On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry

Nishanth Gudapati

On 3+1 Lorentzian Einstein Manifolds with One Rotational Isometry

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arxiv 1703.06331 v1 pith:CWMHB4PK submitted 2017-03-18 gr-qc math.APmath.DG

Nishanth Gudapati This is my paper · ORCID

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keywords einsteinequationslorentzianmanifoldsassumedconsidercoupledexplicit

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abstract

We consider 3+1 rotationally symmetric Lorentzian Einstein spacetime manifolds with $\Lambda >0$ and reduce the equations to 2+1 Einstein equations coupled to `shifted' wave maps. Subsequently, we prove various (explicit) positive mass-energy theorems. No smallness is assumed.

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On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
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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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