From neutron stars to extremal black holes. The optical geometry approach

The optical geometries of black holes and relativistic stellar objects are discussed and compared. Gravitational trapping of relativistic particles in compact objects is treated in terms of the appearance of necks in the optical geometry. Indications are given for essentially two mechanisms which are responsible for the existence of necks and hence trapping. The two mechanisms correspond to properties of the equation of state of matter at high pressure. Phase transitions in the stellar interior can lead to trapping via one of the mechanisms which is due to a softening of the equation of state in some pressure region. It is also pointed out that there are similarities between the optical geometries of high-pressure uniform density stars and extremal Reissner-Nordstrom black holes.