Mathematics of MTW gravitation.

In summary, the "Mathematics of MTW gravitation" refers to the mathematical framework and equations used to describe the theory of gravity proposed by Charles Misner, Kip Thorne, and John Wheeler (MTW) in their book "Gravitation". This theory combines Einstein's theory of general relativity with Maxwell's theory of electromagnetism and Dirac's theory of quantum mechanics, making it more comprehensive than other theories of gravity. The main equations used include the Einstein field equations, Maxwell equations, Dirac equation, and equation of motion for charged particles. The theory explains gravity as a result of the curvature of spacetime caused by the distribution of matter and energy, and has practical applications in the study of black holes, gravitational
  • #1
center o bass
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Hi. I would like to learn the mathematics from Gravitation by MTW, but i find the book hard to follow mainly due to its style. Many other authors seem to work mainly with components and do not employ the exterior derivative etc. Does anyone know some text which treats GR similarly to MTW, but with a more "fluent" walktrough of the math?
 
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  • #2
Have you seen T's manuscript http://www.pma.caltech.edu/Courses/ph136/yr2011/ ?
Some relevant parts are near the start and some are near the end.
 

1. What is the "Mathematics of MTW gravitation"?

The "Mathematics of MTW gravitation" refers to the mathematical framework and equations used to describe the theory of gravity proposed by Charles Misner, Kip Thorne, and John Wheeler (MTW) in their book "Gravitation". This theory is also known as the Einstein-Maxwell-Dirac theory as it combines Einstein's theory of general relativity with Maxwell's theory of electromagnetism and Dirac's theory of quantum mechanics.

2. How does the MTW theory differ from other theories of gravity?

The MTW theory differs from other theories of gravity, such as Newton's theory of gravity and Einstein's theory of general relativity, in that it takes into account the effects of both gravity and electromagnetism. It also incorporates elements of quantum mechanics, making it a more comprehensive theory.

3. What are the main equations used in the Mathematics of MTW gravitation?

The main equations used in the Mathematics of MTW gravitation include the Einstein field equations, which describe the relationship between the curvature of spacetime and the distribution of matter and energy, and the Maxwell equations, which describe the behavior of electromagnetic fields. Other important equations include the Dirac equation, which describes the behavior of quantum particles, and the equation of motion for charged particles in a gravitational field.

4. How does the MTW theory explain the behavior of gravity?

The MTW theory explains the behavior of gravity as a result of the curvature of spacetime caused by the presence of matter and energy. This curvature is described by the Einstein field equations, which show how the distribution of mass and energy affects the curvature of spacetime. The theory also incorporates the effects of electromagnetism and quantum mechanics, providing a more complete understanding of gravity.

5. What are some practical applications of the Mathematics of MTW gravitation?

Some practical applications of the Mathematics of MTW gravitation include the study of black holes, gravitational waves, and the behavior of particles in extreme gravitational fields. It is also used in the development of technologies such as GPS and satellite communications, which rely on precise calculations of the effects of gravity on electromagnetic signals.

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