Stability of 4D Gravity Model: Examining Possibilities

Gold Barz
Messages
464
Reaction score
0
I know that gravity can be extended to 4D but the conclusion always seem to be unstable, is the reason why they come up with unstable orbits and atoms is because they take how gravity acts here in 3D physics and apply it the same way to 4D physics? How about modificating the model? but we just don't know what kind of modifications can be made so we don't make any modifications...is this even remotely correct?

Is there no way that a isotropic 4D gravity model can become stable?

I might even suggest something even more wackier, like might there be new forms of matter in 4D physics, I would think that there would be a significant effect to elementary particles.
 
Physics news on Phys.org
Who else feels that we can't just extend basic mathematical equations to 4D models?...
 
Why are you so much interested in 4D models? They are not physical, unless you assume (a-la strings) that one of them is small or unobservable.

What need is there for that? In String Theory, the formalism requires the extra dimensions to work properly. In your case, why would you prefer to work with one extra dimension?
 
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...
Thread 'Dirac's integral for the energy-momentum of the gravitational field'
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(...
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...
Back
Top