Conformal mechanics on rotating Bertotti-Robinson spacetime

TL;DR

This paper explores the conformal mechanics of the rotating Bertotti-Robinson spacetime, revealing its symmetry properties, geodesic behavior, and the structure of its asymptotic symmetry algebra, with implications for black hole near-horizon physics.

Contribution

It characterizes the conformal mechanics and asymptotic symmetries of the rotating Bertotti-Robinson spacetime, extending understanding of near-horizon geometries of extremal rotating black holes.

Findings

Conformal mechanics matches that of a charged particle in BR background.

Transition to global coordinates yields a discrete energy spectrum.

Asymptotic symmetry algebra is a Virasoro algebra times U(1).

Abstract

We investigate conformal mechanics associated with the rotating Bertotti-Robinson (RBR) geometry found recently as the near-horizon limit of the extremal rotating Einstein-Maxwell-dilaton-axion black holes. The solution breaks the $SL(2,R)\times SO(3)$ symmetry of Bertotti-Robinson (BR) spacetime to $SL(2,R)\times U(1)$ and breaks supersymmetry in the sense of $N=4, d=4$ supergravity as well. However, it shares with BR such properties as confinement of timelike geodesics and discreteness of the energy of test fields on the geodesically complete manifold. Conformal mechanics governing the radial geodesic motion coincides with that for a charged particle in the BR background (a relativistic version of the De Alfaro-Fubini-Furlan model), with the azimuthal momentum playing the role of a charge. Similarly to the BR case, the transition from Poincar\'e to global coordinates leads to a redefinition of the Hamiltonian making the energy spectrum discrete. Although the metric does not split into a product space even asymptotically, it still admits an infinite-dimensional extension of $SL(2,R)$ as asymptotic symmetry. The latter is shown to be given by the product of one copy of the Virasoro algebra and U(1), the same being valid for the extremal Kerr throat.