Obstacle to provide that black holes really exist?

Answer 1

The biggest obstacle for proof of existence of black holes has always been our inability to observe them directly, due to their nature of absorbing light and never emitting it (since the escape velocity of a black hole exceeds the speed of light). However, there is abundant evidence of their existence. For example, studies of the orbits of stars near the supermassive black hole at the Milky Way's core have shown that no object other than a black hole could explain their path - otherwise, the stars in orbit would hit the object (i.e., it is so small and so massive, that there is no other possible explanation).