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

Maxwell field in general relativity

  1. Mar 9, 2015 #1
    Hello everyone,
    I'm studying some applications of AdS/CFT and I came across an expression of the Maxwell field written in the following way:
    $$
    A=A_t(r)dt+B(r)xdy.
    $$
    How does this notation work? Is it simply a way of writing the four-vector? If so, why do we use this notation?
    Thanks a lot!
     
  2. jcsd
  3. Mar 9, 2015 #2

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Are you sure this is transcribed correctly? Can you give the reference for where you got it? It doesn't look right to me; the Maxwell field should be a 2-form, i.e., it should be expressed as a sum of wedge products of the form ##dt \wedge dx##, ##dy \wedge dz##, etc.
     
  4. Mar 9, 2015 #3
  5. Mar 9, 2015 #4

    wabbit

    User Avatar
    Gold Member

    Looks like the expression is the potential, not the field.

    Edit : no idea why he picks this form, didn't read the rest of the paper sorry
     
    Last edited: Mar 9, 2015
  6. Mar 9, 2015 #5
    He calls it field but yes, I pretty sure he means the potential. Does this simply mean that the four-potential have component ##A_t(r)## and ##A_y(r,x)=B(r)x##? If so, where does that notation come from?
     
  7. Mar 9, 2015 #6

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Yes, he does.

    Yes, although I also think ##r = \sqrt{x^2 + y^2 + z^2}##, so any function of ##r## is really a function of ##x, y, z##.

    It's differential form notation; the 1-form ##A## is expressed in terms of its components as ##A_{\mu} dx^{\mu}##, where ##dx^{\mu}## are the basis 1-forms ##dt##, ##dx##, ##dy##, and ##dz##. The electromagnetic field itself is then expressed as the 2-form ##F = dA##, which in components is ##F = \frac{1}{2} F_{\mu \nu} dx^{\mu} \wedge dx^{\nu}##, and ##F_{\mu \nu} = \partial_{\mu} A_{\mu} - \partial_{\mu} A_{\nu}##. This notation is often used in field theory.
     
    Last edited: Mar 10, 2015
  8. Mar 10, 2015 #7
    Oh great thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook