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· The Famous E=mc2 is the most profound mathematics in the history of the world. It tells us that no matter can travel the speed of light because of the mass that would be needed to generate the speed would slow it down with drag.

· The Einstein Field Equations (EFE) is a tensor equation relating a set of symmetric 4 x 4 tensors. Each tensor has 10 independent components. Given the freedom of choice of the four space time coordinates, the independent equations reduce to 6 in number.

· The Vacuum Field Equations ,If the energy-momentum tensor Tμν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting Tμν = 0 in the full field equations, the vacuum equations can be written as

The solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution.

Manifolds with a vanishing Ricci tensor, Rμν = 0, are referred to as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds.

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