Circular Orbits in Extremal Reissner Nordstrom Spacetimes

TL;DR

This paper investigates the stability and characteristics of circular null and timelike geodesic orbits in extremal Reissner-Nordstrom spacetimes, revealing a unique stable orbit on the event horizon absent in near-extremal cases.

Contribution

It demonstrates the existence of a stable circular geodesic on the event horizon in extremal RN spacetime, highlighting differences from near-extremal geometries.

Findings

Existence of a stable null geodesic on the event horizon.

Stable circular timelike orbit as a global minimum of the effective potential.

Absence of such orbits in near-extremal RN spacetimes.

Abstract

Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetimes, 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 {\it on} the event horizon, which coincides with its null geodesic generator. Such an orbit also emerges as a global minimum of the effective potential for circular {\it 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.