08. October 2018

BREMEN-OLDENBURG RELATIVITY SEMINAR
University of Oldenburg

Abstract: Since Albert Einstein first predicted the existence of black holes in his theory of general relativity in 1915, many more black hole solutions have been found. However, the spacetime presented in this talk is special because of its extraordinary horizon geometry. It was found by Dietmar Klemm in 2014 as a special case of the Carter-Plebanski solution of Einstein-Maxwell-Λ theory [1]. The black spindle is a four-dimensional, non-rotating black hole whose horizons have two cusp ends, defining its characteristic spindle shape and giving the spacetime its name. Interestingly, the horizons of the black spindle have a finite area, although their poles extend towards infinity. These properties make this spacetime particularly interesting for further investigations, promising deeper insights into black hole physics. Since the existence of black holes is yet to be confirmed, having an effective tool to study them theoretically is important, especially for exotic spacetimes like the black spindle. The orbits of test particles provide information about a black hole, therefore geodesics are an excellent tool to examine black holes. In this talk I will present the derivation and analytic solution of the geodesic equations in terms of the elliptic Weierstraß ℘-, σ- and ζ-functions. To characterize the spacetime more accurately, we determine the location of the singularity and the event horizons. Furthermore, we use parametric diagrams and effective potentials to find all possible orbit types. This will reveal some very interesting looking orbits. With the analytic solution of the geodesic equations we are able to display the photon motion graphically. At the end of my talk I will present examples of some of these orbits plotted in both spherical and cylindrical coordinates.
[1] D. Klemm, “Four-dimensional black holes with unusual horizons,” Phys. Rev. D, vol. 89, no. 8, p. 084007, 2014.