Horizon Straddling ISCOs in Spherically Symmetric String Black Holes

TL;DR

This paper investigates the behavior of innermost stable circular orbits and photon orbits in extremal string black holes, revealing they coincide with the event horizon, unlike in classical Reissner-Nordström black holes.

Contribution

It demonstrates that in extremal string black holes, key circular orbits coincide with the event horizon, a behavior distinct from classical black hole solutions.

Findings

ISCO, CPO, and MBCO all coincide with the event horizon in extremal string black holes.

Proper radial distance to these orbits becomes zero, indicating they are null geodesic generators.

This behavior differs from extremal Reissner-Nordström 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 Painlev\'{e}-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 Nordstr{\o}m black hole.