I recently derived the Einstein tensor and the stress energy momentum tensor for the Godel solution to the Einstein field equations. Now as usual I will give you the page where I got my line element from so you can have a reference: http://en.wikipedia.org/wiki/Gödel_metric Here is what I got for my Einstein tensor Gμν: G00 , G11 , and G22 all equal 1/2 G03 and G30 = ex / 2 G33= (3/4) e2x Every other element was 0. As a result of this being the Einstein tensor, the stress energy momentum tensor Tμν is as follows: T00 , T11 , and T22 all equal c4/(16πG) T03 and T30 = ( c4ex) / (16πG) T33= (3c4e2x)/ (32πG) Every other element was 0. Now my research has told me that this metric contains closed time-like curves within it. Can someone please tell me how these tensors showcase the possibility of closed time-like curves? I suppose what I really need is a solid understanding of how to interpret the physical implications of these general relativistic tensors. I notice that when you do dimensional analysis on my stress energy tensor, you'll find that it contains all force terms (assuming that the exponential terms are unit-less constants since the number e itself is a constant, correct me if I am wrong). Does this mean that if I want to warp a region of space time into a Godel space time, then I would need to apply a force that is equivalent in magnitude to the elements in my stress energy tensor in the directions that said elements represent? In other words, does this mean that I would have to apply the following forces in the following directions: c4/(16πG) Newtons in the temporal direction, the xx direction, and the yy direction ( c4ex) / (16πG) Newtons in the time-z direction and the z-time direction (3c4e2x)/ (32πG) Newtons in the zz direction If my interpretation is correct, how exactly would one apply a force in the temporal direction considering that the temporal dimension is time itself? Also, I notice that the angular velocity (ω) terms that I started out with just totally disappeared by the time I got to the Einstein tensor (though this may have to do with the fact that my tensors are in a coordinate basis). What becomes of these? Surely angular velocity has significance in interpreting the physical implications of these tensors (especially if this metric contains closed time-like curves). Finally, what exactly do the Einstein tensor elements tell you about space-time curvature? This Einstein tensor in particular contains all constants. Please help understand the physical meanings of these tensors, as well as where the CTC's come from. Thank you.