# Find Null Geodesics with affine parameter

• myra2016
In summary, finding null geodesics with affine parameter involves determining the path of a massless particle in curved spacetime using a parameter that measures the distance traveled along the geodesic. This parameter is chosen to be affine, meaning that the geodesic remains unchanged under affine transformations. This method is commonly used in general relativity to study the behavior of light in gravitational fields.
myra2016

## Homework Statement

The metric is given by
https://dl.dropboxusercontent.com/u/86990331/metric12334.jpg
H is constant; s is an affine parameter, and so r(0)=t(0)=0.

Apologise in advance because I'm not very good with LaTex. So I used Word for equations, and upload handwritten attempt at solution

## Homework Equations

Need to show that the null geodesics from r=0, t=0 are given by
https://dl.dropboxusercontent.com/u/86990331/metricquestion.jpg

## The Attempt at a Solution

I get the required t but the sign is different.
https://dl.dropboxusercontent.com/u/86990331/metricattemptatsolution.jpg

Last edited by a moderator:
Hello, please attempt to re-upload the images, currently the links appear to be broken and may very well be the reason no one can help.

## What is the concept of null geodesics with affine parameter?

Null geodesics are paths in spacetime that represent the motion of light or other massless particles. They are characterized by having a tangent vector that is parallel transported along the path, meaning that the direction of motion does not change. Affine parameter is a special type of parameterization of the geodesic, which allows for the proper time along the path to be measured and compared to other paths.

## How can one find null geodesics with affine parameter?

To find null geodesics with affine parameter, one must first determine the metric tensor of the spacetime in question. Then, using the geodesic equation, which describes the path of a geodesic in terms of the metric tensor, one can solve for the null geodesic with affine parameter.

## What is the significance of finding null geodesics with affine parameter?

Finding null geodesics with affine parameter is important in understanding the behavior of light and other massless particles in a given spacetime. It allows for the calculation of proper time along the path, which is necessary for making predictions and understanding the effects of gravity on these particles.

## What are some applications of finding null geodesics with affine parameter?

The concept of null geodesics with affine parameter has many applications in the field of astrophysics. It is used in the study of black holes, gravitational lensing, and the behavior of light in curved spacetime. It also has applications in cosmology, helping to explain the expansion of the universe and the effects of dark matter and dark energy.

## Are there any limitations to finding null geodesics with affine parameter?

One limitation is that it can only be applied in situations where the curvature of spacetime is relatively small. In cases of extreme curvature, such as near a black hole, the geodesic equation and affine parameter may break down and other methods must be used to accurately describe the path of light and other massless particles.

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