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in this applet when i putted the "spherical mass" bar to zero , it should have given me a flat spacetime ....... i can see the flatness is space but i see a curved path in time ..... shouldn't it be flat in both space and time ??!!

seeing this also made me remember an old question i had when i first started relativity , why do we use hyperbolic functions "sinh .. cosh ... etc" in the rotation equations of lorentz transformation instead of ordinary trigonometric functions ??

thanks in advance ...