I'm a bit puzzled about some calculations regarding the Ellis wormhole metric, prompted by Exercise 2.1(b) in Eric Poisson's "A Relativist's Toolkit". Suppose the metric has the form: Then, calculating the Ricci and Einstein tensors, and assuming EFE, one can easily show that this spacetime violates NEC, WEC, SEC and DEC at . But when I have the metric in the following form (as in Poisson's book): with suitable restrictions on , and calculate Ricci and Einstein tensors at , I get and as only non-zero terms, and and . In that case, all the above energy conditions are respected. I don't know what's going on here: I checked the calculations with some software. What am I missing?
Ellis wormhole and energy conditions
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