Horizon Straddling ISCOs in Spherically Symmetric String Black Holes

Abstract

The causal geodesics in the equatorial plane of a static extremal charged black holes in heterotic string theory are examined with regard to their geodesic stability, and compared with similar geodesics in the non-extremal situation. Extremization of the effective potential for time-like and null circular geodesics implies that in the extremal limit, the radius of ISCO(Inner-most Stable Circular Orbit) $(r_{ISCO})$, circular photon orbit (CPO) $(r_{ph})$ and marginally bound circular orbit (MBCO) $(r_{mb})$ are coincident with the event horizon $(r_{hor})$ i.e. $r_{ISCO}=r_{ph}=r_{mb}=r_{hor}=2M$. Since the proper radial distance on a constant time slice both in Schwarzschild and Painlevé-Gullstrand coordinates become zero, thus these three orbits indeed coincide with the \emph{null geodesic generators of the event horizon}. This strange behavior is quite different from the static, spherically symmetric extremal Reissner Nordstrøm black hole.