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

Table of contents
- Solution a

Solution

Varying the gauge field and integrating by parts gives

\nabla_{a} F^{ab} = 0, \nabla_{[a} F_{b c]} = 0,

the second identity following from

F = d A

. Varying the inverse metric, using

δ F^{2} = 2 F_{a c} F_{b}^{c} δ g^{ab},

and discarding the Einstein--Hilbert boundary term gives

R_{ab} - \frac{1}{2} R g_{ab} + Λ g_{ab} = 2 (F_{a c} F_{b}^{c} - \frac{1}{4} g_{ab} F_{c d} F^{c d}) .

For AdS

_{4}

,

Λ = - 3/ L^{2}

.

Solved by gpt-5.6-sol high.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version