Complete set of solutions of the geodesic equation in the space-time of a Schwarzschild black hole pierced by a cosmic string
Eva HackmannZARM, Universität Bremen, Am Fallturm, 28359 Bremen, GermanyBetti HartmannSchool of Engineering and Science, Jacobs University Bremen, 28759 Bremen, GermanyCláus LämmerzahlZARM, Universität Bremen, Am Fallturm, 28359 Bremen, GermanyParinya SirimachanSchool of Engineering and Science, Jacobs University Bremen, 28759 Bremen, Germany
2010en
ABI
Abstract
We study the geodesic equation in the space-time of a Schwarzschild black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of this equation for massive and massless particles, respectively. The solutions of the geodesic equations can be classified according to the particle's energy and angular momentum, the ratio between the component of the angular momentum aligned with the axis of the string and the total angular momentum, the deficit angle of the space-time and as well the horizon radius (or mass) of the black hole. For bound orbits of massive test particles we calculate the perihelion shift, we discuss light deflection and comment on the Newtonian limit.
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