On the Rotational and Machian Properties of the Universe

We find a Classical explanation on the origin of the Cosmological "constant" term, as a rotating feature of the Universe. We give a picture on "creation" of the Universe. By analogy with the original Brans-Dicke relation, several other similar relations were obtained in a previous paper (Berman, 2007d), which we now extend, by relating the angular momentum L, absolute temperature T, and the cosmological "constant", with R, where R, M stand for the radius (scale-factor) and the mass of the causally related Universe. We show here that these properties, which characterize Machian Universes, can be put in the form of equalities, which can be derived, from the conjecture that the total energy of the Universe is null, alike with the effective energy density, and we therefore imply that R depends linearly with M ; the angular momentum runs like squared R ; T, like R to the power -1/2 ; lambda, as R to the power -2 so that the total entropy of the Universe grows with R to the power 3/2, and, then, also as M to the power 3/2. The "loss of information paradox", for black holes, is dismantled. It must be obvious, from this paper, that each type of energy contribution, to the total energy of the Universe, divided by M multiplied by c-squared, yields a constant, during all times, so that, for instance, if the present contribution of the cosmological "constant", drives the present Universe, it also must have driven alike, in all the lifespan of the Machian Universe: the relative contributions of densities of each kind, towards the total density, remain the same during all times. Berman (2008; 2008a; 2008b) found similar hidden rotational states of the Universe in Relativistic theories which obey Robertson-Walker's metric.