Embedding spacetime via a geodesically equivalent metric of Euclidean signature

Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzi an spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x( t). This geodesically equivalent, or dual, metric can be embedded in ordina ry Euclidean space. On the embedded surface freely falling particles move o n the. shortest path. Thus one can visualize how acceleration in a gravitat ional field is explained by particles moving freely in a curved spacetime. Freedom in the dual metric allows us to display, with substantial curvature , even the weak gravity of our earth. This may provide a nice pedagogical t ool for elementary lectures on general relativity. I also study extensions of the dual metric scheme to higher dimensions.