3. Consider the line element of the sphere of radius a: ds² = a² (d0² + sin² 0 do²). The only non-vanishing Christoffel symbols are Ꮁ 06 sin cos 0, го θα ГФ 1 фо tan O' гр μν 2.90 a) Write down the metric and the inverse metric, and use the definition 1 гр (µ9vo + v9μo – 8e9µ) = I νμ to reproduce the results written above for F 00 and ro 80° [You can also check that the other

3. Consider the line element of the sphere of radius a: ds² = a² (d0² + sin² 0 do²). The only non-vanishing Christoffel symbols are Ꮁ 06 sin cos 0, го θα ГФ 1 фо tan O' гр μν 2.90 a) Write down the metric and the inverse metric, and use the definition 1 гр (µ9vo + v9μo – 8e9µ) = I νμ to reproduce the results written above for F 00 and ro 80° [You can also check that the other