Why Schwarzschild Metric for Deflection of Light & Precession of Perihelia?

In summary, the Schwarzschild metric is used instead of the FLRW metric when deriving the deflection of light by the sun and the precession of perihelia of planets. This is because the FLRW metric assumes a uniformly distributed matter in spacetime, making it a bad approximation for the scale of the solar system. However, despite the solar system not being isotropic or static, the Schwarzschild metric still provides accurate results for the precession of perihelia of Mercury due to the Sun's large mass compared to the rest of the solar system. There is no special reason for using the nearest distance, or perihelion, instead of the farthest distance, or aphelion, when computing the angle, it
  • #1
davidge
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Why one uses Schwarzschild metric instead of FLRW metric when deriving things such

- deflection of light by the sun
- precession of perihelia of planets

Also, as our solar system is not isotropic nor static, it seems that by using the Schwarzschild metric we would get only an approximation on the results. So why we still get accurate result for the precession of perihelia of Mercury?
 
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  • #2
davidge said:
Why one uses Schwarzschild metric instead of FLRW metric when deriving things such

- deflection of light by the sun
- precession of perihelia of planets
Because the FLRW metric assumes that spacetime is filled with uniformly distributed matter. A bad approximation on the scale of the solar system.
davidge said:
Also, as our solar system is not isotropic nor static, it seems that by using Schwarzschild metric we get only a approximation on the results. So why we still get accurate result for precession of perihelia of Mercury?
Because it's a very good approximation because the mass of the Sun is such a huge percentage of the total mass of the solar system.
 
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Ah, ok. Thanks.

A bit off topic... but, the name precession of perihelia is due to the fact the we use the nearest distance ##r## of the planet from the sun when computing the angle? Is there a special motivation for non using the aphelion distance instead?
 
  • #4
No, it's just common use in astronomy.
 
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  • #5
vanhees71 said:
No, it's just common use in astronomy.
Thanks.
 

1. Why is the Schwarzschild metric used for the deflection of light and precession of perihelia?

The Schwarzschild metric is used because it accurately describes the curvature of space-time around a spherically symmetric mass, such as a star or planet. This curvature is what causes the deflection of light and the precession of perihelia.

2. How does the Schwarzschild metric explain the deflection of light?

The Schwarzschild metric shows that massive objects cause a curvature in space-time. When light travels near a massive object, it follows this curvature, causing it to appear to bend or be deflected from its original path.

3. What is the significance of the Schwarzschild radius in the Schwarzschild metric?

The Schwarzschild radius represents the distance from the center of a massive object at which the escape velocity equals the speed of light. This is important because it marks the boundary at which the object's gravitational pull becomes so strong that not even light can escape.

4. How does the Schwarzschild metric account for the precession of perihelia?

The Schwarzschild metric shows that the orbit of a planet around a star is not a perfect ellipse, but rather a slightly distorted shape due to the curvature of space-time. This distortion causes the perihelion, or closest point to the star, to shift slightly with each orbit, resulting in the precession of perihelia.

5. Are there any limitations to the Schwarzschild metric in explaining the deflection of light and precession of perihelia?

The Schwarzschild metric is a solution to Einstein's field equations and accurately describes the behavior of light and planetary orbits in a vacuum. However, it does not account for other factors such as the presence of other massive objects or the effects of gas and dust in space. Additionally, it does not apply to extreme cases such as black holes or objects with strong gravitational fields. In these cases, more complex metrics are needed to accurately describe the behavior of light and orbits.

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