It has been established that Black Hole (BH) spacetimes obeying some general
set of assumptions always possess, at least, one light ring (per rotation
sense) [arXiv:2003.06445]. This theorem was originally established for
asymptotically flat, stationary, axial symmetric, 1+3 dimensional circular
spacetimes harbouring a non-extremal and topologically spherical Killing
horizon. Following the mantra that a theorem is only as strong as its
assumptions in this work we extend this theorem to non topologically spherical
(toroidal) BHs and to spacetimes harbouring more than one BH. As in
[arXiv:2003.06445], we show that each BH still contributes with, at least, one
LR (per rotation sense).
It has been established that Black Hole (BH) spacetimes always possess at least one light ring per rotation sense, given a set of general assumptions. Originally, this theorem applied to asymptotically flat, stationary, axial symmetric, 1+3 dimensional circular spacetimes with a non-extremal and topologically spherical Killing horizon.
In this work, we aim to extend this theorem to include non topologically spherical (toroidal) BHs and spacetimes with more than one BH. We adhere to the principle that a theorem is only as strong as its assumptions, and demonstrate that each BH still contributes with at least one light ring per rotation sense, just as in previous research.
Roadmap for the Future
Challenges:
- Generalizing the theorem to include non topologically spherical BHs may require a deeper understanding of the underlying physics and mathematical frameworks.
- Extending the theorem to spacetimes with multiple BHs introduces additional complexities, such as interactions between the BHs and potential interference with light rings.
Opportunities:
- By including non topologically spherical BHs, we can expand our understanding of the properties and behavior of these types of black holes.
- Studying spacetimes with multiple BHs can provide insights into the dynamics and structure of these systems, potentially leading to new discoveries about the nature of gravity and the formation of BHs.
In conclusion, the theorem that Black Hole spacetimes possess at least one light ring per rotation sense has been extended to accommodate non topologically spherical BHs and spacetimes with multiple BHs. While there may be challenges in terms of understanding the underlying physics and dealing with increased complexities, this extension opens up new opportunities for further exploration and gaining deeper insights into the properties and dynamics of black holes.