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## Main Question or Discussion Point

hello everyone,

following the book of Landau&Lifsitz I managed to understand the Schwarzchild solution.

At the end, it finds this formula for the mass of the spherical body generating the gravitational field:

[tex]

M=\frac{4\pi}{c^2} \int^a_0 \epsilon(r) r^2 dr

[/tex]

in which [tex]\epsilon(r)[/tex] is the energy density of the spherical body and "a" is its radius.

This gravitational mass is smaller than the one calculated the "easy way", which is:

[tex]

M=\frac{4\pi}{c^2} \int^a_0 \epsilon(r) r^2 \sqrt{\gamma} dr

[/tex]

in which [tex]\gamma[/tex] is the determinant of the 3-D spatial metric.

This is called "gravitational mass defect".

Can you suggest me some resources to do the same for the cylindrically symmetric case (weyl metric) ?

following the book of Landau&Lifsitz I managed to understand the Schwarzchild solution.

At the end, it finds this formula for the mass of the spherical body generating the gravitational field:

[tex]

M=\frac{4\pi}{c^2} \int^a_0 \epsilon(r) r^2 dr

[/tex]

in which [tex]\epsilon(r)[/tex] is the energy density of the spherical body and "a" is its radius.

This gravitational mass is smaller than the one calculated the "easy way", which is:

[tex]

M=\frac{4\pi}{c^2} \int^a_0 \epsilon(r) r^2 \sqrt{\gamma} dr

[/tex]

in which [tex]\gamma[/tex] is the determinant of the 3-D spatial metric.

This is called "gravitational mass defect".

Can you suggest me some resources to do the same for the cylindrically symmetric case (weyl metric) ?