(n,m) to (n+1,m) derivatives in Wald

  • Thread starter Thread starter nickj1
  • Start date Start date
  • Tags Tags
    Derivatives
nickj1
Messages
2
Reaction score
0
Could someone please explain the partial and covariant derivatives with upstairs index that appears all of a sudden in Wald in section 4.2 with no explanation? I haven't seen it anywhere else.

Homework Statement



(n,m)→(n+1,m) derivatives

Homework Equations



section 4.2--when the stress tensor is introduced, with downstairs indexes

The Attempt at a Solution



it was mentioned earlier by Wald; just didn't see it
 
Physics news on Phys.org
Can you perhaps scan the relevant extract ? I don't have Wald handy right now.
 

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

Derivation of the Eqation of Motion from Fermi Lagrangian density
Replies
3
Views
3K
Covariant Derivative Homework: Solve ∇_c ({∂}_b X^a)
Replies
2
Views
2K
Derivation of the energy of an alloy
Replies
1
Views
2K
A Covariant derivative definition in Wald
Replies
33
Views
5K
Is the Sign in the Covariant Derivative Important for Local Gauge Invariance?
Replies
2
Views
2K
Four Tensor Derivatives -- EM Field Lagrangian Density
Replies
16
Views
2K
Deriving MTW's Equation 21.90 from Equation 21.83
Replies
1
Views
1K
A Landau's Maximum Mass Limit Derivation in Shapiro & Teukolsky (1983)
Replies
23
Views
3K
A Making sense of the Differential of F at p, (where F: R^n -> R^m)
Replies
1
Views
1K
Order of a^m when gcd(m,n) = 1
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top