Periodic Reporting for period 3 - Ampl2Einstein (Scattering Amplitudes for Gravitational Wave Theory)
Reporting period: 2024-01-01 to 2025-06-30
Ever since its historic detection eight years ago of gravitational waves from a coalescing pair of black holes, the LIGO-VIRGO-KAGRA collaboration has observed nearly a hundred events. Its catalog will continue to grow in years to come as refinements to the detectors increase sensitivity. The observations will offer a new window on the universe. They will answer long-standing questions about the inner structure of neutron stars. They will test Einstein's theory of gravity in regimes of strong fields. They may have a chance of detecting exotic objects that will shed light on current puzzles in cosmology.
The current detectors will pave the way for a newer generation of detectors to come on line in a decade's time: the Einstein Telescope (in Europe) and Cosmic Explorer (in the United States). A space-based detector (LISA) should join them later in the 2030s, opening a new frequency range to observation.
These observatories are all trying to find tiny signals buried under a background of random noise. The noise arises both from external sources such as seismic rumblings and from sources internal to the detectors. They are able to do so thanks to detailed theoretical knowledge of the shapes of the signals from different sources. Once they detect an event, the measurement of its properties, such as the masses of the two black holes in a coalescing binary, also come from comparing the detected signals with theoretical predictions of signals.
Expanding the catalog of theoretical shapes will allow for the detection of a wider class of events, or finding somewhat fainter events in known classes. More importantly, increasing the precision of theoretical shapes will improve the precision of the measurements of parameters of detected events. Until a few years ago, the required calculations were done within Einstein's theory of gravitation.
The aim of the current Project (and its peers) is to import modern methods of calculating quantum scattering amplitudes and to apply them to the predicting the required shapes for gravitational-wave observation and measurement. Quantum scattering amplitudes are important ingredients for making theoretical predictions for particle colliders, used to probe matter at very short distances. At first glance, these quantities have nothing to do with gravitational waves. It is possible, however, to assemble them and take a limit in which they provide shapes similar to those needed for gravitational-wave observatories. One of the Project's results thus far is Establishing a procedure for doing so. With this framework in hand, one can take advantage of the powerful methods developed in recent decades for calculating quantum amplitudes to obtain a calculation that is simpler than a direct one in Einstein's theory. The Project's overall aim is to develop these ideas more fully, to deepen our theoretical understanding of the theory, and also to contribute new theoretical shapes for gravitational-wave observations.
The current detectors will pave the way for a newer generation of detectors to come on line in a decade's time: the Einstein Telescope (in Europe) and Cosmic Explorer (in the United States). A space-based detector (LISA) should join them later in the 2030s, opening a new frequency range to observation.
These observatories are all trying to find tiny signals buried under a background of random noise. The noise arises both from external sources such as seismic rumblings and from sources internal to the detectors. They are able to do so thanks to detailed theoretical knowledge of the shapes of the signals from different sources. Once they detect an event, the measurement of its properties, such as the masses of the two black holes in a coalescing binary, also come from comparing the detected signals with theoretical predictions of signals.
Expanding the catalog of theoretical shapes will allow for the detection of a wider class of events, or finding somewhat fainter events in known classes. More importantly, increasing the precision of theoretical shapes will improve the precision of the measurements of parameters of detected events. Until a few years ago, the required calculations were done within Einstein's theory of gravitation.
The aim of the current Project (and its peers) is to import modern methods of calculating quantum scattering amplitudes and to apply them to the predicting the required shapes for gravitational-wave observation and measurement. Quantum scattering amplitudes are important ingredients for making theoretical predictions for particle colliders, used to probe matter at very short distances. At first glance, these quantities have nothing to do with gravitational waves. It is possible, however, to assemble them and take a limit in which they provide shapes similar to those needed for gravitational-wave observatories. One of the Project's results thus far is Establishing a procedure for doing so. With this framework in hand, one can take advantage of the powerful methods developed in recent decades for calculating quantum amplitudes to obtain a calculation that is simpler than a direct one in Einstein's theory. The Project's overall aim is to develop these ideas more fully, to deepen our theoretical understanding of the theory, and also to contribute new theoretical shapes for gravitational-wave observations.
The project has thus far focused on developing new techniques for computing the gravitational waves emitted by an interacting pair of bodies, such as black holes. Thanks to work the project members have done (and our colleagues elsewhere), the connection between our starting point (quantum scattering amplitudes) and the classical quantities we seek is now well understood when the black holes aren't spinning. Project members have also contributed to developing this link when the black holes are spinning, which is technically more complicated. In addition, the project is working on improving the amplitudes-based tools that are used by theorists in the course of their calculations.
The project has developed a new approach to obtaining the signals expected from two black holes passing by each other. It has also shown how to compute these signals more precisely, for the first time going beyond work done with older methods in the 1970s. We expect to extend this approach to orbiting black holes, and also to continue it to yet higher precision. The developments have already been useful to other theorists working on predictions for the gravitational-wave observatories, and will later be useful to the observers determining the precise nature of these binary systems from the observed gravitational waves.