Bowen-York model solution redux


Altas E., Tekin B.

EUROPEAN PHYSICAL JOURNAL C, vol.81, no.4, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 81 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1140/epjc/s10052-021-09139-z
  • Title of Journal : EUROPEAN PHYSICAL JOURNAL C

Abstract

Initial value problem in general relativity is often solved numerically; with only a few exceptions one of which is the "model" solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between [0, 0.592). This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is 59.2% of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.