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A result in math says that $S^n$ carries a Lorentzian metric iff $n$ is odd.

Using it we can observe that a 2-sphere spacetime is impsossibleimpossible, a 3-sphere spacetime is geometrically possible, but again a 4-sphere spacetime is impossible, and so on.

Are there resources in the literature that deal with geometrically impossible spacetime or offering a general result to be used and checked?

A result in math says that $S^n$ carries a Lorentzian metric iff $n$ is odd.

Using it we can observe that a 2-sphere spacetime is impsossible, a 3-sphere spacetime is geometrically possible, but again a 4-sphere spacetime is impossible, and so on.

Are there resources in the literature that deal with geometrically impossible spacetime or offering a general result to be used and checked?

A result in math says that $S^n$ carries a Lorentzian metric iff $n$ is odd.

Using it we can observe that a 2-sphere spacetime is impossible, a 3-sphere spacetime is geometrically possible, but again a 4-sphere spacetime is impossible, and so on.

Are there resources in the literature that deal with geometrically impossible spacetime or offering a general result to be used and checked?

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Geometrically Impossible Spacetime

A result in math says that $S^n$ carries a Lorentzian metric iff $n$ is odd.

Using it we can observe that a 2-sphere spacetime is impsossible, a 3-sphere spacetime is geometrically possible, but again a 4-sphere spacetime is impossible, and so on.

Are there resources in the literature that deal with geometrically impossible spacetime or offering a general result to be used and checked?