While a curved space can be viewed as having an intrinsic curvature, it also can be viewed as curved in an embedding flat space of a higher number of dimensions. For example, a sine wave is a 1D line that can be embedded in a 2D plane. However a spiral (like one part of DNA) is a 1D line that can be embedded only in a flat 3D space. These are just examples for clarification, I understand that 1D lines have no intrunsic curvature.
My question is about the real hyperbolic spacetime curved by gravity. In General Relativity this curvature is treated as strictly intrinsic, because no higher dimensions have been physically observed. However, purely mathematically I should be able to view the 4D spacetime as curved in a flat manifold with a higher number of dimensions. What would be the number of dimensions and the metric signature of such a space embedding the real spacetime that is curved as prescribed in a general case of General Relativity?