In this article, we study the tensor mode equation of perturbation in presence nonzero-Lambda as dark energy, dynamic nature which depends on Hubble parameter H and/or its time derivative. Dark according to total vacuum contribution, has a slight effect during radiation-dominated era, but it reduces squared amplitude gravitational waves (GWs) up 60% for wavelengths that enter horizon matter-dom...

The purpose of the classical Einstein and Landau-Lifshitz pseudotensors is for determining the gravitational energy. Neither of them can guarantee a positive energy in holonomic frames. In the small sphere approximation, it has been required that the quasilocal expression for the gravitational energymomentum density should be proportional to the Bel-Robinson tensor Bαβμν . However, we propose a...

Gravitational waves are predicted by Einstein’s general relativity. They are time dependent solutions of the Einstein field equations which radiate or transport energy. Although they have not been detected yet, the existence of gravitational waves has been proved indirectly from observations of the pulsar PSR 1913+16. This rapidly rotating binary system should emit gravitational radiation, henc...

The previous discussions have taken place in the context of linearized GR, which is not a fully consistent theory. We will now discuss some aspects of GR in the nonlinear regime, with particular attention to isolated systems. Our eventual goal is to compute the energy loss of a system emitting gravitational waves. We introduced the concepts in the last lecture, and are now ready to proceed to t...

It has been argued that the energy content in time varying spacetimes can be obtained by using the approximate Lie symmetries of the geodesics equations in that spacetime. When applied to cylindrical gravitational waves, it gives an enhancement of the waves. While, according to this proposal, the energy of the waves does go to zero asymptotically, it decreases as the inverse square root of the ...

We analyze the general covariant energy-momentum tensor of the gravitational system in genreal five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is...

a numerical model for two-phase debris flows is developed in this paper, on the basis of understanding of the physical characteristics of debris flows from field investigations and experiments. employing a moving coordinate, the kinetic energy equation of gravel particles in unit volume in debris flow is developed by considering the potential energy of the particles, energy from the liquid phas...

Wepresent a revised formof the energy balance for the coupled thermodynamics of liquid water flowing in porousmedia and give examples of situations where a commonly used formulation based on transport of enthalpy leads to erroneous results. Assuming negligible contribution from kinetic energy as well as sources and sinks such as energy from radioactive decay, total energy conservation is reduce...

The energy-momentum for a gravitating system can be considered by the tetard teleparalle gauge current in orthonormal frames. Whereas the Einstein pseudotensor used holonomic frames. Tetrad expression itself gives a better result for gravitational energy than Einstein’s. Inspired by an idea of Deser, we found a gravitational energy expression which enjoys the positive energy property by combini...