  Gravitational memory effect has emerged as a new window and opened up several
intriguing avenues in the field of gravitational wave astronomy together with
its inter-connection to asymptotic symmetries (AS). The recent developments in
this direction have drawn considerable attention from theoretical as well as
observational perspectives. It has been shown that such effects can also be
recovered near the horizon of black holes which might play a crucial role in
understanding the information paradox. With this motivation, we have studied
the gravitational memory effect near the horizon of black holes analogous to
the one obtained at asymptotic null infinity.
  We first study how the AS emerge near the horizon of black holes and how they
can be detected via some ideal detectors as some permanent change of
configurations (Memory) once GW passes through the setup. The emergence of AS
is studied from two different perspectives. First, how AS emerge as soldering
freedoms when two black holes are being glued along a common null surface.
Secondly, in the form of AS that preserve the asymptotic form of the near
horizon metric of a black hole. We have established an analogous form of the
displacement memory near the horizon of non-extreme and extreme black holes for
both these perspectives. We also discuss the detection prospects of the
supertranslation memory or hair. In this direction, other than the memory
effect, we have explored the possibility of detecting a supertranslated black
hole through standard tests of General Relativity. We propose a scenario in
which such a configuration may be distinguished from ordinary black holes by
examining the photon trajectories near the horizon. As we know that the
gravitational memory has not been detected yet, in this direction, our study
might serve as a useful contribution towards investigation of the signatures of
AS in the future.

General Relativity and Quantum Cosmology;High Energy Physics - Theory