Covariant divergence question from Landau and Lifshitz

In summary, Vivek is struggling with section 86 of Landau and Lifgarbagez volume 2 and is unable to derive equation (86.6) from equations (86.4) and (86.5). He has attached a jpg file with his working and question and is seeking help. George suggests looking at section 1.7 in Eric Poisson's notes or finding a copy of the book A Relativist's Toolkit. Vivek's school library does not have the book, but he can try accessing it through Google Books or Amazon.
  • #1
maverick280857
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Hi everyone,

I'm trying to work through section 86 of Landau and Lifgarbagez volume 2 (The Classical Theory of Fields).

Basically, I am unable to get equation (86.6) from equations (86.4) and (86.5). I've detailed my working/question in the attached jpg file. I would appreciate any inputs.

Thanks in advance!
Cheers
Vivek
 

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  • #2
I bet they've calculated [tex] \partial \sqrt{-g} / \partial x^{\mu} [/tex] somewhere.
 
  • #3
Take a look at section 1.7 in Eric Poisson's excellent notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf.

Better yet, see if your library has a copy of the excellent book, A Relativist's Toolkit: The Mathematics of Black Hole Mechanics, into which the notes evolved.
 
  • #4
George, thanks a lot for this very useful link! Unfortunately, my school library does not have this book.
 

1. What is the covariant divergence in Landau and Lifshitz?

The covariant divergence, also known as the covariant derivative, is a mathematical operation that describes the rate of change of a vector field in curved space. It is defined as the sum of the partial derivative of the vector field with respect to each coordinate, multiplied by the corresponding basis vector.

2. How is the covariant divergence calculated?

The covariant divergence can be calculated using the formula DabVa, where Da is the covariant derivative operator, b is the index of the vector field V, and a is the index of the basis vector.

3. What is the physical significance of the covariant divergence?

The covariant divergence is a fundamental concept in general relativity, and it is used to describe the behavior of matter in curved space. It is also related to the conservation of energy and momentum, as it represents the rate of change of a vector field in space-time.

4. How does the covariant divergence differ from the ordinary divergence?

The covariant divergence takes into account the curvature of space, while the ordinary divergence does not. This means that the covariant divergence is a more general and accurate measure of the rate of change of a vector field in curved space.

5. What are some applications of the covariant divergence in physics?

The covariant divergence is used in various areas of physics, such as general relativity, fluid dynamics, and electromagnetism. It is also an important tool in studying the behavior of matter in gravitational fields and in understanding the structure of space-time.

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