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Nov
7
comment (Strong) causality condition
What he proves is not that a compact set has closed causal curves, but that a compact space-time has closed causal curves. Take Mikowski space-time and a compact subset, it will not have closed causal curves.
May
11
comment How to proof Frobenius Theorem in general?
The case k=1 follows from an existence and uniqueness theorem for ODE's. The step to k=2 from the proof you know should be the same as the on from k-1 to k in the induction.
Apr
20
comment Link between a topological space and a manifold
This doesn't make sense! The manifold $M$ comes with a topology i.e. with the collection of subsets $T$.
Apr
4
comment Can we define a induced metric like this?
The induced metric is just the restriction of $g$ to the tangent space of the submanifold. Or the restriction of $h$. The $h$, if you raise one index, is the projection operator.
Mar
10
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