- #1
jakepdog
- 3
- 0
i just need someone that can do the calculations to prove it
I think i figured out gravity, really
- Thread starter jakepdog
- Start date
-
- Tags
- Gravity
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...
Similar threads
Hot Threads
-
A Minimal property of Spacelike geodesics in GR/curved spacetime?
- Started by Kostik
- Replies: 76
- Special and General Relativity
-
A Dirac's "GTR" Eq (27.4): how momentum ##p^\mu## varies
- Started by Kostik
- Replies: 50
- Special and General Relativity
-
B No object actually approaches the speed of light
- Started by Atlan0001
- Replies: 9
- Special and General Relativity
-
A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates
- Started by Kostik
- Replies: 53
- Special and General Relativity
-
I Black hole and coordinate time from the perspective of Alice outside
- Started by Bellaella
- Replies: 26
- Special and General Relativity
Recent Insights
-
Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect
- Started by Greg Bernhardt
- Replies: 7
- Quantum Physics
-
Insights What Exactly is Dirac’s Delta Function? - Insight
- Started by Greg Bernhardt
- Replies: 3
- General Math
-
Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight
- Started by Greg Bernhardt
- Replies: 1
- Special and General Relativity
-
Insights Fixing Things Which Can Go Wrong With Complex Numbers
- Started by PAllen
- Replies: 7
- General Math
-
Insights Fermat's Last Theorem
- Started by fresh_42
- Replies: 105
- General Math
-
Insights Why Vector Spaces Explain The World: A Historical Perspective
- Started by fresh_42
- Replies: 0
- General Math