2
votes
Is the equation $g_{\mu\nu} = const. + T_{\mu\nu}$ equivalent to Einstein's field equations?
My guess is that the OP means $G_{\mu \nu}$ (the Einstein tensor) instead of $g_{\mu \nu}$ (which is the metric tensor). If that's the case then according to OP we should have
$$ G_{\mu \nu}=T_{\mu \...
- 1,032
2
votes
Accepted
Why are the axial and circumferential normal stresses in an axially loaded fluid cylinder equal?
As in your diagrams, let the membrane initially be horizontal at z = 0. Let $r_0$ be the radial location measured from the z axis in the initial flat membrane. Let the location of a material point ...
- 32.2k
2
votes
Maxwell stress tensor for electromagnetic wave
four years later you might not be that interested in the answer, but better late than never.
The way you write your waves is right and convenient, so I'll work with that notation.
$$\vec{E} = (E_1\...
1
vote
Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$
\begin{align*}
\partial_\mu T^{\mu\nu}_{\text{EM}}
&= \partial_\mu \left(F^{\mu\lambda} F^\nu_{\ \lambda}\right) - \frac{1}{4} \eta^{\mu\nu} \partial_\mu \left(F^{\lambda\sigma} F_{...
- 127
1
vote
Making background curvature variable in QFT on curved spacetime
Not sure if this is what you are asking (question needs some better formatting), but I think what you are asking is "can you write the metric so that it receives corrections from the QFT?" I ...
- 390
1
vote
Energy-Momentum-Tensor of classical electrodynamics is conserved
\begin{align*}
\partial_\mu T^{\mu\nu}_{\text{EM}}
&= \partial_\mu \left(F^{\mu\lambda} F^\nu_{\ \lambda}\right) - \frac{1}{4} \eta^{\mu\nu} \partial_\mu \left(F^{\lambda\sigma} F_{...
- 127
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