Final answer:
The concept of locally inertial frames applies even theoretically at the center of a black hole, yet the gravitational effects there are non-negligible from a broader perspective. Observational evidence via accretion disks, among other phenomena, supports the existence of black holes, where all mass is concentrated to a point, presenting extreme spacetime curvature.
Step-by-step explanation:
In the context of Einstein's theory of general relativity, the idea of a locally inertial frame where gravitation seems absent is a cornerstone. At every spacetime point, including the theoretical location at the very center of a black hole, one could imagine such a locally inertial frame. However, at the central singularity of a black hole, known as the 'center' where densities approach infinity, the laws of physics as we understand them, including general relativity, break down. Thus, it's problematic to discuss gravitational effects as we would in other contexts.
Observational evidence confirms that black holes, with immense gravity, warp spacetime dramatically. This curvature is so extreme that anything, including light, which passes beyond the black hole's event horizon, cannot escape. While a locality in free fall might experience 'weightlessness,' and a local observer may not detect gravity directly, this doesn't negate the presence of gravity from a broader perspective.
A black hole's mass is indeed concentrated at its center, resulting in a gravitational pull that acts as if it originates from a single point. This central singularity, however, isn't just a point of intense gravity but represents where our current understanding of physics ceases to apply. Accretion disks around black holes provide significant observational evidence for their existence, showcasing the effects of their gravity on surrounding matter.