2016/02/14 by Gustav Holzegel · 22 citations
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Classical mechanics #Conservation law #Cosmology and Gravitation Theories #Deriving the Schwarzschild solution #Event horizon #General relativity #Gravitation #Hypersurface #Kerr metric #Linearized gravity #Mathematical analysis #Mathematical physics #Null (SQL) #Perturbation (astronomy) #Physics #Quantum mechanics #Schwarzschild geodesics #Schwarzschild metric #Schwarzschild radius #Spacetime #gr-qc #math.AP
paper · pdf · doi:10.1088/0264-9381/33/20/205004
published in Classical and Quantum Gravity 33(20), 205004 (IOP Publishing) · 21 pages, 2 figures
arxiv created 2016/02/14 · openalex created_date 2016/06/24 · openalex publication_date 2016/09/21 · arxiv updated 2016/10/05 · openalex updated_date 2026/08/05
We derive an energy conservation law for the system of gravitational perturbations on the Schwarzschild spacetime expressed in a double null gauge. The resulting identity involves only first derivatives of the metric perturbation. Exploiting the gauge invariance up to boundary terms of the fluxes that appear, we are able to establish positivity of the flux on any outgoing null hypersurface to the future of the initial data. This allows us to bound the total energy flux through any such hypersurface, including the event horizon, in terms of initial data. We similarly bound the total energy radiated to null infinity. Our estimates provide a direct approach to a weak form of stability, thereby complementing the proof of the full linear stability of the Schwarzschild solution recently obtained in Dafermos et al (2016 The linear stability of the Schwarzschild solution to gravitational perturbations arXiv:1601.06467).