  It has been suggested in the literature that, given a black hole spacetime, a
relativistic membrane can provide an effective description of the horizon
dynamics. In this paper, we explore such a framework in the context of a
2+1-dimensional BTZ black hole. Following this membrane prescription, we are
able to translate the horizon dynamics (now described by a string) into the
convenient form of a 1+1-dimensional Klein-Gordon equation. We proceed to
quantize the solutions and construct a thermodynamic partition function.
Ultimately, we are able to extract the quantum-corrected entropy, which is
shown to comply with the BTZ form of the Bekenstein-Hawking area law. We also
substantiate that the leading-order correction is proportional to the logarithm
of the area.
