Muraari Vasudevan

Complete Integrability of Geodesic Motion in General Higher-Dimensional Rotating Black-Hole Spacetimes

We explicitly exhibit n-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.

Constants of geodesic motion in higher-dimensional black-hole spacetimes

In [Phys. Rev. Lett. 98, 061102 (2007)], we announced the complete integrability of geodesic motion in the general higher-dimensional rotating black-hole spacetimes. In the present paper we prove all the necessary steps leading to this conclusion. In particular, we demonstrate the independence of the constants of motion and the fact that they Poisson commute. The relation to a different set of constants of motion constructed in [J. High Energy Phys. 02 (2007) 004] is also briefly discussed.

Separability of the Hamilton–Jacobi and Klein–Gordon equations in Kerr–de Sitter metrics

We study separability of the Hamilton–Jacobi and massive Klein–Gordon equations in the general Kerr–de Sitter spacetime in higher dimensions. Complete separation of both equations is carried out in 2n + 1 spacetime dimensions with all n rotation parameters equal, in which case the rotational symmetry group is enlarged from (U(1))n to U(n). We explicitly construct the additional Killing vectors associated with the enlarged symmetry group which permit separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.

Integrability of particle motion and scalar field propagation in Kerr-(Anti) de Sitter black hole spacetimes in all dimensions

We study the Hamilton-Jacobi and massive Klein-Gordon equations in the general Kerr-(Anti) de Sitter black hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black hole rotation parameters. We analyze explicitly the symmetry properties of these backgrounds that allow for this Liouville integrability and construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties. This work greatly generalizes previously known results for both the Myers-Perry metrics, and the Kerr-(Anti) de Sitter metrics in higher dimensions.

Particle motion and scalar field propagation in Myers–Perry black-hole spacetimes in all dimensions

We study separability of the Hamilton–Jacobi and massive Klein–Gordon equations in the general Myers–Perry black-hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black-hole rotation parameters, which significantly enlarges the rotational symmetry group. We explicitly construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.

Charges of exceptionally twisted branes

The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labelled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dimensions see the simple currents of A2 and D4, respectively.

Integrability of some charged rotating supergravity black hole solutions in four and five dimensions

Abstract We study the integrability of geodesic flow in the background of some recently discovered charged rotating solutions of supergravity in four and five dimensions. Specifically, we work with the gauged multicharge Taub–NUT–Kerr–(anti-)de Sitter metric in four dimensions, and the U ( 1 ) 3 gauged charged-Kerr–(anti-)de Sitter black hole solution of N = 2 supergravity in five dimensions. We explicitly construct the nontrivial irreducible Killing tensors that permit separation of the Hamilton–Jacobi equation in these spacetimes. These results prove integrability for a large class of previously known supergravity solutions, including several BPS solitonic states. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties. Finally, we also examine the Klein–Gordon equation for a scalar field in these spacetimes and demonstrate separability.

A Note on particles and scalar fields in higher dimensional Nutty spacetimes

Abstract In this note, we study the integrability of geodesic flow in the background of a very general class of spacetimes with NUT-charge(s) in higher dimensions. This broad set encompasses multiply NUT-charged solutions, electrically and magnetically charged solutions, solutions with a cosmological constant, and time-dependant bubble-like solutions. We also derive first-order equations of motion for particles in these backgrounds. Separability turns out to be possible due to the existence of non-trivial irreducible Killing tensors. Finally, we also examine the Klein–Gordon equation for a scalar field in these spacetimes and demonstrate complete separability.