Changes

In their general form, the Einstein field equations are written as a single [[tensor]] equation in [[abstract index notation]] relating the curvature of spacetime to sources of curvature such as energy density and momentum.

In their general form, the Einstein field equations are written as a single [[tensor]] equation in [[abstract index notation]] relating the curvature of spacetime to sources of curvature such as energy density and momentum.

:<math> G_{\mu\nu} = 8\,\pi\,G\,T_{\mu\nu} </math>

:<math> G_{\mu\nu} = 8\,\pi\,G\,T_{\mu\nu} - \Lambda g_{\mu\nu}</math>

In this form, <math>G_{\mu\nu}</math> represents the ''Einstein tensor,'' <math>G</math> is the same ''gravitational constant'' that appears in the [[Law of Universal Gravitation|law of universal gravitation]], and <math>T_{\mu\nu}</math> is the ''stress-energy tensor'' (sometimes referred to as the ''energy-momentum tensor).'' The indices <math>\mu</math> and <math>\nu</math> range from zero to three, representing the time coordinate and the three space coordinates in a manner consistent with [[Special theory of relativity|special relativity]].

In this form, <math>G_{\mu\nu}</math> represents the ''Einstein tensor,'' <math>G</math> is the same ''gravitational constant'' that appears in the [[Law of Universal Gravitation|law of universal gravitation]], and <math>T_{\mu\nu}</math> is the ''stress-energy tensor'' (sometimes referred to as the ''energy-momentum tensor).'' The indices <math>\mu</math> and <math>\nu</math> range from zero to three, representing the time coordinate and the three space coordinates in a manner consistent with [[Special theory of relativity|special relativity]]. <math>\Lambda </math> is the cosmological constant.

The left side of the equation — the Einstein tensor — describes the curvature of spacetime in the region under examination. The right side of the equation describes everything in that region that affects the curvature of spacetime.

The left side of the equation — the Einstein tensor — describes the curvature of spacetime in the region under examination. The right side of the equation describes everything in that region that affects the curvature of spacetime.