Recent content by chinared

Hi all, I am trying to find the Christoffel connections of this metric: ds2= -(1+2∅)dt2 +(1-2∅)[dx2+dy2+dz2] where ∅ is a general function of x,y,z,t. I tried to solve this through the least action principle, but some of my results(t-related terms) were different from the answer with a minus...

Thank you, I will check my result again

Sorry for that I did not write down the other non-zero terms of Riemann curvature tensor which can be deduced by symmetry and anti-symmetry properties. However, I still have a contradiction that Rt _ztz-b''(z)-[b'(z)]2 but Rz_tzt=[b''(z)+[b'(z)]2]e2b(z) Did you also get the same result?

Need to find the Ricci scalar curvature of this metric: ds2 = e2a(z)(dx2 + dy2) + dz2 − e2b(z)dt2I tried to find the solution, but failed to pass the calculation of Riemann curvature tensor: <The Christoffel connection> Here a'(z) denotes the first derivative of a(z) respect to z...

Homework Statement Need to find the Ricci scalar curvature of this metric: ds2 = e2a(z)(dx2 + dy2) + dz2 − e2b(z)dt2 Homework Equations The Attempt at a Solution I tried to find the solution, but failed to pass the calculation of Riemann curvature tensor: <The Christoffel...

I got some trouble from this question: For a given metric: ds2 =t-2(dx2-dt2), derive the energy-momentum tensor which satisfies the Einstein equation: Rαβ- 1/2Rgαβ=8\piGTαβ. I got the Ricci scalar R=2, but Tαβ=0 for all α,β. Does this means a curved spacetime without any source(energy-momentum...