1
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0answers
21 views

How to show isotropy of $SU(2)$ Yang Mills stress energy tensor?

When I vary the action of the YM Lagrangian density $$L = -\frac{1}{4} F^a_{\mu \nu}F^{\mu \nu}_a + J_a^\mu A^a_\mu$$ with respect to the metric, I obtain: $$T_{\mu \nu} = \frac{-2}{\sqrt{|g|}} ...
1
vote
1answer
71 views

Tensors in special relativity [duplicate]

I'm trying to understand tensors, but I've come across the following question: Let $T^{\mu\nu}$ by a $(2,0)$ tensor. Give the definitions of $T_\mu^{\,\nu}$, $T_{\mu\nu}$, and ...
3
votes
0answers
21 views

Existence and uniqueness of solutions to $\nabla^a T_{ab}$ in general (or special) relativity

The equation in the title of this question can be a relativistic analogue of the Navier-Stokes equation (in the sense that, in the low-velocity limit, it reduces to Euler's equation when $T_{ab}$ is ...
1
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1answer
81 views

Learning the stress-energy tensor

I am learning dynamics in special relativity and come across the stress-energy tensor. I have real trouble understanding it. I would love answers on How to motivate the definition of this tensor. ...
3
votes
0answers
45 views

The question about MTW 4-momentum integral expression and lorentz nature

In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as $$ \tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu ...
2
votes
1answer
82 views

Why is general relativity only formulated in continuum terms?

So, when we are discussing Newtonian mechanics, we treat particles as point particles. In continuum mechanics, which I understand to be a version in which mass is continuously distributed, we have ...
0
votes
1answer
132 views

Can inertial mass affect gravity of the object? [duplicate]

Every time I watch this TV program that discusses about all the facts about the universe , and it came to a point where they said that as an object approaches the speed of light the mass of the object ...
6
votes
1answer
517 views

Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...
2
votes
0answers
146 views

Solving the equation of relativistic motion

How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
0
votes
1answer
137 views

Tensor manipulation

Having a bit of trouble applying what I know about tensor manipulation, given, $T^{\mu \nu} = \left( g^{\mu \nu} - \frac{p^\mu n^\nu + p^\nu n^\mu}{p \cdot n} \right)$, I need to compute quantities ...
1
vote
1answer
117 views

What's the relativistic energy of a moving strained spring as $k\to\infty$ [closed]

Suppose a spring with stiffness $k$, is strained by constant forces on each end. In a frame where the strained spring moves at a constant velocity, what's the total relativistic energy of the moving ...
3
votes
3answers
215 views

Having trouble seeing the similarity between these two energy-momentum tensors

Leonard Suskind gives the following formulation of the energy-momentum tensor in his Stanford lectures on GR (#10, I believe): $$T_{\mu \nu}=\partial_{\mu}\phi \partial_{\nu}\phi-\frac{1}{2}g_{\mu ...
10
votes
2answers
557 views

The derivation of the Belinfante-Rosenfeld tensor

It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...