Please explain these Equations in GR, Modified Universal law of Gravity.

In summary, Space time Geometry and GR is a topic discussed in the lecture notes from the course CM334 at King's College London. On pages 3 and 4, it is mentioned that Newton's law of universal gravity is being modified, and the question is raised about where this modification comes from. The alternative explanation is that Coulomb's law and the Principle of superposition are solutions to Gauss's law, leading to Poisson's equation with the assumption of time independence. It is unclear which explanation came first historically, but undergraduate textbooks typically follow the latter approach.
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Space time Geometry and GR, taken from lecture notes

http://www.mth.kcl.ac.uk/courses/cm334.html

http://www.mth.kcl.ac.uk/courses/cm334/Lectures0910.pdf
from pages 3 and 4

Newton's universal law of gravity is getting modified.

it says using the result, from where this result comes from?

Screenshot1.png


and as follows with this page

Screenshot2.png


after equation 4, it says that using the fact that... where this equation is coming from and how can I understand this, can anyone explain please?
 
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Related to Please explain these Equations in GR, Modified Universal law of Gravity.

1. What is the theory of General Relativity (GR)?

General Relativity is a theory of gravity developed by Albert Einstein in the early 20th century. It states that gravity is not a force between masses, but rather the curvature of space and time caused by the presence of massive objects.

2. What is the Modified Universal Law of Gravity?

The Modified Universal Law of Gravity is an extension of Newton's Law of Universal Gravitation, which states that the force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The modified version takes into account the effects of General Relativity, especially in situations where the gravitational field is very strong.

3. How do these equations help explain the behavior of gravity?

The equations in GR and the Modified Universal Law of Gravity provide a mathematical framework for understanding how gravity works. They allow us to make predictions about the behavior of massive objects and how they interact with each other in the presence of strong gravitational fields.

4. What are some real-world applications of these equations?

These equations have numerous applications in astrophysics, cosmology, and space exploration. They help us understand the motion of planets, stars, and galaxies, as well as the bending of light in the presence of massive objects. They also play a crucial role in the study of black holes and the expanding universe.

5. How do these equations differ from other theories of gravity?

GR and the Modified Universal Law of Gravity differ from other theories of gravity, such as Newton's Law of Universal Gravitation, in that they take into account the effects of space and time. They also provide a more accurate description of gravity in extreme situations, such as near black holes or during the early stages of the universe.

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