On Wednesday, September 4, 2019 at 1:48:15 PM UTC-5, Alan Grayson wrote:
>
>
>
> 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
>
V = -GMm/r
Read the following where by using H = 0, zero energy and just Newtoin's
laws it is easy to derive the FLRW equations for k = 0 or a flat spatial
surface.
LC
https://physics.stackexchange.com/questions/257476/how-did-the-universe-shift-from-dark-matter-dominated-to-dark-energy-dominate/257542#257542
>
>>
>> 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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