antiparticles, but once the black hole evaporates to a small enough size, it will also radiate massive particles as well. Because there are no long-range forces that couple to baryon number or lepton number, a black hole is under no obligation to conserve them, and thus should radiate equal amounts of matter and antimatter, regardless of what fell into it.
This is unlike, say, energy-momentum, electric charge, and angular momentum, the presence of which makes a difference in the long-range gravitational and/or electromagnetic fields. Thus the total amount of charge the black hole will radiate should match the total amount that fell into it, etc.
Unless, of course, quantum gravity gives us more surprises, which is definitely possible.
I'm assuming that by "inside the black hole" you mean inside the event horizon. In that case, the answer is no. The local space of a particle inside the event horizon is the same as outside - The difference is just that the spacetime points inside and out are causally disconnected.
Right at the singularity, no one knows for sure what happens, but I think it's not likely that matter would turn to antimatter.
This is from my general relativity course from many years ago. I don't think there have been any discoveries since that would invalidate it.
There is this thing called the no hair theorem for black holes. It states that only a few quantities apply -- mass, angular momentum, and charge I think. Most notably, baryon number is NOT one of the few quantities which applies. Black holes do not have a baryon number.
So when a black hole evaporates, the total baryon number of what comes out will NOT be the total baryon number of what went in.
Interestingly, in theory this provides a way to have total conversion of matter -- dump whatever you have laying around into a black hole, wait for it to evaporate, and capture and use the resulting energy (presumably either something like photons or equal amounts of matter and anti-matter).