Abstract
This research provides second-order approximate Noether symmetries of geodetic Lagrangian of time-conformal plane symmetric spacetime. A time-conformal factor is of the form e ϵ f ( t ) which perturbs the plane symmetric static spacetime, where ϵ is small a positive parameter that produces perturbation in the spacetime. By considering the perturbation up to second-order in ϵ in plane symmetric spacetime, we find the second order approximate Noether symmetries for the corresponding Lagrangian. Using Noether theorem, the corresponding second order approximate conservation laws are investigated for plane symmetric gravitational waves like spacetimes. This technique tells about the energy content of the gravitational waves.
Highlights
Gravitational waves are ripples in the fabric of space-time produced by some of the most violent and energetic processes like colliding black holes or closely orbiting black holes and neutron stars
In 1905, Henri Poincare [6] proposed that gravitational waves are the outcomes of disturbances or distortions in the fabric of spacetime produced by the accelerated motion of heavy masses like black holes and neutron stars
Two classes of time conformal plane symmetric spacetimes are given in the same section (Section 4) along with second order approximate Noether symmetries and second order approximate conservation laws
Summary
Gravitational waves are ripples in the fabric of space-time produced by some of the most violent and energetic processes like colliding black holes or closely orbiting black holes and neutron stars (binary pulsars). The ultimate aim of the approximate Noether symmetry is to search plane symmetric spacetimes which are gravitational wave like spacetimes and re-scale the energy and momentum in the respective spacetimes. Approximate Noether symmetry [17,18,19,20,21,22] techniques have been used frequently by the researchers to re-scale the energy and momentum in gravitational waves like spacetimes for which Rμν → 0 as x → ∞. Two classes of time conformal plane symmetric spacetimes are given in the same section (Section 4) along with second order approximate Noether symmetries and second order approximate conservation laws. The system of 19 determining partial differential equations is shifted to the Appendix A at the end of the paper
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