Cosmological post-Newtonian expansions to arbitrary order

Aug, 2009
27 pages
Published in:
  • Commun.Math.Phys. 295 (2010) 431-463
e-Print:

Citations per year

20092013201720212023120
Abstract: (arXiv)
We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter \ep=v_T/c (0<\ep < \ep_0), where cc is the speed of light, and vTv_T is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M\cong [0,T)\times \Tbb^3, and converge as \ep \searrow 0 to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter \ep to any specified order with expansion coefficients that satisfy \ep-independent (nonlocal) symmetric hyperbolic equations.