# How to reduce the integral equation for light deflection?

• Bishal Banjara
In summary, the integral equation for light deflection is derived from the theory of General Relativity and involves solving the Einstein field equations and applying the principle of least action. Factors such as mass, distribution of mass, distance, speed of light, and spacetime curvature affect the amount of light deflection. While the equation can be simplified, it may not accurately predict all scenarios. Light deflection can cause distortions in our observations of distant objects, making it challenging to study them accurately. However, understanding light deflection is crucial for precise measurements in astronomy and astrophysics, as well as for applications such as gravitational lensing and gravitational wave detection.

#### Bishal Banjara

1. At pg.212, Hartle book (2003) writes equation 9.81 as an approximation of 9.80, directly. 2. $$ΔΦ=\int_0^{w_1}\frac{(1+\frac{M}{b}w)}{(1+\frac{2M}{b}w-w^2)^\frac{1}{2}}dw$$ equation(9.80)
$$ΔΦ≈\pi+4M/b$$ equation(9.81)
3. I am expecting anyone to give me a well-explained reference particularly with this method or clarify me without scaping proper steps.

Last edited:
Unless you can express w1 as w1(m,B) I don't think the definite integral can be approximated as shown.

$$w$$ is defined as $$b/r$$. You could see the book. Otherwise, I will write a few steps back.

## 1. How is the integral equation for light deflection derived?

The integral equation for light deflection is derived from the theory of General Relativity, which describes how gravity affects the path of light. It involves solving the Einstein field equations and applying the principle of least action.

## 2. What factors affect the amount of light deflection?

The amount of light deflection is affected by the mass and distribution of mass in the gravitational field, as well as the distance between the light source and the observer. Additionally, the speed of light and the curvature of spacetime also play a role in the deflection of light.

## 3. Can the integral equation for light deflection be simplified?

Yes, the integral equation for light deflection can be simplified by making certain assumptions and approximations, such as using the weak field limit or assuming a spherically symmetric mass distribution. However, these simplifications may not accurately describe all scenarios and may result in less precise predictions.

## 4. How does light deflection affect our observations of distant objects?

Light deflection can cause distortions in the images of distant objects, making them appear to be in a different location or even creating multiple images of the same object. This can make it challenging to accurately study and understand the properties of these objects, such as their mass and structure.

## 5. Are there any practical applications of understanding light deflection?

Yes, understanding light deflection is crucial for making precise measurements in astronomy and astrophysics. It also plays a role in technologies such as gravitational lensing, where the deflection of light by massive objects is used to magnify and study distant objects, and in the development of gravitational wave detectors.