content_image/302822.jpg content_image/302824.jpg content_image/302825.jpg content_image/302821.jpg content_image/302823.jpg
where we are using Einstein summation convention. 

Going from a flat (Minkowski) manifold to the generically curved one of spacetime, which is an example of a pseudo-Riemannian manifold, we have the general symmetric metric tensor g$_{µν}$ (as opposed to the flat η$_{µν}$ ). The line element now becomes 

<img src='content_image/302822.jpg'>

The essence of General Relativity, hereafter referred to as GR, is reflected in the Einstein Field Equation , which is 

where R$_{µν}$ is the Ricci Tensor , given by 

where R µ νβα is the Riemann Tensor , given by 

where Γ µ νβ is the Christoffel Symbol , given by 

<img src='content_image/302824.jpg'>

<img src='content_image/302825.jpg'>

<img src='content_image/302821.jpg'>

<img src='content_image/302823.jpg'>

