Circular orbits in extremal Reissner–Nordstrom spacetime

Abstract

Circular null geodesic orbits, in extremal Reissner–Nordstrom spacetime, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely on the event horizon which coincides with the null geodesic generator. Such a null orbit on the horizon is also indicated by the global minimum of the effective potential for circular timelike orbits. This type of geodesic is of course absent in the corresponding near-extremal spacetime, as we show here, testifying to differences between the extremal limit of a generic RN spacetime and the exactly extremal geometry.