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 is examined with regard to their geodesic stability and compared with similar geodesics in the nonextremal situation. Extremization of the effective potential for timelike 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 (PG) coordinates become zero, thus these three orbits indeed coincide with the null geodesic generators of the event horizon. This strange behavior is quite different from the static, spherically symmetric extremal Reissner–Nordstrøm (RN) BH.