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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - MoGEs (Modelling of Generic Extreme mass-ratio inspirals)

Teaser

Summary

\"The detection of gravitation waves (GWs) has opened up a new avenue for learning about the universe an its contents. Observable GWs primarily originate from the distant mergers of compact objects such as black holes or neutron stars. Current GW observing facilities (LIGO and Virgo) are sensitive mostly mergers of objects with similar masses. Future facilities --- such as ESA\'s space-based GW observatory, LISA, and the next generation of ground-based observatories, Einstein Telescope and Cosmic Explorer --- will be sensitive to the mergers of compact objects with greatly different masses.

One class of such mergers are called Extrene Mass Ratio Inspirals or EMRIs. EMRIs consist of a compact object between 1 and 50 times as massive as the sun mergering with a supermassive black hole in the center of a galaxy. Detection of one such an event with LISA will allow us to determine many of the properties of the host supermassive black hole to exquist detail shining light on many of the mysteries that surround these behemoths and the star clusters that surround them, as well as sensitively probe Nature for deviations from our current best theory of gravity, Einstein\'s General Relativity.

EMRIs are detectable at great distances, billions of lightyears away. By detecting many we can map out the accelerated expansion of the universe independently from observations using electromagnetic waves such as light. This will help shed light on the mysteries of dark energy and matter.

The detection and analysis of GW signals requires accurate theoretical models of the source systems. The scientific community has been very successful in modelling compact binary mergers with similar masses, such as detected by LIGO and Virgo. Systems with very small mass-ratios, such as EMRIs, however are well beyond the reach for current modelling methods. The MoGEs project aims to improve the modelling of small mass-ratio binaries using the Gravitation Self-Force (GSF) formalism which describes the motion of the object as an perturbative series in the mass-ratio.

The main objectives of the MoGEs project was tackling longstanding problems surrounding applying the GSF formalism to rotating black holes, and using the obtained results to improve the highly successful \"\"Effective One-body\"\" model for compact mergers currently used by LIGO and Virgo.\"

Work performed

\"The core work of the MoGEs project consisted of two main branches.

The first branch focussed on calculating the correction to the motion of a small body on a general orbit around a spinning black hole. This correction is encoded in a quantity known as the \"\"gravitational self-force\"\" or GSF. In a computational tour-de-force, the MoGEs project has succeeded in the first calculation of the GSF for a completely generic orbit (i.e. an orbit not restrict by additional simplifying restriction). These landmark results were published in an article in Physical Review D, which was highlighted as an \"\"Editors\' Suggestion\"\".

The computer code used for these calculations will be integrated in the publically available Black Hole Perturbation Toolkit (bhptoolkit.org).

The second branch of the project was aimed at using GSF results to improve the \"\"Effective One-body\"\" (or EOB) models used black hole mergers observed by LIGO and Virgo. Previous attempts to do so were hindered by the appearance of spurious infinities. MoGEs has developed an alternative formulation of the EOB formalism that avoids such divergences. The first tentative results were announced at the 21st Capra meeting on Radiation Reaction in General Relativity (hosted by the fellow at the Max Planck Institute for Gravitational Physics in Potsdam, Germany).

In addition to these two main branches of inquiry, MoGEs has pursued several investigations into various aspects of the small mass-ratio limit of binary dynamics.

The first was an efficient scheme for integrating the GSF to obtain the inspiral of an EMRI and the resulting gravitational wave template. This scheme was up to a million times faster than previous schemes for doing so. This is important because to analyse a gravitational wave signal it needs to be compared to many billions of theoretical templates. This scheme was published in the journal Classical and Quantum Gravity, and highlighted in their only magazine CQG+.

MoGEs has further made important progress in understanding the dynamics of EMRIs when the smaller secondary black hole is also spinning. This included the first calculation of the correction to the motion of the secondary spin when the secondary object is restrict to a circular equatorial orbit (published in Physical Review D), and a complete analytic determination of the zeroth order approximation of the motion of the secondary spin for generic orbits (article in preparation).\"

Final results

The work done by MoGEs represents a major step forward in the understanding of the dynamics of inspiralling black holes, specifically in the regime were one of the black holes is much smaller than the other. Now, our modelling of these systems is no longer restricted to special systems constrained by simplifying assumptions, but can be applied to any EMRI.

This is a key step towards modelling the types of gravitational wave sources that will be observed by Laser Interferometer Space Antennae (LISA), a space-based gravitational wave obser due for launch in in the 2030s. Much work remains to be done. The methods developed by MoGEs need to be further optimized to be used in data analysis applications, and needed to be generalized to the next order in perturbation theory to achieve the required accuracy.

However, it is clear that the contributions from MoGEs will serve as cornerstone for the interpretation of LISA observations, which will lead to increased understanding of the mysteries of our universe, including the exact nature of black holes, gravity, and the formation and evolution of galaxies.