Space-time is an irrational idea as so-called space is a physical reality and time is a concept. They cannot get married. Existing of black holes is a controversial idea. Mathematics does not explain a thing.

That was, indeed, the idea behind it.

However the Vaidya geometry is a classical geometry, that describes gravitational radiation. That’s why it doesn’t have anything to do with processes involving Hawking radiation.

Stam Nicolis thank you,

you mean in classical limit of a quantum gravity of the evaporation we expect a Vaidya-like solution?

Not necessarily-since just what is quantum gravity isn't, yet, known. This review:

Preprint Geometry of Vaidya spacetimes

might be useful.

In classical gravity black holes don't evaporate, because they can't. One can't, just, define ``outgoing'' Vaidya spacetime, because the boundary conditions at infinity do matter.

Stam Nicolis thanks

Black holes are talk of a meaningless solution to Einstein's equation. Einstein himself considered this a misunderstanding.

This is the result of a simplification of the theory that Einstein made in 1915. In order for the equations of the gravitational field to satisfy the conservation law, the energy of the gravitational field must be present in the equation. Einstein did not cope with this task and Einstein's equation turned out to be incomplete.

This task has been solved

Preprint Gravitational Field Equation and the Structure of Black Holes

Valery Borisovich Morozov how do you consider GR without the energy conservation?

and why do you believe that BH are meaningless?