Non-Singular Black Hole in Asymptotically Free Mimetic Gravity

Abstract

In General Relativity the works of Hawking and Penrose have shown that sin- gular solutions are in-avoidable. The most famous of which are the Schwarzschild and Kerr black hole solutions and Friedman Cosmological solution. In 2013, Chamseddine and Mukhanov have proposed a theory of gravity, with minimal modification where the scale factor is exchanged with a constrained scalar mode that plays the role of time coordinate. The modification is minimal in the sense that the new theory has only additional half degree of freedom corresponding to the presence of dark matter in the form of dust, and thus the name “mimetic gravity”. And in recent work, Chamseddine, Mukhanov and Russ, have obtained exact non-singular black hole (NSBH) and cosmological solutions, and this thesis addresses the Schwarzschild-like NSBH solution. In this work, we study in detail the properties of the Schwarzschild-like so- lution near time t=0 showing how the singularity is avoided. In addition, and more importantly we study motion near the horizon, where particles curiously oscillate in and out of the horizon. The study also explores the whole spectrum of dynamics for massive and massless particles alike, and new results arise in contrast to the regular Schwarzschild solution. We find a new class of bound orbits for such particles with non-zero angular momentum, orbiting across the internal and external regions of the non-singular black hole, all the while avoiding any physical contradictions. A particularly interesting result obtained was stable photon orbits in the inner region of space-time metric. And even though it was found that black hole evaporation yields a stable black hole remnant of minimal mass, this work studies dynamics in the limit where the mass is less than that of a minimal black hole remnant. And while this limit is not prohibited in the theory, it has a prominent feature: the absence of horizons, implying that any additional dynamical features are potentially observed.