Gravitational field calculation question

[Monster99d]

I do believe that somewhere I have read that an electromagnetic field does produce a gravitational field.

So, considering the statement above, how can one calculate the strength of a gravitational field if the strength of an electromagnetic field is given?

 

[Dale]

Hi Monster99d, welcome to PF!

The first step is to calculate the electromagnetic stress energy tensor. Then, from that, you solve the Einstein field equations like normal. It is complicated because everything becomes coupled and non linear, so usually you just do it perturbatively.

 

[Monster99d]

Ok. So I substitute the electromagnetic stress-energy tensor (T^μv) into the equation:

[8(3.1415)G/c^4] * Tμv

as Tμv, correct?

 

[Dale]

Yes.

 

[Monster99d]

And for the electromagnetic stess-energy tensor; would I calculate it in SI units or CGS units? Also do I need to solve it as a matrix or just as an equation?

 

[Mentz114]

The SET of the EM field is
<br /> T^{\mu\nu} = F^{\mu\alpha}F^\nu_\alpha - \frac{1}{4}g^{\mu\nu}F^{ab}F_{ab}<br />
where F is the field tensor.

It's explained better here

http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor

and the solution of the EFE is the electro-vacuum

http://en.wikipedia.org/wiki/Electrovacuum_solution

 

[Monster99d]

Another question; in Dr. Mallett's papers, he has shown that a ring laser does produce a gravitational field.

So, if one constructed a machine that creates a non rotating sphere of lasers by taking a laser source and simply bouncing it off of several mirrors, would that create a gravitational field?

Another question; would time dilation be increased if you were as close to a black hole as possible without being ripped apart or rotating around it?