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kent davidge
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Im trying to visualize what form the light cones take in Rindler coordinates. Below is my drawing + reasoning. Is it right?
So it seems like I have obtained the correct diagram from wrong equations.pervect said:Wiki has a derivation of the null geodesics in <<link>>
pervect said:I don't believe that the null geodesics should be able to cross the Rindler horizon
kent davidge said:So it seems like I have obtained the correct diagram from wrong equations.
It seems that I should have considered the geodesic equations first.
Ah, ok. What seems weird to me is that if you let ##n \rightarrow \infty## the past light cone of the particle will cover only half of the space. Is that right? So it seems that there are events that will never cross the particles world line.PeterDonis said:Your equations aren't wrong. What you did, for this simple case, is equivalent to solving the geodesic equations for null geodesics. In the Wikipedia article, that corresponds to setting ##P = Q = 0## and ##y = z = 0##.
In the more general case where we put back the other two spatial dimensions, what you did is equivalent to solving the restricted set of null geodesic equations that only apply to "radial" geodesics--geodesics that only move in the ##n - p## plane, not in the other two coordinate directions.
Yes, there are events that will never be in the past light cone of the accelerating observer. That’s the Rindler horizon at work.kent davidge said:So it seems that there are events that will never cross the particles world line.
A light cone in Rindler coordinates is a visualization of the paths that light rays take in a spacetime diagram using a specific coordinate system known as Rindler coordinates. It is used to understand the relationship between space and time in a flat, accelerating universe.
A light cone in Rindler coordinates is different from a light cone in Minkowski coordinates because it takes into account the effects of acceleration and non-inertial frames of reference. This allows for a more accurate representation of the paths of light rays in a non-uniform universe.
The visualization of a light cone in Rindler coordinates tells us about the causal structure of spacetime, specifically the relationship between events that can be influenced by each other. It also helps us understand the effects of acceleration on the paths of light rays.
A light cone in Rindler coordinates is used in various fields of physics, including general relativity and cosmology. It is used to study the effects of acceleration on the behavior of light and other particles, as well as to understand the structure of spacetime in non-uniform environments.
Yes, a light cone in Rindler coordinates can be used to visualize the paths of any type of particle or object in a non-uniform universe. This includes not only light, but also matter particles and even entire galaxies. It is a useful tool for understanding the behavior of objects in accelerating and non-inertial frames of reference.