Background and Motivation
The stress energy tensor of general relativity, as conventionally defined, has sixteen components.
One of those component, conventionally component T00, also called ρ, is mass-energy density, including the E=mc2 conversion for electromagnetic fields.
The other...
My attempt:
Realize we can work in whatever coordinate system we want, therefore we might as well work in the rest frame of the fluid. In this case ##u^a=(c,\vec{0})##.
The conservation law reads ##\nabla^a T_{ab}=0##. Let us pick the Levi-Civita connection so that we don't have to worry about...
I have trouble understanding some terms in the stress-energy-tensor. For instance T^(12) stands for the flux of the x-component of momentum in the y-direction. But what does it means for the x-component of momentum to flow in the y direction? Since momentum is a vector should't the x-component...
Starting from the following definition of stress-energy tensor for a perfect fluid in special relativity :
$${\displaystyle T^{\mu \nu }=\left(\rho+{\frac {p}{c^{2}}}\right)\,v^{\mu }v^{\nu }-p\,\eta ^{\mu \nu }\,}\quad(1)$$
with ##v^{\nu}=\dfrac{\text{d}x^{\nu}}{\text{d}\tau}## and...
Say I wanted to set up EFE for the earth and moon. How do I actually go about filling the stress energy tensor? I'm referencing the wikipedia page.
So the time-time should be approximately E/c^2V, so for the earth moon system
##T_{00} = \frac{3}{4\pi r_E^3}\frac{1}{c^2}(M_Ec^2 + 2/5...
When I read the speed of light in vacuum is c, does it imply that light doesn't actually travel at this speed in nature? My guess is no, light always travels at c, it's just that in the definition, we're trying to ignore the affects on light from other stuff like the comological constant and the...
How do I calculate the gravitational mass of a cylinder of compressed gas, including the effects of pressure? By gravitational mass, I mean what I would measure on an ideal mass balance.
(I know that the pressure is negligibly small in a realistic container, but I want to have a conceptual...
I usually come across expressions for the Stress energy tensor showing them as three densities (normally over a space-like slice.
In wikipedia's article on the spin tensor, they clearly (it does not appear to be an error) both write about and express the components of the stress energy tensor as...
Homework Statement
(a) Find faraday tensor in terms of ##\vec E## and ## \vec B ##.
(b) Obtain two of maxwell equations using the field relation. Obtain the other two maxwell equations using 4-potentials.
(c) Find top row of stress-energy tensor. Show how the b=0 component relates to j...
Im studying Quantum Field Theory as part of my undergraduate course, and am currently looking at Noether's Theorem which has led me to the following calculation of the divergence of the Stress-Energy Tensor. I'm having difficulty in seeing how we get from line (31) to line (32). Is the 2nd term...