Reflection symmetric exterior gravitational fields

What is it about?

Stars possess a reflection symmetry about the equatorial axis. Gravitational fields which are stationary and possess an axis of symmetry are in general thought to represent external fields of stars. In this research reflection symmetry for a star is proven to correspond to a simple relation that a specific gravitational variable that captures the essential physics of this class of models, the Ernst potential, obeys on solely the axis of symmetry. So once this variable is chosen in the prescribed way on the axis the rest of the solution is reflection symmetric about the equatorial plane.

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Why is it important?

An important physical property of a star, reflection symmetry, can be prescribed by choosing the right Ernst potential, a variable that captures the physics of the external field solution, on solely the axis of symmetry.

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