Overview of General Relativity and Einstein Field Equations

1. Theory of General Relativity explains the Cause for Existance of Gravitational Force and the Factors Affecting it. It can explain and predict the Trajectories of Stars, Planets and Other Astronomical Bodies (or in fact any matter through Space-Time) with much more precision than Newton's Law of Gravitation. It can also explain many Astronomical Phenomena (for e.g. Bending of Light along Curvature of Space-Time) which cannot be explained by Newton's Law of Gravitation.
2. As per Theory of General Relativity
   1. The Curvature of the Space-Time causes the Matter to Move in a Specific Trajectory.
   2. The Presence of Matter/Energy (which are equivalent and interconvertible as per Special Theory of Relativity) causes the Space-Time to Curve in a Specific Manner.
3. Theory of General Relativity is mathematically expressed in terms of Einstein Field Equations. These equations are a Set of 10 Non-Linear Differential Equations which can be summarised in form of following Single Equation
   
   \(R_{\mu\nu} - \frac{1}{2}R g_{\mu\nu} + \Lambda g_{\mu\nu}=\kappa T_{\mu\nu}\)   ...(1)
   
   OR by setting \(G_{\mu\nu}=R_{\mu\nu} - \frac{1}{2}R g_{\mu\nu}\)
   
   \(G_{\mu\nu} + \Lambda g_{\mu\nu}=\kappa T_{\mu\nu}\)   ...(2)
   
   where
   
   \(G_{\mu\nu}=\)  \(4\times 4\) Symmetric Matrix called the Einstein Tensor
   \(R_{\mu\nu}=\)  \(4\times 4\) Symmetric Matrix called the Ricci Curvature Tensor
   \(g_{\mu\nu}=\)  \(4\times 4\) Symmetric Matrix called the Metric Tensor
   \(T_{\mu\nu}=\)  \(4\times 4\) Symmetric Matrix called the Stress-Energy-Momentum Tensor
   \(R=\)  Ricci Scalar
   \(\Lambda=\)  Cosmological Constant
   \(\kappa=\frac{8\pi G}{c^4}=\)  Einstein Gravitational Constant. Here \(G\) is the Newtonian constant of gravitation and \(c\) is the Speed of Light in Vacuum