On geodesics with negative energies in the ergoregions of dirty black holes

TL;DR

This paper investigates equatorial geodesics with negative energies in the ergoregion of generic rotating black holes surrounded by matter, showing that such geodesics cannot form stable circular orbits and must originate and end inside the event horizon.

Contribution

It generalizes previous results for Kerr black holes to generic 'dirty' black holes, demonstrating the absence of negative energy circular geodesics under broad conditions.

Findings

No circular negative energy geodesics exist in the ergoregion of generic dirty black holes.

Such geodesics must originate and terminate inside the event horizon.

Results extend previous Kerr black hole analyses to more general rotating black holes.

Abstract

We consider behavior of equatorial geodesics with the negative energy in the ergoregion of a generic rotating "dirty" (surrounded by matter) black hole. It is shown that under very simple and generic conditions on the metric coefficients, there are no such circular orbits. This entails that such geodesic must originate and terminate under the event horizon. These results generalize the observation made for the Kerr metric in A. A. Grib, Yu. V. Pavlov, and V. D. Vertogradov, Mod. Phys. Lett. 29, 1450110 (2014) [arXiv:1304.7360].