# Can gravity radiate?

In electromagnetism, when a charge accelerates, it emits radiation. We know this because we can write the retarded potentials, apply $$\vec E=- \nabla V-\frac{\partial \vec{A}}{\partial t}$$ and $$\vec B= \nabla \times \vec{A}$$ and we get Jefimenko's equations, which can be separated into velocity and acceleration fields, the latter of which are null if the particle is not accelerating.

Nothing is stopping us from applying the exact same procedure to an accelerating body with some mass $$m$$. We can write the gravitational potential in terms of retarded time, and according to gravitoelectromagnetism, we should get the same result: gravity does, indeed, radiate. There is no need to do any calculations since in the weak field limit, gravity follows a set of equations analogous to Maxwell's equations, so the behavior should be the same, and we should get a sort of Jefimenko's equations for the gravitoelectric and gravitomagnetic field, resulting in gravitational radiation. Is this really what would happen?

As a bonus, when charges accelerate, they emit radiation, which is essentially composed of photons. Therefore, if gravity does indeed radiate, then would this radiation be in the form of gravitons?

Yes, that is indeed what roughly happens. In linearized gravity, the Lorenz gauge can be chosen such that the linearized Einstein field equations take the form $$\Box^2 \bar{h}_{\mu\nu} = -16\pi G T_{\mu\nu},$$ where $$\bar{h}_{\mu\nu} = h_{\mu\nu} - h\eta_{\mu\nu}/2$$ is the trace-reversed metric perturbation. This is analogous to the wave equation for the electromagnetic potential $$\Box^2 A^\nu = -\mu_0 J^\nu$$. The actual gravitational waves are contained in the transverse-traceless (TT) part of the spatial components $$h_{ij}$$, denoted $$h^{\mathrm{TT}}_{ij}$$. This is gauge-independent and contains precisely the two propagating degrees of freedom which correspond to the two polarizations of gravitational waves.