Classical theory cannot provide a satisfying scenario for a unitary thermodynamic evolution of black holes. To preserve information one requires quantum mechanical effects on scales reaching beyond the traditional horizon radius. Therefore, common to many of the theories attempting to resolve the paradox is the existence of exotic horizon structures. The recent advent of gravitational wave astronomy provides a possible means for detecting the existence of such structures through gravitational wave emission in the ringdown phase of binary black hole mergers. Such emission is described by quasinormal modes (QNMs) in which the gravitational waves originates outside the black hole, in the vicinity of the photon spheres. Requiring reflective properties of the horizon structure results in the existence of gravitational echoes that may be detected by facilities such as LIGO etc.. This thesis studies geodesic motion of such echoes in the equatorial plane of a rotating black hole. Depending on the extent of the horizon structure, and the particular mode of emission, one can expect different timescales for the echoes. For a horizon structure extending <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CLambda%20r%20=" /> <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?10%5E%7B-12%7D" /> <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?M" /> outside the traditional horizon of a  <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?M%20=%2022.6%20M_%7B%5Codot%7D" />, <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?a%20=%200.74%20M" /> black hole one would ideally find echoes appearing as integer multiples of <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%20t_%7Becho%7D" /><img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?=%200.0204%20s" /> after the primary signal. The time delay is expected to increase by at least an order of magnitude if one lets <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%20r%20%5Csim%2010%5E%7B-80%7D%20M" />. The expected echo timescales for gravitational waves emitted from any point around the black hole, in arbitrary modes, is an interesting further study.