# What is the metric form ##g_{μν}## in this context?

• A
hykhor0601
TL;DR Summary
Does anyone know how to solve this?
##ds^2=g_{μν}(x)dx^μdx^ν= -(r^6/l^6)[1-(Ml^2/r^2)]dt^2+{1/[(r^2/l^2)-M]}dr^2+r^2dΦ^2##

Does anyone know how to solve this?

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What do you mean by "solve"? There is nothing to "solve", there is just a line-element.

• vanhees71
2022 Award
Solve in what sense? It appears to be just a statement of a metric, missing a definition of ##l## and assuming ##d\Phi## is a solid angle element.

• vanhees71
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Can you provide some context here? Where di this equation come from? What book course etc...?

and what have you tried so far?

ds^2=gμν(x)dx^μdx^ν= -(r^6/l^6)[1-(Ml^2/r^2)]dt^2+{1/[(r^2/l^2)-M]}dr^2+r^2dΦ^2

Basically the changes were to bracket the equation on both sides with double # and to replace the gμν with g_{μν} to make them into subscripts.

hykhor0601
Can you provide some context here? Where di this equation come from? What book course etc...?

and what have you tried so far?

Basically the changes were to bracket the equation on both sides with double # and to replace the gμν with g_{μν} to make them into subscripts.
https://arxiv.org/pdf/0909.1347.pdf The metric is given in (9)

hykhor0601
Solve in what sense? It appears to be just a statement of a metric, missing a definition of ##l## and assuming ##d\Phi## is a solid angle element.
https://arxiv.org/pdf/0909.1347.pdf

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https://arxiv.org/pdf/0909.1347.pdf
This still does not answer the question you have been asked about what you mean by ”solve”.

hykhor0601
∂∨μ[(√-g)g∨μν∂∨ν(Φ)]-m^2√(-g)Φ=0
What is the meaning of ∂∨μ,√-g,∂∨ν(Φ) in this equation?

How to give the form of g^μν from the metric (9) in the article?(or how do i get the form of ∂∨μ[(√-g)g∨μν∂∨ν(Φ)]-m^2√(-g)Φ=0 )
https://arxiv.org/pdf/0909.1347.pdf

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https://arxiv.org/pdf/0909.1347.pdf
Again, what do you mean by "solve"? The metric is not a thing you solve. What are you trying to find out?

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Why are you interested in this particular paper if you are not familiar with basics of general relativity?

• Replusz
hykhor0601
Again, what do you mean by "solve"? The metric is not a thing you solve. What are you trying to find out?
just the form of gμν that can be sub into the equation of motion

Staff Emeritus
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just the form of gμν that can be sub into the equation of motion

• Replusz
hykhor0601
can you write it in the form after substitude into
∂µ[√ (−g)gµν∂ν(ϕ) ]− m^2√ (−g)ϕ = 0

• 