Bondi-Metzner-Sachs Group: Structure and Applications
The Poincaré group is the symmetry group of Special Relativity that leaves the line element in Minkovsky space invariant. For General Relativity, or in other words, for curved spacetimes, there is no such symmetry group. However, it is possible to find such a symmetry group when considering asymptotically flat spaces. Surprisingly, the symmetry group of asymptotically flat spaces is not simply the Poincaré group but an extension called the Bondi-Metzner-Sachs (BMS) group. In this course, we will discuss the structure of the BMS group and its application to some physical systems.
Lecturer
Date
17th September ~ 17th December, 2025
Location
Weekday | Time | Venue | Online | ID | Password |
---|---|---|---|---|---|
Wednesday | 10:40 - 12:15 | Shuangqing-B627 | ZOOM 08 | 787 662 9899 | BIMSA |
Wednesday | 14:20 - 16:05 | Shuangqing-B627 | ZOOM 08 | 787 662 9899 | BIMSA |
Prerequisite
Basics in group theory, special relativity, and general relativity
Syllabus
The Poincaré group
Conformal infinity
Bondi-Sachs coordinates and boundary
Bondi-Sachs metric
Bondi-Sachs solutions of the Einstein equations
The Bondi-Metzner-Sachs group
Bondi-Metzner-Sachs Lie algebra
Application to gravitational scattering
Application to waveforms
Conformal infinity
Bondi-Sachs coordinates and boundary
Bondi-Sachs metric
Bondi-Sachs solutions of the Einstein equations
The Bondi-Metzner-Sachs group
Bondi-Metzner-Sachs Lie algebra
Application to gravitational scattering
Application to waveforms
Reference
Alessio & Esposito, Int. J. Geom. Meth. Mod. Phys. 15 (2018) 02, 1830002; Alessio, arXiv:1801.01714 (2018); Esposito & Vitale, Symmetry 16 (2024) 7, 867; Mädler & Winicour, Scholarpedia 11 (2016) 33528; Boyle, Phys.Rev.D 93 (2016) 8, 084031
Audience
Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Alejandro Torres Orjuela obtained his Physics Bachelor's degree from the Free University of Berlin (Germany) and his Physics Master's degree, as well as his Bachelor's and Master's degrees in Mathematics from the Technical University of Berlin (Germany). Later, he moved to China to do his Ph.D. in Astrophysics at Peking University, where he worked with Prof. Xian Chen and Prof. Pau Amaro Seoane from 2017 to 2021. After his Ph.D., Alejandro moved to the TianQin Center at Sun Yat-Sen University in Zhuhai (China), where he worked for two years as a PostDoc in the Theoretical Study group led by Prof. Jianwei Mei. In 2023 and 2024, Alejandro took a position as a Post-Doctoral Fellow at the University of Hong Kong, where he was part of Prof. Lixin Jane Dai's group. In November 2024, Alejandro joined BIMSA as an Assistant Professor in the "General Relativity and Partial Differential Equations" group. Alejandro works on different aspects of gravitational wave astronomy with a particular focus on the effect of the environment on gravitational wave detection with two major goals: understanding how environmental effects impact - and potentially bias - detection and how these effects can be used to study the environment of the source. His research further includes gravitational wave sources with electromagnetic counterparts and their use as standard sirens to measure the expansion of the universe. Alejandro's studies involve different kinds of gravitational wave detectors across the spectrum, with a particular focus on space-based detectors TianQin and LISA in the mHz band, atom interferometry detectors in the dHz band, and kHz detectors LIGO-Virgo-KAGRA.