Periodic Solutions of the Einstein Equations for Binary Systems

Abstract

This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with outgoing waves. A variational principle is found which has the power to provide an accurate estimate of the relationship between the mass and angular momentum of the system, the masses and angular momenta of the components, the rotational frequency of the frame of reference in which the system is periodic, the frequency of the periodicity of the system, and the amplitude and phase of each multipole component of gravitational radiation. Examination of the boundary terms of the variational principle leads to definitions of the effective mass and effective angular momentum of a periodic geometry which capture the concepts of mass and angular momentum of the source alone with no contribution from the gravitational radiation. These effective quantities are surface integrals in the weak-field zone which are independent of the surface over which they are evaluated, through second order in the deviations of the metric from flat space.

18 pages, RevTeX 3.0, UF-RAP-93-12

References in corpus (1)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action

Cited by in corpus (32)

• Inspiral, merger and ring-down of equal-mass black-hole binaries
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Circular orbits and spin in black-hole initial data
• Thermodynamics of binary black holes and neutron stars
• Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
• Coalescence of black hole--neutron star binaries
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Non-conformally flat initial data for binary compact objects
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• Formulation for the internal motion of quasi-equilibrium configurations in general relativity
• Construction of initial data for 3+1 numerical relativity
• New code for equilibriums and quasiequilibrium initial data of compact objects. IV. Rotating relativistic stars with mixed poloidal and toroidal magnetic fields
• Binary black hole spacetimes with a helical Killing vector
• Models of helically symmetric binary systems
• Quasi-stationary binary inspiral II: Radiation-balanced boundary conditions
• The Periodic Standing-Wave Approximation: Overview and Three Dimensional Scalar Models
• Post-Minkowski action for point particles and a helically symmetric binary solution
• Radiation-balanced simulations for binary inspiral
• Thermodynamics of magnetized binary compact objects
• The periodic standing-wave approximation: eigenspectral computations for linear gravity and nonlinear toy models
• Massive Graviton Geons
• Formulation for nonaxisymmetric uniformly rotating equilibrium configurations in the second post-Newtonian approximation of general relativity
• Quasistationary binary inspiral. I. Einstein equations for the two Killing vector spacetime
• Standing waves in general relativity
• Helical Symmetry in Linear Systems
• Variational Principles in General Relativity
• Fourth-post-Newtonian-exact approximation to General Relativity
• A fast stroboscopic spectral method for rotating systems in numerical relativity
• Dark matter influence on black hole objects thermodynamics
• The geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem
• Quasi-equilibrium models of magnetized compact objects
• Numerical study of the Kerr solution in rotating coordinates