Phase transition of spacetime: particles as black holes in anti-de Sitter space
In this work, we re-examined the ancient complex metric in the recent quantum picture of black holes as Bose-Einstein condensates of gravitons. Both black holes and particles can be described by the complex Kerr-Newman metric in a 6-D complex space, which appears as a 4-D spacetime for a real or imaginary observer because of the barrier of the horizon. As two kind of complex black holes, particle and black hole are complex conjugated and can convert into each other through a phase transition. From the view of an observer in 3-D real space, an elementary particle with spin appears as an imaginary black hole in an anti-de Sitter space. The self-gravitational interaction of a particle as an imaginary black hole makes it obtain its wave-like nature in 4-D spacetime.