I would like to write a book related to my question Singular semi-Riemannian Geometry: usefulness and state of the art.
In fact, I have some 120 pages of drafts, but I would like to detail more some parts which I wrote too quickly, and to explain more between the equations.
The planned content is pretty much the same as it is now, but more elaborated, and with more examples:
I. Singular semi-Riemannian manifolds Semi-Riemannian Manifolds with variable signature metricVariable Signature Metric
1. Tensor Operations on Degenerate Inner Product Spaces
2. Tensor Operations in Singular Semi-Riemannian Geometry).
3. Differential Operations on Singular Semi-Riemannian Manifolds
4. Curvature of Semi-Regular Semi-Riemannian Manifolds
5. Warped Products of Semi-Regular Semi-Riemannian Manifolds
II. Applications to the Singularities in General Relativity
1. Einstein Equation on Spacetime with Degenerate Metric
2. Time Evolution in Singular General Relativity
3. Black Hole Information Paradox in Singular General Relativity
I have some additional directions in which I intend to develop the subject, and I want to add them to the book. Also I would like to make sure that I was not reinventing the wheel.
