Owe Kristiansen
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- TL;DR Summary
- Title: Reframing Light Bending Using Density Instead of Radius
I’ve been exploring an alternative way to express gravitational light bending:
θ = (4G / c²) * (4π / 3)^(1/3) * M^(2/3) * ρ^(1/3)
Instead of using radius r, I substituted it using the density ρ of a spherical mass.
Title: Reframing Light Bending Using Density Instead of Radius
I’ve been exploring an alternative way to express gravitational light bending, starting from the classical general relativity approximation:
θ = (4 * G * M) / (r * c²)
Instead of using radius r, I substituted it using the density ρ of a spherical mass. It should be correct at the radius of a sphere with uniform density.
For a sphere:
ρ = M / V = M / ((4/3) * π * r³)
Solving for r gives:
r = (3M / (4πρ))^(1/3)
Substituting this into the original bending formula gives:
θ = (4G / c²) * (4π / 3)^(1/3) * M^(2/3) * ρ^(1/3)
This reframing expresses light bending as a function of mass and density, rather than radius. It seems to offer a more material-based interpretation of curvature — compactness and mass together determine how much light bends.
The beauty of this is that more mass or more density increase the bending.
I’m curious whether this formulation has been explored before, or if it might offer any new insights into gravitational lensing or curvature fields. Would love to hear your thoughts.
I’ve been exploring an alternative way to express gravitational light bending, starting from the classical general relativity approximation:
θ = (4 * G * M) / (r * c²)
Instead of using radius r, I substituted it using the density ρ of a spherical mass. It should be correct at the radius of a sphere with uniform density.
For a sphere:
ρ = M / V = M / ((4/3) * π * r³)
Solving for r gives:
r = (3M / (4πρ))^(1/3)
Substituting this into the original bending formula gives:
θ = (4G / c²) * (4π / 3)^(1/3) * M^(2/3) * ρ^(1/3)
This reframing expresses light bending as a function of mass and density, rather than radius. It seems to offer a more material-based interpretation of curvature — compactness and mass together determine how much light bends.
The beauty of this is that more mass or more density increase the bending.
I’m curious whether this formulation has been explored before, or if it might offer any new insights into gravitational lensing or curvature fields. Would love to hear your thoughts.
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