- #1
zepp0814
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Hi I was wondering if there is an equation for finding the gravitational pull on on all object in the universe (including that's that are massless)
Energy-Mass Gravity: Universe's Gravitational Pull
I started reading a National Geographic article related to the Big Bang. It starts these statements:
Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits.
First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward.
My first reaction was that this is a layman's approximation to...
See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then
\begin{align}
0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\
&= \left(...
In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this:
$$
\partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}.
$$
The integrability conditions for the existence of a global solution ##F_{lj}## is:
$$
R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0
$$
Then from the equation:
$$\nabla_b e_a= \Gamma^c_{ab} e_c$$
Using cartesian basis ## e_I...
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