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Based on general (1+3) threading of the spacetime (M,g), we obtain a new and simple splitting of both the Einstein field equations (EFE) and the conservation laws in (M,g). As an application, we obtain the splitting of EFE in an almost FLRW universe with energy-momentum tensor of a perfect fluid. In particular, we state the perturbation Friedmann equations in an almost FLRW universe

advances in mathematical physics

On the Splitting of the Einstein Field Equations with respect to General <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mn fontstyle="italic">1</mml:mn><mml:mo>+</mml:mo><mml:mn fontstyle="italic">3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> Threading of Spacetime

On the Splitting of the Einstein Field Equations with respect to General (1+3) Threading of Spacetime