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## Main Question or Discussion Point

Can a 4-dimensional manifold with the Schwarzschild metric be embedded into a flat manifold of 5 (or more if necessary) dimensions? In other words, are there functions of [tex]t,r,\theta , \phi [/tex] and [tex] M[/tex] such that if

[tex]

x_1 = f_1 (t,r,\theta ,\phi ,M)[/tex]

[tex]

x_2 = f_2 (t,r,\theta ,\phi ,M)

[/tex]

.

.

etc.

then

[tex] ds^2=dx_1 ^2 +dx_2 ^2 +dx_3 ^2 +dx_4 ^2 +dx_5 ^2[/tex]

[tex]=(1-\frac{2GM}{c^2 r})c^2 dt^2-\frac{dr^2}{1-(2GM/c^2 r)} - r^2 sin^2 \theta d\phi ^2 - r^2 d\theta ^2?[/tex]

I like the idea of a Euclidean (or Minkowskian) hyperspace that contains gravitational fields, even if it turns out to have no practical application.

[tex]

x_1 = f_1 (t,r,\theta ,\phi ,M)[/tex]

[tex]

x_2 = f_2 (t,r,\theta ,\phi ,M)

[/tex]

.

.

etc.

then

[tex] ds^2=dx_1 ^2 +dx_2 ^2 +dx_3 ^2 +dx_4 ^2 +dx_5 ^2[/tex]

[tex]=(1-\frac{2GM}{c^2 r})c^2 dt^2-\frac{dr^2}{1-(2GM/c^2 r)} - r^2 sin^2 \theta d\phi ^2 - r^2 d\theta ^2?[/tex]

I like the idea of a Euclidean (or Minkowskian) hyperspace that contains gravitational fields, even if it turns out to have no practical application.