An alternative method for calculating the energy of gravitational waves

In the expansive nondecelerative universe model, creation of matter occurs due to which the Vaidya metrics is applied. This fact allows for localizing gravitational energy and calculating the energy of gravitational waves using an approach alternative to the well established procedure based on quadrupole formula. Rationalization of the gradual increase in entropy of the Universe using relation describing the total curvature of space-time is given too. As a source of gravitational waves, any physical system with time dependent mass distribution can be considered. The amount of such energy, emitted within a time unit is described by known quadrupole formula: dE dt = Pqw = − G 45c ... Kαβ (1) where Kαβ is the tensor of quadrupole mass distribution in the source of emission. For Kαβ it holds: Kαβ(t) = ∫ ρ(t,x).(3XαXβ−δαβXκX )∆V (2) In the expansive nondecelerative universe (ENU) model [1], the creation of matter and of gravitational energy simultaneously occur. The laws of energy conservation still hold since the energy of gravitational field is negative in ENU. The total energy of the Universe is thus exactly zero [2] and the Universe can continuously expand with the velocity of light c. This postulate is expressed in the ENU by equation: a = c.tc = 2GMu c (3) where a is the gauge factor, tc is the cosmological time, Mu is the mass of ENU. In such a model, due to the matter creation the Vaidya metrics [3] must be used which enables to localise gravitational energy. Weak fields are in first approximation described by Tolman’s relation [4] ǫg = − R.c 8π.G = − 3m.c 4πa.r (4) in which εg is the density of the gravitational energy being emitted by a body with the mass m at the distance r, R denotes the scalar curvature (contrary to the more frequently used Schwarzschild metrics, in the Vaidya metrics, R 6= 0). Using relations (3) and (4), equation expressing gravitational output Pg is obtained: Pg = d dt ∫ ǫgdV = − m.c a = − 2 tc (5) If the total mass of universe, Mu is substituted from (3) to (5), relation for the total output of the gravitational energy Ptot (its absolute value) by the Universe appears Ptot = − c 2G ≈ ∣