O bservable properties oforbits in exact bum py spacetim es

W eexplorethepropertiesoftest-particleorbitsin \bum py"spacetim es| stationary,reectionsym m etric,asym ptotically atsolutionsofEinstein equationsthathave a non-Kerr(anom alous) higher-order m ultipole-m om ent structure but can be tuned arbitrarily close to the Kerr m etric. Futuredetectorsshould observegravitationalwavesgenerated during inspiralsofcom pactobjects into superm assive centralbodies. Ifthe centralbody deviates from the Kerr m etric,this will m anifestitselfin the em itted waves. Here,we explore som e ofthe featuresoforbitsin non-Kerr spacetim esthatm ightlead to observablesignatures.Asabasisforthisanalysis,weuseafam ily of exactsolutionsproposedbyM anko& Novikovwhichdeviatefrom theKerrm etricinthequadrupole and higherm om ents,butwealso com pareourresultsto otherwork in theliterature.W eexam ine