Studies of Singularities, Black Holes, and Gravitational Radiation

Oakland University, Rochester MI

Investigators

Abstract

This project will study two aspects of gravity: gravitational collapse and gravitational radiation. When an object's gravity becomes strong enough to trap light, the object becomes a black hole. Inside the black hole the object continues to become smaller and smaller under the influence of its own gravity until it becomes a point with infinite density and infinite gravitational field called a singularity. This project involves working out the properties of the singularities formed in gravitational collapse, and in particular the forces felt by any observer who approaches the singularity. Just as the electric currents in a radio transmitter make radio waves, so moving masses make gravitational waves. One of the most exciting recent developments in physics is the direct detection of these gravitational waves using huge laser interferometers as the detectors. One interesting aspect of gravitational radiation is something called gravitational wave memory: even after the wave has passed, there is a permanent change in the gravitational wave detector. This project will study the causes and properties of this gravitational wave memory. Gravitational collapse results in the formation of black holes and spacetime singularities, and the emission of gravitational radiation. This project will study all of these aspects of gravitational collapse, and in particular will concentrate on the approach to the singularity, gravitational wave memory, and critical behavior at the threshold of black hole formation. The project will study the formation of small scale structure in the approach to the generic spacelike singularity. In addition, simulations will be done of the collapse of vacuum, asymptotically flat spacetimes in order to test the conjecture that both strong spacelike singularities and weak null singularities form in this case. In previous work, this group developed a treatment of gravitational wave memory that uses a perturbative approach in which the Weyl tensor is the basic variable and thus has manifest gauge invariance in first order perturbation theory. This project will extend this approach to treat the memory of gravitational radiation (Christodoulou memory) using second order perturbation theory. Simulations will be performed of critical gravitational collapse to develop a better understanding of the Choptuik critical solution, in particular the structure inside the horizon of the slightly supercritical case, and the spacetime near the Cauchy horizon for the critical solution. Einstein-Aether theory will be studied to see whether some of its black hole solutions are unstable. In addition an initial value formulation of this theory will be developed for the general case of no symmetry. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.