Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Components of The Electromagnetic Field Strength Tensor

  1. Sep 27, 2015 #1
    Source: http://gmammado.mysite.syr.edu/notes/RN_Metric.pdf

    Section 2
    Page: 2
    Eq. (15)

    The radial component of the magnetic field is given by
    [tex]B_r = g_{11} ε^{01μν} F_{μν}[/tex]
    Where does this equation come from?

    Section 4
    Page 3

    Similar to the electric charges, the Gauss's flux theorem for the magnetic field gives
    [tex]const = P/√4π[/tex]
    where P is the total magnetic charge of black hole.

    Why does the magnetic charge exist here?
     
  2. jcsd
  3. Sep 27, 2015 #2

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    1. You can think of it this way: The magnetic field is part of the space-space submatrix of the Field Tensor.
    (The electric field is part of the time-space submatrix of the Field Tensor, as in Eq.12.)
    Alternatively, one could say that the magnetic field is part of the time-space submatrix of the Hodge-dual of the Field Tensor.
    (From poking around... check out
    http://gmammado.mysite.syr.edu/notes/Electromagnetic_Field_Strength_Tensor.pdf )

    2. The abstract says that magnetic monopoles are assumed.
     
  4. Sep 27, 2015 #3
    Thank you!
     
  5. Oct 5, 2015 #4
    Ok now I get confused. So, I am trying to find the radial component of the magnetic field from the Hodge-dual of the Field Tensor, but then end up like this

    [tex]*F_{\mu\nu}=\frac{1}{2} \epsilon_{\mu\nu\lambda\rho}F^{\lambda\rho}=
    \begin{bmatrix}
    0 B_x B_y B_z \\
    -B_x 0 -E_z E_y \\
    -B_y E_z 0 -E_x \\
    -B_z -E_y E_x 0
    \end{bmatrix}[/tex]
    [tex]*F_{01}=B_r=\frac{1}{2} \epsilon_{01\lambda\rho}F^{\lambda\rho}=\frac{1}{2} g_{11}\epsilon^{01\lambda\rho}F_{\lambda\rho}g_{00}[/tex]
    which is different from Eq. (15)
    [tex]B_r=g_{11}\epsilon^{01\mu\nu}F_{\mu\nu}[/tex]
    What did I do wrong?
     
  6. Oct 11, 2015 #5
    Never mind, just found the answer
     
  7. Jan 10, 2016 #6

    RRM

    User Avatar

    Hi Darida, How did you find the answer?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Components of The Electromagnetic Field Strength Tensor
Loading...