Does the existence of a trapped surface in a region of space (not necessarily either of the vacuum or symmetric spacetime) indicates (theoretically) the existence of a "black hole" there? And if yes, is it sufficient to describe the existence of a "black hole" (at least theoretically) by the existence of a trapped surface there?
Note: Penrose, in his famous paper in 1965 ["Gravitational collapse and space-time singularities". Phys. Rev. Lett. 14 (3): 57–59] claimed that [Source: Wikipedia],
A trapped surface is one where light is not moving away from the black hole.
But it is also well known that singularity can be avoided in the quantum treatment of such problem. Now the notion of singularity is eternally related to the concept of a trapped surface!
Along-with the previously cited references, I also had a look into the following references, but unfortunately my doubts remained uncleared (may be I've missed something there, which can clearly point out and answer my doubts):
"Lecture Notes on General Relativity" by Matthias Blau, Albert Einstein Center for Fundamental Physics, Institut f¨ur Theoretische Physik, Universit¨at Bern. (Chapter 29, Section E; updated version of October 8, 2022)
Senovilla, Jose M. M. (September 15, 2011). "Trapped Surfaces". International Journal of Modern Physics D. 20 (11): 2139–2168. arXiv:1107.1344 [gr-qc].
Hawking, Stephen & Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press. (Preface, page $7-8$ and Chapter 8, page $266-267$; reprinted edition of 1994)
Bengtsson, Ingemar (December 22, 2011). "Some Examples of Trapped Surfaces". arXiv:1112.5318 [gr-qc].
Kanai, Yuki. Siino, Masaru. Hosoya, Akio (August 3, 2010). "Gravitational collapse in Painlevé-Gullstrand coordinates". arXiv:1008.0470v1 [gr-qc].
So what's the way out? How the existence of a trapped surface and the existence of a black hole is (theoretically) connected to each other?