At present, a complete unification of general relativity (which describes gravity on a large scale) and quantum field theory (which describes the behavior of subatomic particles and their interactions) has not been achieved. The two theories have different frameworks and mathematical descriptions that make it challenging to combine them consistently.
Black holes are fascinating objects where the effects of extreme gravity are significant, and quantum phenomena are expected to play a role near their singularities. However, without a complete theory of quantum gravity, our understanding of black hole singularities remains limited.
According to classical general relativity, the singularity at the center of a black hole is thought to be a point of infinite density and curvature, often referred to as a "singularity." However, these infinities are considered indications that general relativity breaks down in this extreme regime. The predictions of quantum mechanics suggest that quantum effects might become important and resolve these singularities.
Various approaches have been proposed to tackle the problem of combining general relativity and quantum mechanics, such as string theory, loop quantum gravity, and others. These theories aim to provide a more comprehensive framework that incorporates both quantum and gravitational phenomena.
While these approaches offer promising directions, a definitive theory of quantum gravity that can accurately describe the behavior of black hole singularities is still an active area of research. Until a successful theory of quantum gravity is developed, it remains uncertain whether it will enable us to precisely determine the actual radius of black hole singularities.