Some people may remember awhile back when I made a thread showing how when I derived the Einstein tensor and the stress energy momentum tensor for a certain traversable wormhole metric, that the units of the energy momentum tensor were not the same for each element and how a couple of the elements had the wrong units. Link to the thread: https://www.physicsforums.com/threa...hin-the-stress-energy-momentum-tensor.773968/ Now here was the metric: ds2= -c2dt2 + dl2 + (b2 + l2)(dΘ2+ sin2(Θ)dΦ2) Now in my first attempt, here was the coordinate basis and the metric tensor that I used: x0= ct x1= l (the radial coordinate) x2= Θ x3= Φ b is just the radius of the throat of the wormhole. g00= -1 g11= 1 g22= b2 + l2 g33= (b2 + l2)sin2(Θ) Every other element was 0. When I derived the Einstein tensor using this metric and then multiplied it by c4/(8πG) to get the stress energy momentum tensor, I got: T00= (-b2c4)/[(8πG)(b2 + l2)2] T11 just happened to equal the same thing as T00. T22= (b2c4)/[(8πG)(b2 + l2)] T33= (b2c4sin2(Θ))/[(8πG)(b2 + l2)] Every other element was 0. Now if you do dimensional analysis on these elements (I used SI units), you will notice that only T00 and T11 have the units of energy density/ momentum flux. Those units are: Kg/(m * s2) T22 and T33 however, had units of force instead: (kg* m)/ s2 which is equal to the newton. I was soon informed within the thread that I mentioned earlier, that the reason that this occurred was because Θ and Φ were angles whereas ct and l were lengths. The person then told me that I should rearrange my coordinate basis so that I was differentiating with respect to lengths rather than angles. This led to my 2nd attempt with a slightly modified coordinate basis and metric tensor: x0= ct x1= l x2= Θ(b2 + l2)¼ x3= Φ[(b2 + l2)sin2(Θ)]¼ g00= -1 g11= 1 g22= (b2 + l2)½ g33= sin(Θ)[(b2 + l2)½] Now when I derived the stress energy momentum tensor in the same manner as before with this particular metric, I got this: T00= [(-8b2 + 4l2)c4]/[(64πG)(b2 + l2)2] T11= 0 (It just came out this way.) T22= (4b2c4(b2 + l2)½)/[(64πG)(b2 + l2)2] T33= [(4b2 - 4l2)c4sin(Θ)]/[(64πG)(b2 + l2)(b2 + l2)½] Now when you do dimensional analysis on this stress energy momentum tensor, you will see that T00 once again has the proper units of energy density: Kg/(m * s2) T11 was 0, so that one is fine as well. However, once again it is T22 and T33 that have different units. This time, the units for both of these two elements were: kg / s2 Now these units do not equal those of force like in the first case, but I did notice something interesting here. In both cases, it was always the T22 and T33 elements that had the wrong units. Additionally, the wrong units for these two elements would always be the same as each other in both cases. Furthermore, T00 and T11 in both cases were always the acceptable ones with the right units. Having noticed this recurrence in both attempts, I deduced that this could not be coincidence and that perhaps the two angular elements were meant to have slightly different units after all. What do you guys think of this? Do you have any explanation for the strange occurrence that I have noticed in both attempts? Am I doing something wrong? P.S. Some people have recommended that I try using an orthonormal basis. I have tried to learn how to do that, but the farthest I've gotten is learning how to derive the 4 basis vectors. I don't know how to use that to get me to the Einstein tensor or even the Christoffel symbol for that matter. In fact, I've noticed that if I dot product all of those basis vectors with each other, it just gives me the inverse metric tensor that I already had in the first place. Also, how does this get me around the unit problem?