Abstract: Einstein's Field equations in general relativity lack conformal invariance, unlike most field equations. A conformal version of these equations introduces Bach's Equations in dimension 4. We first examine the Initial Value and Hamiltonian formalism for both Einstein's and Bach's Equations. Then, we provide an overview of Fischer, Marsden, and Moncrief's research on the linearization stability of Einstein's equations and propose analogous conjectures for the linearization stability of Bach Equations in dimension 4.
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