  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.
