I can think already of quite a few papers that show that black holes can’t exist. My favourite is the “fuzzball” unification of black holes and string theory in which strings ball up to form a sphere of the same diameter as the supposed black hole – but it isn’t black.
However, Mersini-Houghton’s approach is totally different. It says, not that black holes don’t exist, but that they can’t be formed by a star going supernova. The technical arXiv article is here
“A star collapsing gravitationally into a black hole emits a flux of radiation, knowns as Hawking
radiation. When the initial state of a quantum field on the background of the star, is placed
in the Unruh vacuum in the far past, then Hawking radiation corresponds to a flux of positive
energy radiation travelling outwards to future infinity. The evaporation of the collapsing star can
be equivalently described as a negative energy flux of radiation travelling radially inwards towards
the center of the star. Here, we are interested in the evolution of the star during its collapse. Thus
we include the backreaction of the negative energy Hawking flux in the interior geometry of the
collapsing star and solve the full 4-dimensional Einstein and hydrodynamical equations numerically.
We find that Hawking radiation emitted just before the star passes through its Schwarzschild radius
slows down the collapse of the star and substantially reduces its mass thus the star bounces before
reaching the horizon. The area radius starts increasing after the bounce. Beyond this point our
program breaks down due to shell crossing. We find that the star stops collapsing at a finite radius
larger than its horizon, turns around and its core explodes. This study provides a realistic
investigation of the backreaction of Hawking radiation on the collapsing star.”
This looks to me like someone has slipped more than a couple of decimal places in their calculation. Hawking radiation for an object as large as a stellar mass black hole ought to be negligible. It only become significant for much smaller black holes.