About null and timelike geodesics

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In summary: Null Geodesics are the only curves that light can follow. This was first observed by Edward Johnstone in 1919 when he noticed that light shifted its position near the Sun.
  • #1
Astronomer107
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Can you explain a little more about null and timelike geodesics (I think that's how you spell it)? I was reading Hawking and Penrose's The Nature of Space and Time, but it got a little technical. I would really like to know more about these though... thanks!
 
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  • #2
To put it simply, a null geodesic is a path light can take, a timelike geodesic is a path everything else can take.
 
  • #4
a geodesic is a the shortest path from point to point in a specific space, i.e. straight line on a piece of paper, a curve on a sphere
timelike means future pointing.
timelike geodeise is the shortest path an object can travel from event A to event B in spacetime.

hope this is right or i'll fail my exam in 2 weeks time...
 
  • #5
You're right, but don't forget Null Geodesics. These are the ones that only light (and massless particles) can follow. It was a null geodesic that the light followed in Eddington's 1919 observation of light shifting near the Sun. Also "shortest time" for a geodesic should be replaced with "stationary action" - but perhaps your course hasn't got to that yet.
 
  • #6
Originally posted by thankqwerty
a geodesic is a the shortest path from point to point in a specific space, i.e. straight line on a piece of paper, a curve on a sphere

I wrote up a web page on this a while back. Its located here
http://www.geocities.com/physics_world/ma/geodesic.htm

There are three basic ways to obtain the geodesic equation that I know of and so I posted those three derivations.

Please note that a geodesic is not defined as the shortest path from one point to another. It's a path of extremal length (where length has a meaning defined by the metric). There may be multiple paths between the same two points which are geodesics and each may have a different length.

Consider the cylinder r = R. Let the z-axis be the axis of the cylinder. consider the two points.

Point 1: r = R, theta = 0, z = 0
Point 2: r = R, theta = 0, z = b

The straight line from Point 1 to Point 2 is a geodesic. However the helix

x(t) = R cos(t) i + R sin(t) j + (b/2*pi)t k

is also a geodesic. See Figure 4 at
http://www.geocities.com/physics_world/euclid_vs_flat.htm

Notice that there are an infinite number of geodesics between those two points. You can define a helix which has one end at Point 1 and hich coils around the cylinder N times before passing through Point 2 where N is an arbitrary integer. And of course there are two helices for each end which differ only in the direction that it winds.

If you were to draw each of these curves onto the clyinder and cut the cylinder along its length then lay it out flat then each curve would be a straight line.

Think of a geodesic as the straightest possible curve.
 

1. What is the difference between null and timelike geodesics?

The main difference between null and timelike geodesics is their curvature. Null geodesics have zero curvature, meaning that they are straight lines in spacetime. Timelike geodesics, on the other hand, have a nonzero curvature and are curved paths in spacetime.

2. How are null and timelike geodesics related to the concept of light cones?

Null geodesics are paths that follow the light cone, which is the boundary between the past and future light cones. Timelike geodesics are paths that fall inside the light cone and are confined to the future light cone. These concepts are important in understanding the behavior of light and matter in spacetime.

3. Can null and timelike geodesics intersect?

No, null and timelike geodesics cannot intersect. This is because null geodesics are lines with zero curvature, while timelike geodesics are curved paths. Therefore, they cannot cross paths in spacetime.

4. How do null and timelike geodesics affect the geometry of spacetime?

Null and timelike geodesics are essential in defining the geometry of spacetime. They determine the shape and curvature of spacetime, as well as the behavior of light and matter within it. Without geodesics, we would not be able to accurately describe the structure of the universe.

5. What are some real-world applications of studying null and timelike geodesics?

Studying null and timelike geodesics is crucial in the field of general relativity, which is the modern theory of gravity. It helps us understand the behavior of light and matter in the presence of massive objects, such as stars and galaxies. This knowledge has practical applications in fields such as astrophysics, cosmology, and aerospace engineering.

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