Maxwell's four equations can be used to describe the propagation of electromagnetic waves. What is the equivalent for gravitational waves - if that question makes sense?
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Gravitational waves are a prediction of linearised gravity in General Relativity, analogous to that of electromagnetic waves in Electromagnetism. The equations predicting gravitational waves can be written as :
$$\partial^b\overline{\gamma_{ab}}=0$$ $$\partial^c\partial_c\overline{\gamma_{ab}}=-16\pi T_{ab}$$
where $\gamma_{ab}$ is the 'small' deviation from a flat spacetime $\eta_{ab}$ and $T_{ab}$ is the stress-energy tensor.
The above equations are similar to that of the maxwell equations :
$$\partial^aA_a=0$$ $$\partial^a\partial_aA_b=-4\pi j_b$$
where $A^a$ is the vector potential and $j_b$ is the current density. [The first equation is the Lorenz gauge condition and the second is the combined Maxwell's equation]
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Yuzuriha Inori
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