# Does rotational energy have effect on gravity/metric?

Intuitively, if energy can be stored in rotational motion, it has to obey $E=mc^2$. Does rotation of typical stellar-sized objects - BHs, pulsars, binaries - have measurable effect on their overall gravity?

(I'm not talking about nearby effects, like frame dragging described by Kerr metric, the effect on measurements from the Earth is of interest)

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The source in the Einstein field equations is the stress-energy tensor, not the scalar mass-energy. Adding rotation will affect multiple elements of the stress-energy tensor. You can sometimes get rough estimates of effects in GR by using $E=mc^2$ and pseudo-Newtonian arguments, but sometimes these are way off. As an example where it's way off, two light rays propagating in parallel (not antiparallel) directions experience zero gravitational interaction.