Hamiltonian theory for the axial perturbations of a dynamical spherical background

Abstract

We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial gravitational wave in a Hamiltonian pair of variables. Then, switching to a more geometrical description of the system, we construct the only scalar combination of them. We obtain the well-known Gerlach and Sengupta scalar for axial perturbations, with no known equivalent for polar perturbations. The strategy suggested and tested here will be applied to the polar case in a separate article.

12 pages, accepted by Classical and Quantum Gravity

References in corpus (3)

• xPerm: fast index canonicalization for tensor computer algebra
• Second and higher-order perturbations of a spherical spacetime
• High-order gauge-invariant perturbations of a spherical spacetime

Cited by in corpus (8)

• Breaking of isospectrality of quasinormal modes in nonrotating loop quantum gravity black holes
• Linear perturbations of self-gravitating spherically symmetric configurations
• The quasi normal modes of growing dirty black holes
• Axial perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Polar perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology
• Master variables and Darboux symmetry for axial perturbations of the exterior and interior of black hole spacetimes
• Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes
• Effective Regge-Wheeler equations of a hybrid loop quantum black hole