Recent content by ngkamsengpeter

What confuse me is what is meant by inside and outside of the circulating cylinder of light. Consider the laser beam with beam radius d and move in a circle with radius r0, the exterior solution mean the solution outside of d or r0?

Thanks. From the paper, it mentioned exterior and interior solution, what is the meaning and difference between these two solutions?

Thanks for your references. I have the carroll books and will go through your references. The stress-energy tensor given in the paper is for infinitely long circulating cylinder of light. How about a single circulating cylinder of light or a finite length circulating cylinder of light? Is the...

Thanks for you clarification. The fig.1 really make me confuse. \eta^t is the frequency, so \eta^\phi should be the wave vector k in \phi direction right?

Yes. From fig.1 it seems that the laser beam is moving in upwards in z-direction. That's make me confuse. Is that mean the author model the solenoidal laser beam as an infinitely number of circulating cylinder of light stack together? I am not familiar with matter dust fields also. I am new in...

The paper link:http://www.phys.uconn.edu/~mallett/Mallett2003.pdf I am not quite understand. Is that mean that for constant time, the null dust is circulating in ##\phi## direction and it become helix as time move forward? How does the null dust link to the circulating cylinder of light...

Given a particular system, how would one construct the stress-energy tensor? I was reading Mallett's paper and the stress-energy given for an infinitely long circulating cylinder of light is of the form T_{\mu\nu}=\epsilon \eta_\mu \eta_\nu where \eta_\mu=(\eta_0,0,\eta_2,0) and ε is the energy...

Ok. Although I still don't understand much on the killing vector part, You help a lot. Thanks.

Can i say that for any periodic coordinate which change to timelike corresponding to the existence of closed timelike curve?

What is the meaning of coordinate corresponding to an axial killing vector field? I am new to this, can you provide an example or reference on how to calculate this axial killing vector field? Thanks.

For this metric gmn=-A(r)dt2+2B(r)dzdt+C(r)dθ^2+D(r)dr2+E(r)dz2, can I say that it contain closed timelike if C<0? The curve are closed if the killing vector field exist? Thanks.

How to know if a metric is axially symmetry? Why is gmn=-A(r)dt2+2B(r)dθdt+C(r)dθ^2+D(r)(dr2+dz2 is axially symmetry? Because it only depend on r? Is gmn=-A(r)dt2+2B(r)dzdt+C(r)dθ^2+D(r)dr2+E(r)dz2 axially symmetry? Yes. You help a lot. Thanks.

Can I say that for any axissymmetry metric of the form gmn=-A(r)dt2+2B(r)dθdt+C(r)dθ^2+D(r)(dr2+dz2 contain a closed timelike curve if C(r)<0?

The paper said that if l<0, then it contain CTC. That's why it give me an impression that a metric contain CTC if it change sign. Is he use the condition you gave in post #2 to reduce the metric to ds^2=-l dθ^2 and then argue that the metric contain CTC if l<0?

I am not quite understand. Is there any meaning for the change of sign? Mallett spacetime contain close timelike curve, can you show me how to prove that Mallett spacetime contain close timelike?