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Why definition of mass is not stated as " the property of object to change radius of curvature of space time fabric is called mass"

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  • $\begingroup$ Mainly because curvature of space isn't easily measurable. Remember that physics are experimental sciences, if you can't compare results, you're in dead end. $\endgroup$ – FGSUZ Jun 26 '18 at 19:20
  • $\begingroup$ Plus, spacetime is bend by energy not only by mass, massless entities can bend it too. $\endgroup$ – user3408085 Jun 26 '18 at 19:29
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    $\begingroup$ Plus, "fabric of spacetime" isn't a rigorous scientific concept. See David Z's answer to this question: physics.stackexchange.com/questions/41625/… $\endgroup$ – D. Halsey Jun 26 '18 at 22:34
  • $\begingroup$ Along side reasons given by other comments, curvature of space was not known at the time definition of mass was stated. $\endgroup$ – kpv Jul 1 '18 at 6:17
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Thinking about classical mechanics, you take the concept of mass for one point-particle with a quantity, say $m$, that relates to the inertia of the point-particle. Still, you can take whatever you want to describe: an elephant, an ant, a planet, a marshmallow; as your point-particle and then introduce by hand the number $m$ for it. Later, according to Newton's laws, this masses will act towards their media by their dynamics. That's at least the classical treatment, because you can better your description for the mass due to density and geometric shapes, for example. But you always collapse it to a point-particle here.

When talking about General Relativity, you can watch the action of space-time in the masses by studying the geodesics of it (as also the stress-energy tensor will speak about the character and nature of the mass distribution). In a gravitational field, say $\phi$, you will study the geodesics for your mass present in the nearby, geometrically local vicinity, and then see how it (gravitational field, geometric term) acts upon it (mass) (Remember $g_{00}=\pm(1-2\phi/c^2)$ depending on your signature).

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