Chapter07.pdfCan Killing Vectors Derive the Schwarzschild Metric?

In summary, maximally symmetric subspaces are subspaces within a larger space that possess the maximum amount of symmetry. They are important in science as they allow for the study of fundamental principles and laws of nature. Examples of maximally symmetric subspaces include spheres, cubes, and regular polygons. In physics, they are used to describe the symmetries of physical systems, particularly in the study of particle physics. These subspaces are closely related to symmetry groups, which are mathematical structures that describe the symmetries of a given space or object.
  • #1
Ray
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"Is it possible to derive the Schwarzschild metric from Killing vectors, thus saving all that work with the Ricci tensor etc."
 
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  • #2
Given Killing vectors may not determine the metric uniquely. For example, in a specific static case with three Killing vectors on S^2 one still needs the weak field limit imposed on it to recover the metric precisely.

cf Chapt. 7 of
http://pancake.uchicago.edu/~carroll/notes/
 
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FAQ: Chapter07.pdfCan Killing Vectors Derive the Schwarzschild Metric?

What are maximally symmetric subspaces?

Maximally symmetric subspaces are subspaces within a larger space that possess the maximum amount of symmetry. This means that any transformation or operation done within the subspace will not change its appearance or properties.

What are some examples of maximally symmetric subspaces?

Some examples of maximally symmetric subspaces include spheres, cubes, and regular polygons. These shapes have symmetries that allow them to be rotated, reflected, or translated without changing their appearance.

Why are maximally symmetric subspaces important in science?

Maximally symmetric subspaces are important in science because they allow for the study of fundamental principles and laws of nature. By studying the symmetries within these subspaces, scientists can gain a deeper understanding of how the universe works.

How are maximally symmetric subspaces used in physics?

In physics, maximally symmetric subspaces are used to describe the symmetries of physical systems. This is particularly important in the study of particle physics, where symmetries play a crucial role in understanding the fundamental forces and particles of the universe.

What is the relationship between maximally symmetric subspaces and symmetry groups?

Maximally symmetric subspaces are closely related to symmetry groups, which are mathematical structures that describe the symmetries of a given space or object. The symmetries within a maximally symmetric subspace can be described by a specific symmetry group, which helps to categorize and understand its properties.

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