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Jun1411, 06:57 PM

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How does conservation of energy work in general relativity, and how does this apply to cosmology? What is the total massenergy of the universe?
Conservation of energy doesn't apply to cosmology. General relativity doesn't have a conserved scalar massenergy that can be defined in all spacetimes.[MTW] There is no standard way to define the total energy of the universe (regardless of whether the universe is spatially finite or infinite). There is not even any standard way to define the total massenergy of the *observable* universe. There is no standard way to say whether or not massenergy is conserved during cosmological expansion. Note the repeated use of the word "standard" above. To amplify further on this point, there is a variety of possible ways to define massenergy in general relativity. Some of these (Komar mass, ADM mass [Wald, p. 293], Bondi mass [Wald, p. 291]) are valid tensors, while others are things known as "pseudotensors" [Berman 1981]. Pseudotensors have various undesirable properties, such as coordinatedependence.[Weiss] The tensorial definitions only apply to spacetimes that have certain special properties, such as asymptotic flatness or stationarity, and cosmological spacetimes don't have those properties. For certain pseudotensor definitions of massenergy, the total energy of a closed universe can be calculated, and is zero.[Berman 2009] This does not mean that "the" energy of the universe is zero, especially since our universe may not be closed. One can also estimate certain quantities such as the sum of the rest masses of all the hydrogen atoms in the observable universe, which is something like 10^54 kg. Such an estimate is not the same thing as the total massenergy of the observable universe (which can't even be defined). It is not the massenergy measured by any observer in any particular state of motion, and it is not conserved. MTW: Misner, Thorne, and Wheeler, Gravitation, 1973. See p. 457. Berman 1981: M. Berman, unpublished M.Sc. thesis, 1981. Berman 2009: M. Berman, Int J Theor Phys, http://www.springerlink.com/content/357757q4g88144p0/ Weiss and Baez, "Is Energy Conserved in General Relativity?," http://math.ucr.edu/home/baez/physic...energy_gr.html Wald, General Relativity, 1984 The following forum members have contributed to this FAQ: bcrowell George Jones jim mcnamara marcus PAllen tinytim vela 


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