# Help Understand Retarded Function: Einstein Eq. Linearized

• I
• needved
In summary, when the Einstein equations are linearized, they become the weak field Einstein equations which can be solved using the Retarded function. This function uses the concept of a retarded time, which is the time it takes for a signal to travel from the source to the observer. The physical situation being described is similar to electromagnetism, where the potential is calculated at a certain location based on the location of the charge.
needved
Hi people, help here please
When the Einstein equation are linearized the results are the weak field Einstein equations

$$\left ( -\frac{\partial^{2}}{\partial t^{2}} + \nabla^{2} \right ) \bar h^{\mu\nu}=-16\pi T^{\mu\nu}$$
a solution for this equations considering the source are the Retarded function
$$\bar h^{\mu\nu} (t,\vec x)=4 \int d^{3}x' \frac{[T^{\mu\nu}(t',\vec x')]_{[ret]}}{|\vec x - \vec x'|}$$
with

$$t' = t_{ret} = t-|\vec x - \vec x'|$$

until i know "t" and "x" in spacetime are the same but what physical situation describes
$$|\vec x - \vec x'|$$
Is similar to electromagnestism, when $$\vec x$$ represent the place where you want calculate the potencial and $$\vec x'$$ represent the place where the charge is located?

Last edited by a moderator:
Your weak field equation is just a separate wave equation for every individual component. The solution is just applying the retarded Green's function of the wave equation.

needved

## 1. What is the Einstein equation and how does it relate to retarded functions?

The Einstein equation is a fundamental equation in the theory of general relativity, which describes the relationship between the curvature of spacetime and the distribution of matter and energy in the universe. Retarded functions, also known as advanced functions, are mathematical functions used to model the propagation of information in a non-instantaneous way, which is necessary in the theory of general relativity. The Einstein equation uses these functions to describe how the curvature of spacetime is affected by the presence of matter and energy.

## 2. Why is it important to linearize the Einstein equation?

Linearization is a mathematical technique used to approximate a nonlinear equation by replacing it with a simpler, linear equation. In the case of the Einstein equation, which is a highly complex nonlinear equation, linearization allows scientists to simplify the equation and make it more manageable for mathematical analysis. This is especially important in the study of general relativity, where the equations can become very complicated and difficult to solve without linearization.

## 3. How does the linearized Einstein equation help us understand the behavior of objects in the universe?

The linearized Einstein equation provides a simplified mathematical model for the behavior of objects in the universe, such as planets, stars, and galaxies. This allows scientists to make predictions and calculations about the movement and interactions of these objects based on the curvature of spacetime caused by the presence of matter and energy. By studying the linearized Einstein equation, we can better understand the fundamental principles of general relativity and how they govern the behavior of objects in the universe.

## 4. What are some real-world applications of the linearized Einstein equation?

The linearized Einstein equation has a wide range of applications in modern physics and astronomy. One of the most significant applications is in the study of gravitational waves, which are ripples in the fabric of spacetime caused by the acceleration of massive objects. The linearized Einstein equation is also used in cosmology to model the large-scale structure of the universe and the distribution of matter and energy. Additionally, it has applications in the study of black holes, neutron stars, and other astronomical objects.

## 5. How has our understanding of the linearized Einstein equation evolved over time?

The linearized Einstein equation is a product of decades of research and development in the field of general relativity. It has undergone several modifications and refinements over the years, as scientists continue to improve their understanding of the fundamental principles of the theory. With advancements in technology and techniques, scientists have been able to make more accurate predictions and observations using the linearized Einstein equation, leading to a deeper understanding of the behavior of objects in the universe.

Replies
4
Views
690
Replies
8
Views
549
Replies
2
Views
986
Replies
7
Views
528
Replies
17
Views
1K
Replies
8
Views
1K
Replies
12
Views
3K
Replies
2
Views
1K
Replies
12
Views
2K
Replies
3
Views
1K