Robert Penna's Research
The classical theory of gravity is Einstein's theory of general relativity. This theory has led to all kinds of puzzles.
General relativity describes black holes, which are regions of spacetime where the curvature of spacetime is so extreme that not even light can escape. At the center of every black hole is a singularity, where the curvature of spacetime becomes infinite. The known laws of physics break down at black hole singularities. Our galaxy has millions of black holes, so there are millions of real places in our galaxy where the known laws of physics break down and new ideas are needed.
General relativity also describes gravitational waves, which are ripples in spacetime caused by the motion of massive objects. Recently, gravitational waves were observed experimentally for the first time by the LIGO experiment. Quantum mechanically, a gravitational wave is a large collection of particles called gravitons. The low energy scattering of gravitons is described by a quantum field theory. But at high energies (above the Planck scale), this quantum field theory breaks down. It is not known how to describe gravitons at these very high energies.
Finally, general relativity describes cosmology, which means the large-scale structure of spacetime, on timescales comparable to the age of the universe itself. Our universe is expanding at an accelerating rate. In such a universe, there are basic conceptual problems that make it unclear how to even define quantum mechanical observables. Roughly, this is because it is difficult to define an isolated observer, because an observer will only become isolated from the gravitational field in the distant future.
A powerful tool to understand these puzzles is symmetry. For example, there is a huge symmetry called the BMS group which governs the interactions of black holes and gravitational waves. There is a hidden symmetry called the Geroch group which makes it possible to solve two dimensional models of graviton scattering exactly. One of the major themes of the gravity research at SUNY Polytechnic is to use these symmetries to shed some light on the basic puzzles described above.
