Lovelock gravity and Weyl's tube formula

Understand

In four space-time dimensions, there are good theoretical reasons for believing that General Relativity is the correct geometrical theory of gravity, at least at the classical level.

• If one admits the possibility of extra space-time dimensions, what would we expect classical gravity to be like? It is often stated that the most natural generalisation is Lovelock's theory, which shares many physical properties with GR.
• But there are also key differences and problems.
• A potentially serious problem is the breakdown of determinism, which can occur when the matrix of coefficients of second time derivatives of the metric degenerates.