\ethThe symbol \eth is used in mathematics and physics, particularly in the field of differential geometry and general relativity. It represents the eth operator, which is a differential operator used in the context of spin-weighted spherical harmonics. The eth operator is used to describe fields on the sphere and is particularly useful in the study of gravitational waves and other phenomena in curved spacetime.
Application of the eth operator on a spherical harmonic function Y_{lm}.
\eth Y_{lm} = \sqrt{(l-m)(l+m+1)} Y_{l,m+1}Using the eth operator in a differential equation context.
\eth \Psi = 0Second application of the eth operator on a function \Phi, often seen in eigenvalue problems.
\eth^2 \Phi = \lambda \Phi