RESUMO
Fine-tuning generic but smooth spherically symmetric initial data for general relativity to the threshold of dynamical black hole formation creates arbitrarily large curvatures, mediated by a universal self-similar solution that acts as an intermediate attractor. For vacuum gravitational waves, however, these critical phenomena have been elusive. We present, for the first time, excellent agreement among three independent numerical simulations of this collapse. Surprisingly, we find no universality, and observe approximate self-similarity for some families of initial data but not for others.
RESUMO
We report on a numerical study of gravitational waves undergoing gravitational collapse due to their self-interaction. We consider several families of asymptotically flat initial data which, similar to the well-known Choptuik's discovery, can be fine-tuned between dispersal into empty space and collapse into a black hole. We find that near-critical spacetimes exhibit behavior similar to scalar-field collapse: For different families of initial data, we observe universal "echoes" in the form of irregularly repeating, approximate, scaled copies of the same piece of spacetime.
RESUMO
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.
