On Wednesday, September 4, 2019 at 4:08:58 AM UTC-6, Lawrence Crowell wrote:
>
> You also have to include the total gravitational energy or T^{ab} due to
> local sources and Λg^{ab}.
>
> The ADM Hamiltonian constraint is NH = 0 where this Hamiltonian is
> determined by the traceless transverse part of the extrinsic curvature or
> Gauss fundamental form. For a general spacetime manifold there is no way to
> define mass-energy and for most Petrov types the mass-energy is simply no
> defined. Think of a spherical space with matter throughout. There is no way
> to construct a Gaussian surface with which to integrate a total mass or
> energy. Also if that putative surface is embedded in mass-energy then that
> surface is subject to diffeomorphisms of local curvature. Energy is then
> not localizable, and in general things that we want invariant are so
> independent of such diffeomorphisms.
>
> LC
>
The energy of the gravitational field is positive for each particle of
average mass. But how does one calculate the negative potential energy for
each average mass particle? I can calculate the potential energy of a test
particle at some location IN a field, but how can I calculate the total
negative potential energy OF the field (for a particle of average mass)? AG
>
>
> On Tuesday, September 3, 2019 at 10:00:55 PM UTC-5, Alan Grayson wrote:
>>
>> Just sum over the estimated total of 10^80 particles, using mc^2 by first
>> estimating the average mass of those particles for the rest energy, adding
>> their average potential gravitational energy and their average kinetic
>> energy. Why not? AG
>>
>
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