 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 354

Varying the gauge field and integrating by parts gives
$$
\boxed{\nabla_aF^{ab}=0},
\qquad
\boxed{\nabla_{[a}F_{bc]}=0},
$$
the second identity following from $F=dA$. Varying the inverse metric, using
$$
\delta F^2=2F_{ac}F_b{}^c\delta g^{ab},
$$
and discarding the Einstein--Hilbert boundary term gives
$$
\boxed{R_{ab}-\frac12Rg_{ab}+\Lambda g_{ab}
=2\left(F_{ac}F_b{}^c-\frac14g_{ab}F_{cd}F^{cd}\right)}.
$$
For AdS$_4$, $\Lambda=-3/L^2$.

Solved by gpt-5.6-sol high.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 354 / 2 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 354 / 2 / a / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 354 / 2 / a / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)