From Phys.org:

(Phys.org)—University of Arizona physicist Andrei Lebed has stirred the physics community with an intriguing idea yet to be tested experimentally: The world's most iconic equation, Albert Einstein's E=mc2, may be correct or not depending on where you are in space.

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The key to understand Lebed's reasoning is gravitation. On paper at least, he showed that while E=mc2 always holds true for inertial mass, it doesn't always for gravitational mass.

"What this probably means is that gravitational mass is not the same as inertial," he said.

According to Einstein, gravitation is a result of a curvature in space itself. Think of a mattress on which several objects have been laid out, say, a ping pong ball, a baseball and a bowling ball. The ping pong ball will make no visible dent, the baseball will make a very small one and the bowling ball will sink into the foam. Stars and planets do the same thing to space. The larger an object's mass, the larger of a dent it will make into the fabric of space.

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