Black holes are arguably the most extreme manifestation of gravity, with horizons
that mark the boundary of no return beyond which nothing, not even light, can escape. Recently,
remarkable progress has been made on the observational fronts, with the detection of
gravitational wave produced by colliding black holes, and “direct” imaging of the supermassive
black holes in the galaxy M87. On the theoretical side however, there remains a lot of unsolved
mysteries in black hole physics. Of these, the information paradox is the most well-known.
Nevertheless, there is another equally puzzling – if not more so – issue, which concerns the very
heart of black holes: their singularities, where general relativity breaks down. What happens
at the singularities of black holes? Can quantum gravity really remove black hole singularities?
Is there a difference between Big Bang singularity and those inside black holes? More
crucially, can singularities become naked, i.e. no longer shrouded by black hole horizon and
therefore visible to ordinary observers? What is the status of the so-called “cosmic censorship
conjecture”? In this review we will go through this topic at a semi-technical level, which is
suitable for an ambitious undergraduate students in physics or mathematics.
