# How did Einstein come up with the field equations?

## How did Einstein come up with the field equations?

Einstein made two heuristic and physically insightful steps. The first was to obtain the field equations in vacuum in a rather geometric fashion. The second step was obtaining the field equations in the presence of matter from the field equations in vacuum.

## How many equations did Einstein field have?

ten equations
The Einstein Field Equations are ten equations, contained in the tensor equation shown above, which describe gravity as a result of spacetime being curved by mass and energy.

What do Einstein’s field equations do?

In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein’s equations) relate the geometry of spacetime to the distribution of matter within it.

### What is the theory of relativity explained simply?

What is general relativity? Essentially, it’s a theory of gravity. The basic idea is that instead of being an invisible force that attracts objects to one another, gravity is a curving or warping of space. The more massive an object, the more it warps the space around it.

### What is Einstein’s theory of relativity for dummies?

Essentially, it’s a theory of gravity. The basic idea is that instead of being an invisible force that attracts objects to one another, gravity is a curving or warping of space. The more massive an object, the more it warps the space around it.

How do you write Einstein’s field equations?

The Einstein field equations (EFE) may be written in the form: where Rμν is the Ricci curvature tensor, R is the scalar curvature, gμν is the metric tensor, Λ is the cosmological constant, G is Newton’s gravitational constant, c is the speed of light in vacuum, and Tμν is the stress–energy tensor.

## What are the Einstein-Maxwell equations?

Einstein–Maxwell equations. If the energy-momentum tensor Tμν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory):…

## What is the relationship between Einstein’s field equations and stress?

The Einstein field equations relate the Einstein tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime manifold.

Is it possible to expand Einstein’s field equations in terms of metric?

Fundamentally, however, they all contain the metric tensor g µν so it is indeed possible to expand the above equation in terms of the metric only (and its derivatives). This is what the fully expanded Einstein field equations look like when written out in terms of the metric: