Field of Point Mass: MTW Ex 7.3C Solution

In summary, the conversation is about finding the term h00 or hbar from equation 7, which is a Laplacian in the static case. The 1/r term and the 16Pi factor are not clear and the person is asking for help in understanding them. The Laplace equation is written as \nabla\cdot (\nabla\bar{h}_{\mu \nu })=-16\pi T_{\mu \nu } and Gauss' Law is applied to it. The final equation is 4\pi r^2 |\nabla\bar{h}_{00}|=-16\pi M, and further details are left to the reader to figure out.
  • #1
zn5252
72
0
hello,
Please see attached snapshot. My question is regarding the way MTW found the term h00 or just for the hbar from equation 7.
Now since we are in the static case, Equation 7 becomes a Laplacian. But I could not figure out how the 1/r term came to be and where did the 16Pi go ?
Any help is much appreciated.
Thanks,
 

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  • #2
Write the Laplace equation as the following:

[tex]\nabla\cdot (\nabla\bar{h}_{\mu \nu })=-16\pi T_{\mu \nu }[/tex]

Now apply Gauss' Law:

[tex]\int \nabla\cdot (\nabla\bar{h}_{\mu \nu })d^3 x=\int (\nabla\bar{h}_{\mu \nu })\cdot \mathbf{n}d^2x= -16\pi \int T_{\mu \nu }d^3x[/tex]

[tex]4\pi r^2 |\nabla\bar{h}_{00}|=-16\pi M[/tex]

I'll let you take it from there.
 

Related to Field of Point Mass: MTW Ex 7.3C Solution

What is the Field of Point Mass?

The Field of Point Mass is a concept in physics that describes the gravitational field around a point mass, which is a mass that is concentrated at a single point in space. This field is responsible for the attraction between objects and is described by the inverse square law.

What is MTW Ex 7.3C Solution?

MTW Ex 7.3C Solution is a specific problem in the classic textbook "Gravitation" by Misner, Thorne, and Wheeler (MTW). It presents a scenario where a point mass is located at the origin of a coordinate system, and the goal is to calculate the gravitational field at various points in space.

How is the Field of Point Mass calculated?

The Field of Point Mass is calculated using the formula F = GmM/r^2, where F is the force of gravity, G is the gravitational constant, m and M are the masses of the objects, and r is the distance between them. This formula is derived from Newton's law of universal gravitation.

What are some applications of the Field of Point Mass?

The Field of Point Mass is used in various fields such as space exploration, astronomy, and engineering. It helps in understanding the motion of objects in space, calculating the trajectories of spacecraft, and designing structures that can withstand gravitational forces.

Are there any limitations to the Field of Point Mass?

The Field of Point Mass is a simplified model that does not take into account the effects of relativity or the distribution of mass in an object. It is only accurate for objects that are small compared to the distance between them. In such cases, more complex calculations are required, such as using the concept of the gravitational potential.

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