# #5 Einstein’s Field Equation

Einstein, an absolute genius, has given a lot of groundbreaking theories and the one which completely changed our understanding was the Theory of Relativity. Both Special and the General theory of relativity being two of the most famous and fundamental scientific theories have a lot of revolutionary equations. In this article, we are going to talk about one such equation which is Einstein’s second most famous equation after E=Mc2. It is Einstein’s Field Equation

where,

$Einstein's Field Equation$

– Einstein tensor

$Einstein's Field Equation$ – Ricci curvature tensor

$Einstein's Field Equation$– Scalar curvature

$g_{\mu\nu}$– Metric Tensor

$\Lambda$– Cosmological constant

$G$– Newton’s gravitational constant

$c$ – Speed of light

$T_{\mu\nu}$– Stress-energy tensor

Did not understand the terms? This equation looks pretty clean and simple but isn’t that simple, it involves many crazy Tensor calculations, matrices, etc. So, don’t get afraid, all these terms are pretty complex and need a lot of explanation which I won’t be doing here because it will be boring (Still want to read about these terms: Read here). Instead, let us know the importance of the equation and why is it so famous.

First of all, you have to know that this is not a single equation, this equation hides and summarizes 10 partial differential equations in it. This small equation that doesn’t look too complex, (at least not as complex as Schrodinger’s wave equation :-)) completely changed our understanding of the universe. It revolutionized the concept of gravity.

According to General Relativity, Gravity is because of mass curving space-time. Einstein’s field equation explains the mass, energy, momentum, pressure distribution across space-time and how does these curve space. The left side of the equation (which has Einstein tensor) is about the curving of space and the right side (which have stress-energy tensor) is about the distribution of energy and mass, so, it relates mass and energy to curvature of space-time.

[bctt tweet=”‘Space-time tells matter how to move; matter tells space-time how to curve’–John Wheeler” username=”Sciencehook”]

This equation has been used to predict the existence of black holes and gravitational waves. It explains how black holes warp space-time. Einstein’s equation can tell us how our universe has changed over time and offers glimpses of the earliest moments of creation. This equation has been used to understand many processes of the universe.

So, that was a glimpse into Einstein’s Field Equation, Hope you liked it.