Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 54 / 4 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 62 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 63 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 72 / 4 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 61 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 61 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 63 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / ii / Paper 1 / 35A / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 63 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 65 / 5 / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 66 / 2 / b / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 66 / 3 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 54 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 54 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 55 / 4 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 56 / 3 / e / Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 57 / 1 / iii / Solution

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= Einstein equation
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With signature $(-,+,+,+)$ and vanishing cosmological constant, the Einstein field equations are
$$
R_{\mu\nu}-\frac12 g_{\mu\nu}R=\kappa T_{\mu\nu}.
$$
In four spacetime dimensions, contraction with $g^{\mu\nu}$ gives the useful trace relation $R=-\kappa T$.


Einstein field equations

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