Spherical symmetry in the kilonova AT2017gfo/GW170817.

The mergers of neutron stars expel a heavy-element enriched fireball that can be observed as a kilonova1-4. The kilonova's geometry is a key diagnostic of the merger and is dictated by the properties of ultra-dense matter and the energetics of the collapse to a black hole. Current hydrodynamical merger models typically show aspherical ejecta5-7. Previously, Sr+ was identified in the spectrum8 of the only well-studied kilonova9-11 AT2017gfo12, associated with the gravitational wave event GW170817. Here we combine the strong Sr+ P Cygni absorption-emission spectral feature and the blackbody nature of kilonova spectrum to determine that the kilonova is highly spherical at early epochs. Line shape analysis combined with the known inclination angle of the source13 also show the same sphericity independently. We conclude that energy injection by radioactive decay is insufficient to make the ejecta spherical. A magnetar wind or jet from the black-hole disk could inject enough energy to induce a more spherical distribution in the overall ejecta; however, an additional process seems necessary to make the element distribution uniform.

Divergent reflections around the photon sphere of a black hole.

From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a perturbed analytical solution to the null-geodesic equation of the Schwarzschild black hole we will reaffirm how each additional orbit is a factor [Formula: see text] closer to the black hole's optical edge. Consequently, the surface of the black hole and any background light will be mirrored infinitely in exponentially thinner slices around the last photon orbit. Furthermore, the introduced formalism proves how the entire trajectories of light in the strong field limit is prescribed by a diverging and a converging exponential. Lastly, the existence of the exponential family is generalized to the equatorial plane of the Kerr black hole with the exponentials dependence on spin derived. Thereby, proving that the distance between subsequent images increases and decreases for respectively retrograde and prograde images. In the limit of an extremely rotating Kerr black hole no logarithmic divergence exists for prograde trajectories.