The spacetime interval in the interior of a uniform spherical mass distribution of mass M and...

 

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The spacetime interval in the interior of a uniform spherical mass distribution of mass M and radius R is, in the linear approximation, ds² = (1 +20)dt² – (1 – 20)dr² — r²d0² — r² sin² 0do² - where = +GMr²/2R³ - 3GM/2R is the Newtonian potential. Find a formula for the volume of a concentric sphere of radius r < R. Assume that || < 1, so √1+ 20 = 1 + $. The spacetime interval in the interior of a uniform spherical mass distribution of mass M and radius R is, in the linear approximation, ds² = (1 +20)dt² – (1 – 20)dr² — r²d0² — r² sin² 0do² - where = +GMr²/2R³ - 3GM/2R is the Newtonian potential. Find a formula for the volume of a concentric sphere of radius r < R. Assume that || < 1, so √1+ 20 = 1 + $.

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The volume of a spherical object is determined by its radius This is true for any object regardless ... View the full answer