Applications of hidden symmetries to black hole physics

TL;DR

This paper reviews how hidden symmetries in black hole spacetimes enable complete integrability of particle and light motion, highlighting recent theoretical advances in understanding these symmetries' origins and implications.

Contribution

It provides a comprehensive review of the role of hidden symmetries in black hole physics and discusses recent results explaining their presence.

Findings

Black holes possess explicit and hidden symmetries.

Hidden symmetries lead to integrability of equations of motion.

Recent results explain the origin of these symmetries.

Abstract

This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set (`tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.