Cylindrical Gravitational Waves in Einstein-Aether Theory

Abstract

Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic in time for both the metric functions $\Psi (r,t)$ and $H(r,t)$. However, in GR, $\Psi (r,t)$ is periodic in time, but $H(r,t)$ is semi-periodic in time, having a secular drifting in the wave frequency. The evolution of wave pulses of a given width is entirely different in both theories in the $H(r,t)$ metric function due to this frequency drifting. Another fundamental difference between the two theories is the gravitational wave velocity. While in GR, the waves propagate with the speed of light, in EA, there is no upper limit to the wave velocity, reaching infinity if $c_{13}\to 1$ and zero if $c_{13}\to -\infty$. We also show that energy-momentum pseudotensor and superpotential get contributions from aether in addition to the usual gravitational field part. All these characteristics are observational signatures that differentiate GR and EA.

arXiv comment26 pages, 10 figures. We have corrected the initial conditions for $H(r,t)$ in order to have $\Psi (r,t)$ not equal to $H(r,t)$

References in corpus (28)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• Einstein-Aether Waves
• Implications of the NANOGrav results for inflation
• Post-Newtonian parameters and constraints on Einstein-aether theory
• Constraints on Einstein-aether theory after GW170817
• Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
• Numerical simulations of gravitational collapse in Einstein-aether theory
• Energy and momentum of cylindrical gravitational waves. II
• Cylindrical Systems in General Relativity
• Energy in the Einstein-Aether Theory
• Gravitational wave forms, polarizations, response functions and energy losses of triple systems in Einstein-Aether theory
• Existence of New Singularities in Einstein-Aether Theory
• Vacuum solutions in the Einstein-Aether Theory
• Spherically Symmetric Analytic Solutions and Naked Singularities in Einstein-Aether Theory
• Thermodynamics of Einstein-Aether Black Holes
• Cylindrical gravitational waves: C-energy, super-energy and associated dynamical effects
• Gravitational plane waves in Einstein-aether theory
• Einstein-Rosen Waves and the Geroch Group
• Chaos and Einstein-Rosen gravitational waves
• Is Birkhoff's Theorem Valid in Einstein-Aether Theory?
• Observable effect of quantized cylindrical gravitational waves
• Renormalization group approach to Einstein-Rosen waves
• Nature of Singularities in Vector-Tensor Theories of Gravity
• Scattering amplitudes for cylindrical gravitational waves

Cited by in corpus (1)

• Complete Classification of Analytical Models in Einstein-Aether Cosmology