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arXiv · 1904.09670

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

Nishanth Gudapati
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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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Nishanth Gudapati. 2019-04-21. Axially Symmetric Perturbations of Kerr Black Holes I: A gauge-invariant construction of ADM Energy. https://arxiv.org/abs/1904.09670

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