To Love or Not to Love

Tidal Love numbers provide us a handle to test the nature of
compact objects, as well as theories of gravity. There have been several
clarifications recently, which makes our understanding of these Love
numbers better. But further investigations have led to more confusion. I
plan to discuss these recent developments and the confusing nature of
recent literature on these issues. I will show that the tidal Love numbers
of a non-rotating black hole identically vanishes in the static case,
which may not be true in the dynamical scenario. While for rotating black
holes the situation is a bit more involved. Besides, I will also discuss
fermionic perturbations leading to non-zero static Love numbers for black
holes. I will also highlight some remarkable novel features, for
ultra-compact objects as well as for quantum BHs.