We study the Lie group structure of asymptotic symmetry groups in General Relativity from viewpoint infinite-dimensional geometry. To this end, we review geometric definition simplicity and emptiness due to Penrose coordinate-wise flatness Bondi et al. Then construct Bondi--Metzner--Sachs (BMS) discuss its theoretic properties. find that BMS is regular sense Milnor, but not real analytic. This ...

In fundamental physics, the first part of the twentieth century has been characterized by two important steps towards a major conceptual revolution: quantum mechanics and general relativity. Each of these two theories has profoundly modified some key part of our understanding of the physical world. Quantum mechanics has changed what we mean by matter and by causality and general relativity has ...

General relativity in three spacetime dimensions is used to explore three approaches to the “problem of time” in quantum gravity: the internal Schrödinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt equation, and covariant canonical quantization with “evolving constants of motion.” (To appear in Proc. of the Lanczos Centenary Conference, Raleigh, NC, December 1...

We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair Schwarzschild-de Sitter spacetimes with different cosmological constants black hole masses written spatially-flat Gullstrand-Painlev\'e (GP) coordinates is solution self-accelerating branch MTBG, while it cannot be normal branch. then illustrate how can become compatib...

In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in “non-renormalizable” theories, using only the degrees of freedom and interactions appropriate for those energies. Whether or not general relativity is truly fundamental, at low energies it is automatically described as a quantum effective field th...

I argue that, contrary to the recent claims of physicists and philosophers of physics, general relativity requires no interpretation in any substantive sense of the term. I canvass the common reasons given in favor of the alleged need for an interpretation, including the difficulty in coming to grips with the physical significance of diffeomorphism invariance and of singular structure, and the ...