How can distortion of space be measured?

[truedeity]

I want to find out what the minimum distortion (or curving) of space should be to prevent light from escaping that distortion.

 

http://physics.stackexchange.com/questions/8477/why-cant-light-escape-from-a-classical-black-hole

 

I am not aware of any way of measuring the "amount" of distortion a mass imposes on space.

 

Can anyone shed some light? If so, would you be able to tell me the minimum amount of distortion needed to capture photons such as in the case of an event horizon.

[ajb]

One way to detect space-time curvature is to examine geodesics and in particular null geodesics; that is the paths that light rays take. However, this is not enough information to actually completely recover the geometry of space-time, you will get at best a class of projective connections and there will be some ambiguities in constricting the metric without some further input.

 

Now, you have not said at all what you mean by curvature. The curvature tensors are tensors and so the components will take different values in different coordinate systems. One needs a scalar measure and often one can use the Kretschmann scalar or one of its relatives. There are some further technicalities about what you can learn from the Kretschmann scalar, for example it is not always the quantity that detects singularities (there are problems when gravitational radiation is present).

 

What you have described as 'capturing photons' is exactly an event horizon. Usually these are associated with black holes, but isolated horizons and so on are discussed in the literature. This is getting more and more technical and outside of my area of expertise.

Edited July 19, 2015 by ajb

[swansont]

One way to detect space-time curvature is to examine geodesics and in particular null geodesics; that is the paths that light rays take.

 

 

Geodesics would include the paths of planets and satellites, e.g. orbits about a star or planet.