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

2019/04/21 by Nishanth Gudapati, Gudapati, Nishanth
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · pdf · doi:10.48550/arxiv.1904.09670

openalex publication_date 2019/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• A Method for Generating Solutions of Einstein's Equations
• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem
• Stability of a Schwarzschild Singularity
• On the Deviation of Geodesics and Null-Geodesics, Particularly in Relation to the Properties of Spaces of Constant Curvature and Indefinite Line-Element

Related

• On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
• Axially Symmetric Perturbations of Kerr Black Holes II: Boundary Behaviour of the Dynamics in the Orbit Space
• A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
• Gravitational Waves on Kerr Black Holes I: Reconstruction of Linearized Metric Perturbations
• Master Variables and Darboux Symmetry for Axial Perturbations of the Exterior and Interior of Black Hole Spacetimes