FORMALISM FOR NUMERICAL RELATIVISTIC SIMULATIONS OF CHARGED BLACK HOLES NEAR EXTREMAL LIMIT: PUNCTURE GAUGE TECHNIQUE

Abstract

The Weak Cosmic Censorship Conjecture states that a spacetime singularity is always hidden inside of a black hole’s event horizon. However, this conjecture is violated for charged black holes that exceed the extremal limit, |Q|/M = 1. To theoretically test the credibility of the weak cosmic censorship conjecture, we can utilize a simulation of a charged black hole that is near the extremal limit and try to exceed the extremal limit by using various tests that could impart more charge on this near-extremal black hole such that its charge by mass ratio increases. In this thesis, we develop the formalism to simulate charged black holes that are near the extremal limit using the puncture gauge technique. We transform the Reissner-Nordstr¨om metric to a new coordinate system containing a radial coordinate that is modified from a quasi-isotropic radial coordinate to avoid difficulties that arise in the simulation. Using this, we derive the initial conditions for the simulation of a nonrotating, charged black hole and verify it using the Hamiltonian and the momentum constraints.