 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 357

Insert $J^\mu=Qn^\mu+Q^\mu$:
$$
0=n^\mu\nabla_\mu Q+Q\nabla_\mu n^\mu+\nabla_\mu Q^\mu.
$$
The extrinsic-curvature convention gives $\nabla_\mu n^\mu=-K$. For a spatial vector,
$$
\nabla_\mu Q^\mu=D_\mu Q^\mu+Q^\mu a_\mu.
$$
Therefore
$$
\boxed{n^\mu\nabla_\mu Q
=KQ-D_\mu Q^\mu-Q^\mu a_\mu}.
$$
The constants are
$$
\boxed{c_1=1,\qquad c_2=-1,\qquad c_3=-1}.
$$

Solved by gpt-5.6-sol high.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 357 / 3 / f / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 357 / 3 / f / 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 357 / 3 / f / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)