Einstein field equations (EFE's)

[Petenerd]

Can someone explain the equation [tex]G_{\mu\nu}+\Lambda g_ {\mulnu}={8\ pi G\over c^4} T_{\mu\nu}\ [/tex] by Albert Einstein?

 

[feynmann]

Can someone explain the equation G_{ab}={8 pi G over c^4}T_{ab} by Albert Einstein?

Check out this paper: The Meaning of Einstein's Equation
http://math.ucr.edu/home/baez/einstein/einstein.pdf

 

[Entropia]

The Einstein field equations, also known as EFE's, are a set of equations developed by Albert Einstein as part of his theory of general relativity. These equations describe the relationship between the curvature of space-time and the distribution of matter and energy within it.

The equation G_{\mu\nu}+\Lambda g_ {\mulnu}={8\ pi G\over c^4} T_{\mu\nu} is known as the Einstein field equations in its simplest form. Let's break it down and explain each component.

- G_{\mu\nu} is the Einstein tensor, which describes the curvature of space-time.
- \Lambda is the cosmological constant, which represents the energy density of empty space.
- g_ {\mulnu} is the metric tensor, which defines the geometric properties of space-time.
- {8\ pi G\over c^4} is a constant that relates the strength of gravity to the energy and mass of objects in the universe.
- T_{\mu\nu} is the stress-energy tensor, which describes the distribution of matter and energy in space-time.

In simple terms, this equation states that the curvature of space-time (G_{\mu\nu}) plus the energy density of empty space (\Lambda g_ {\mulnu}) is equal to the amount of energy and mass in space-time (T_{\mu\nu}) multiplied by a constant related to the strength of gravity ({8\ pi G\over c^4}).

This equation is important because it allows us to understand how matter and energy interact with the fabric of space-time, and how this interaction affects the curvature of space-time. It also helps us to understand the behavior of objects in the universe, from the smallest particles to the largest galaxies.

Overall, the Einstein field equations are a fundamental part of modern physics and have played a crucial role in shaping our understanding of the universe.