Using Einstein field equation

[kashiark]

G_µv + Λg_µv = (8πG/c⁴)T_µv
I have several questions. what is the _µv? when we use it today do we use the cosmological constant even though the universe isn't static or does it mean something different than einstein orignally thought? what are we measuring when we use this if theyre all constants?

 

[CompuChip]

I don't know the alt code either, but here's a copy-paster: Λ (from Wikipedia

The mu and nu are tensor indices, indicating that G, g and T are two-tensors. If you don't know what they are you should first of all learn about them, because they are very important constituents of the language in which GR is formulated (I recommend Carroll's book), but for now you can consider G, g and T as 4 x 4 matrices and mu, nu as simply indices, for example G₀₀ is the top left component, etc.

The cosmological constant was written off a long time ago, but recently interest in it has arisen again. It can quite nicely explain some of the "odd" observed properties, such as the acceleration of the expansion rate of the universe and the fact that there seems to be more energy content than we'd expect. This might get you started, more advanced questions I will leave to the cosmologists out here :)

 

[Entropia]

The µv in this equation represents the indices of the metric tensor, which is a mathematical tool used to describe the curvature of spacetime. In simpler terms, it represents the four-dimensional coordinates of a point in spacetime.

In modern usage, the cosmological constant (Λ) is often included in the Einstein field equation to account for the observed expansion of the universe. This was not originally included in Einstein's theory, as he believed the universe to be static. However, it is now understood that the cosmological constant represents the energy density of empty space and can contribute to the overall curvature of spacetime.

When using this equation, we are essentially measuring the curvature of spacetime and how it is affected by the distribution of matter and energy (represented by Tµv). This allows us to understand how gravity works on a large scale and make predictions about the behavior of the universe. While the constants in the equation remain the same, the values of Tµv can vary depending on the specific situation being studied.