Suppose there is a charged particle far enough of any mass so that there is no gravitational interaction between the particle and any other body. The trajectory of the particle in space-time would appear to us like this(adsbygoogle = window.adsbygoogle || []).push({});

(we are at the origin of our coordinate system).

Consider that at ##t=t_0## a EM wave arrives in the region our particle is in. The particle will accelerate and its trajectory through space-time would appear to us like this

(I'm not being rigorous on the shape of the trajectory. This is just an illustration made by hand at Paint software.The main point is that this is a curved trajectory.)

Since this is a curved trajectory, Minkowski metric will not be correct to describe it anymore. We therefore would have to use another metric to describe it.

It's all okay, for Einstein's equations predicts it: the electromagnetic wave has energy and the momentum-energy tensor will not vanish.

Now by the above analysis, the Einstein's theory does not seem to be a theory of gravity, but a theory of energy, because it states that energy is responsible for space-time trajectories to be curved and, mathematically speaking, for space-time to be curved. Furthermore, in the above example we did not need to mention gravity anywhere.

So in what sense general relativity is a theory of gravity?

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# I General Relativity as a theory of gravity

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