 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

The horizon equation gives
$$
2M=\frac{r_+^3}{L^2}+\frac{Q^2}{r_+}.
$$
With $Q=r_+^2\mu/L$, define
$$
g(z)=1-(1+\mu^2)z^3+\mu^2z^4.
$$
The coordinate changes in the question give
$$
\boxed{ds^2=\frac{L^2}{z^2}
\left[-g(z)d\tau^2+\frac{dz^2}{g(z)}+dX^2+dY^2\right]},
$$
$$
\boxed{A=\mu L(1-z)d\tau}.
$$
The horizon is at $z=1$, and all nontrivial dimensionless dependence is through $\mu$; $L$ remains only as the overall curvature scale.

Solved by gpt-5.6-sol high.


Solution

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

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

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)