Entanglement Entropy: Helicity versus Spin

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish and their Von Neumann entropy has no dependence on the specific form of momentum distribution as long as it is isotropic.Comment: 3 pages, title changed, typos corrected, version to appear in Int. J. Quant. In

Shadows and photon spheres with spherical accretions in the four-dimensional Gauss-Bonnet black hole

We investigate the shadows and photon spheres of the four-dimensional Gauss-Bonnet black hole with the static and infalling spherical accretions. We show that for both cases, the shadow and photon sphere are always present. The radii of the shadow and photon sphere are independent of the profiles of accretion for a fixed Gauss-Bonnet constant, implying that the shadow is a signature of the spacetime geometry and it is hardly influenced by accretion in this case. Because of the Doppler effect, the shadow of the infalling accretion is found to be darker than that of the static one. We also investigate the effect of the Gauss-Bonnet constant on the shadow and photon sphere, and find that the larger the Gauss-Bonnet constant is, the smaller the radii of the shadow and photon sphere will be. In particular, the observed specific intensity increases with the increasing of the Gauss-Bonnet constant.Comment: published versio