The usual definition of asymptotic flatness at spatial infinity requires that the flat metric be approached at a particular rate. However, slower rates of fall off are compatible with well-defined evolution under the Einstein vacuum equations. Since initial data must satisfy the constraint equations, we want to know if we can specify the fall off rate that we want and still have...
I will discuss ongoing work on the construction of asymptotically flat vacuum initial data sets in General Relativity via the conformal method. My collaborators and I have demonstrated that certain asymptotic structures may be prescribed a priori through the method's seed data, including the ADM momentum components, the leading- and next-to-leading-order decay rates, and anisotropy in the...
GR, while one of the most successful and well-tested theories to date, is expected to receive corrections at high energies—through higher-curvature terms, additional degrees of freedom, or both. Given the vast landscape of possible extensions, how can we test them in a systematic way?
In this talk, I will present a general framework for interpreting deviations in gravitational wave data,...
Binary black holes can interact with surrounding matter, producing unique electromagnetic signatures and influencing their long-term evolution. Numerical simulations are crucial to understand the nonlinear behavior of gas and particles moving on this dynamical spacetime. We present a general binary black hole metric approximation valid at all binary separations for all practical purposes. We...
I present a new formulation of General Relativity. The action is quadratic in the curvature and the equations of motion involve the divergence of the Riemann tensor. I show that this formulation is well posed and is equivalent to the Einstein equations. Overall, this formulation provides a surprising and peculiar new point of view on the Einstein equations.
I will present a detailed introduction to my Python package, OGRePy: An Object-Oriented General Relativity Package for Python, which will be of great interest to anyone doing research in general relativity. I will demonstrate the package's usage and features, including its ability to calculate arbitrary tensor formulas involving any combination of...
The horizon of a black hole, the "surface of no return," is characterized by its rotation frequency $\Omega_H$ and surface gravity $\kappa$. A striking signature is that any infalling object appears to orbit at $\Omega_H$ due to frame dragging, while its emitted signals decay exponentially at a rate set by $\kappa$ as a consequence of gravitational redshift. Recent theoretical work predicts...
