A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910729958850560 |
|---|---|
| author | Moncrief, Vincent Gudapati, Nishanth |
| author_facet | Moncrief, Vincent Gudapati, Nishanth |
| contents | We consider the axisymmetric, linear perturbations of Kerr-Newman black holes, allowing for arbitrarily large (but subextremal) angular momentum and electric charge. By exploiting the famous Carter-Robinson identities, developed previously for the proofs of (stationary) black hole uniqueness results, we construct a positive-definite energy functional for these perturbations and establish its conservation for a class of (coupled, gravitational and electromagnetic) solutions to the linearized field equations. Our analysis utilizes the familiar (Hamiltonian) reduction of the field equations (for axisymmetric geometries) to a system of wave map fields coupled to a 2+1-dimensional Lorentzian metric on the relevant quotient 3-manifold. The propagating `dynamical degrees of freedom' of this system are entirely captured by the wave map fields, which take their values in a four dimensional, negatively curved (complex hyperbolic) Riemannian target space whereas the base-space Lorentzian metric is entirely determined, in our setup, by elliptic constraints and gauge conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_12632 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes Moncrief, Vincent Gudapati, Nishanth General Relativity and Quantum Cosmology We consider the axisymmetric, linear perturbations of Kerr-Newman black holes, allowing for arbitrarily large (but subextremal) angular momentum and electric charge. By exploiting the famous Carter-Robinson identities, developed previously for the proofs of (stationary) black hole uniqueness results, we construct a positive-definite energy functional for these perturbations and establish its conservation for a class of (coupled, gravitational and electromagnetic) solutions to the linearized field equations. Our analysis utilizes the familiar (Hamiltonian) reduction of the field equations (for axisymmetric geometries) to a system of wave map fields coupled to a 2+1-dimensional Lorentzian metric on the relevant quotient 3-manifold. The propagating `dynamical degrees of freedom' of this system are entirely captured by the wave map fields, which take their values in a four dimensional, negatively curved (complex hyperbolic) Riemannian target space whereas the base-space Lorentzian metric is entirely determined, in our setup, by elliptic constraints and gauge conditions. |
| title | A Positive-Definite Energy Functional for the Axisymmetric Perturbations of Kerr-Newman Black Holes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2105.12632 |