Space of initial data for self-similar Schwarzschild solutions of the Einstein equations

Phillipo Lappicy
Phys. Rev. D 99, 043509 – Published 13 February 2019

Abstract

The Einstein constraint equations describe the space of initial data for the evolution equations, dictating how space should curve within spacetime. Under certain assumptions, the constraints reduce to a scalar quasilinear parabolic equation on the sphere with various singularities and nonlinearity being the prescribed scalar curvature of space. We focus on self-similar Schwarzschild solutions. Those describe, for example, the initial data of black holes. We construct the space of initial data for such solutions and show that the event horizon is related with global attractors of such parabolic equations. Lastly, some properties of those attractors and its solutions are explored.

  • Figure
  • Received 29 March 2018

DOI:https://doi.org/10.1103/PhysRevD.99.043509

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsNonlinear Dynamics

Authors & Affiliations

Phillipo Lappicy

  • Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Avenida trabalhador são-carlense 400, 13566-590 São Carlos, São Paulo, Brazil

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Issue

Vol. 99, Iss. 4 — 15 February 2019

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