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Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy

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arxiv 1904.09670 v1 pith:QBU2YE7M submitted 2019-04-21 gr-qc math.DG

Nishanth Gudapati This is my paper · ORCID
classification gr-qcmath.DG
keywords axiallyenergyperturbationssymmetricblackfunctionalgauge-invarianthamiltonian
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abstract

Based on the Hamiltonian dimensional reduction of $3+1$ axially symmetric, Ricci-flat Lorentzian spacetimes to a $2+1$ Einstein-wave map system with the (negatively curved) hyperbolic 2-plane target, we construct a positive-definite, (spacetime) gauge-invariant energy functional for linear axially symmetric perturbations in the exterior of Kerr black holes, in a manner that is also gauge-independent on the target manifold. We also show that the positive-definite energy functional serves as a Hamiltonian for the constrained evolution of the linear perturbations

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  1. On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes

    gr-qc 2025-07 conditional novelty 4.0 of 10

    For subextremal Kerr spacetimes, the paper constructs a positive-definite, conserved Hamiltonian energy for axially symmetric linear perturbations, indicating a form of linear stability within this symmetry class.

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