I am now reading a paper (whole paper link)which regarding construct a worm hole by cutting off the stress energy tensor and glue interior and exterior space at $r=a$. ‘Nevertheless, I am confused about the energy stress tensor at this junction surface,I think $i,j$ could choose from $τ,\theta,\phi$which means the curvature $\kappa^{i}_{j}$should have $\phi$component , and furthermore , the energy stress tensor’ s third component should be $P_{\phi}$but why the author only use $\theta$component, could you help me?description here


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