Einstein Field Equation: Overview, Questions, Preparation

Einstein's Field Equation is also known as Einstein's Equation. There are ten differential equations of Einstein explained by Einstein using field equations called Einstein field equations. Einstein himself first published these equations in the year 1915. It was called a tensor equation, later renamed to Einstein field equations.

It is also known as trace- reversed Ricci tensor. It is defined as the spacetime curvature that is in line with the conservation of momentum and energy. The equation can be defined as:

G = R – ½ gR 

Here, R is referred as Ricci tensor

g as metric tensor

R as scalar curvature.

Stress Energy Tensor

The stress-energy tensor is denoted as Tαβ. It is used to define the relationship between energy and momentum density concerning the gravitational field. 

T αβ = T βα

Einstein field equation is as follows:

Gμυ + gμυ Λ = 8πG/ c4 Tμυ

 Here, Gμυ is the Einstein tensor,

• Scalar curvature is denoted as R
• Ricci curvature tensor is denoted as Rμυ
• The cosmological constant is written as 𝚲
• Newton’s gravitational constant is G
• The speed of the light is written as c
• Stress energy tensor is denoted as Tμυ 

One of the most important equations that Einstein was the Einstein field equation. In this theory of equations, he wanted to explain the relationship between curvature and a source of gravity. In simple words, the equation that proves that the gravity and measure source will be equal and is proved in the following illustration. 

The Einstein field equation can be derived as following:

dui / dτ + Για να uv uα = 0

dui / dτ + Γi 00 = 0

dui / dτ + Γi + ½ ∂g00 / ∂xi

dui / dτ  + ∂ϕ / ∂xi = 0

g00 = - (1 + 2 ϕ)

it is known that, ▽2ϕ=4πGρ

hence, R μv = − 8 π GT μv

here, the constant equation is – 8 π GT μv 

Einstein field equation for class 11

The chapter 'Gravitation' holds a weightage of only 4 marks. These four marks are divided into 2 questions in total, including one objective type question of 1 mark and one short question of 3 marks. The Einstein field equation topic doesn't hold much importance over other significant topics of the gravitations chapter.

Example 1: Write the formula of Time Dilation.

Answer:  The formula of time dilation is t′ = t√(1 − v2/c2)

Example 2: State the constant value of Einstein’s field equation.

Answer: The constant value of Einstein’s field equation is – 8 π GT μv

Example 3: State the most famous equation written by Einstein other than field equations.

Answer: Another famous equation, written by Einstein, is E = mc2.

Q: How is stress-energy tensor donated?

Q: What is the other name of Einstein tensor?

Q: What do you mean by Einstein tensor?

Q: How Einstein discovered the field equations?

Q: What do you mean by the Einstein tensor equation?