Examples of Black Holes in Two-Time Physics

Two time theory is derived via localization of the global Sp(2) [or Osp(1/2), Osp(N/2), Sp(2N),...] symmetry in phase space in order to give a self contained introduction to two time theory. Then it is shown that from the two-times physics point of view theories of point particles on many known black hole backgrounds are Sp(2) gauge duals of one another and of course also gauge dual to all other equal dimensional gauges from earlier two time related publications (hydrogen atom, ...). We reproduce the free (quantum) relativistic particle on 1+1 dimensional black hole backgrounds and 2+1 dimensional BTZ ones. Other 2+1 black holes and n+1 ones are touched on but explicitely found only as cross sections of complicated (n+1)+1 backgrounds. Further we give near horizon solutions (e.g. n+1 Robertson-Bertotti). Since two time physics can reproduce these backgrounds all particle actions have hidden symmetries that have not been noticed before.