Definition of polar and axial gravitational radiation from neutron star oscillations exhibits certain characteristic frequencies which are independent of the processes giving rise to these oscillations. These “quasi-normal” frequencies are directly connected to the parameters of neutron star (mass, charge and angular momentum) and are expected to be inside the bandwidth of the constructed gravitational wave detectors.

gravitational radiation from neutron star oscillations exhibits certain characteristic frequencies which are independent of the processes giving rise to these oscillations. These “quasi-normal” frequencies are directly connected to the parameters of neutron star (mass, charge and angular momentum) and are expected to be inside the bandwidth of the constructed gravitational wave detectors.

There are two classes of vector spherical harmonics (polar and axial) which are build out of combinations of the Levi-Civita volume form and the gradient operator acting on the scalar spherical harmonics. The difference between the two families is their parity. Under the parity operator π (under the angular transformation θ→ π − θ, ϕ → π + ϕ), a spherical harmonic with index ℓ transforms as (−1)ℓ, the polar class of perturbations transform under parity in the same way, as (−1)ℓ, and the axial perturbations as (−1)ℓ+1. Finally, since we are dealing with spherically symmetric space-times the solution will be independent of m, thus this subscript can be omitted.

There are two classes of vector spherical harmonics (polar and axial) which are build out of combinations of the Levi-Civita volume form and the gradient operator acting on the scalar spherical harmonics. The difference between the two families is their parity. Under the parity operator π (under the angular transformation θ→ π − θ, ϕ → π + ϕ), a spherical harmonic with index ℓ transforms as (−1)ℓ, the polar class of perturbations transform under parity in the same way, as (−1)ℓ, and the axial perturbations as (−1)ℓ+1. Finally, since we are dealing with spherically symmetric space-times the solution will be independent of m, thus this subscript can be omitted.