The likely detection of gravitational waves from astrophysical sources will open a new window for astronomy and provide new tests of Einstein's theory of general relativity. Interpreting the observations and advancing this new field will require accurate theoretical predictions for the wave signal from a given source. This project will make use of a method known as Direct Integration of the Relaxed Einstein Equations (DIRE), that has been developed by the PI and his students at Washington University, which solves Einstein's equations systematically in a procedure known as the post-Newtonian approximation (appropriate for systems where the velocities are small compared to the speed of light). Using this method, it will be possible to study the detailed motion and radiation from the inspiral of compact binary systems (double star systems containing neutron stars or black holes) to a high degree of accuracy. Post-Newtonian methods will also be used to study unusual aspects of the curved spacetime surrounding rotating black holes, related to the existence of the so-called "Carter" constant of the motion, and to calculate the recoil velocity experienced by black holes formed from compact binary merger. Ways to use gravitational-wave data to test alternative theories of gravity in new regimes and to measure astrophysical and cosmological parameters will also be studied. In particular, a detailed analysis of gravitational radiation from compact binary inspiral in a class of "scalar-tensor" alternatives to general relativity will be carried out, together with a study of data analysis strategies for placing the best possible bound on this class of theories. The possibility of testing general relativity in the strong-field vicinity of the massive black hole in the center of our galaxy using future adaptive optics infrared interferometry will be analyzed by studying orbital perturbations of stars in close orbits near the hole caused by other stars in the central region, by a possible distribution of dark matter, and by tidal distortions of the stars. This will involve a mixture of analytical post-Newtonian calculations and numerical N- body simulations.
The work on equations of motion, gravitational waveforms and analysis of gravitational-wave data will impact the emerging field of gravitational-wave astronomy. The work on recoil velocities may contribute important insights that could impact astrophysical modeling of the growth of massive black holes in galaxies, as well as the interface between post-Newtonian theory and numerical relativity. The work on testing general relativity near the galactic center black hole could impact the development of advanced instrumentation for observational infrared astronomy. Education and training of students will be integrated into the research program.
This project investigated potential ways of testing and verifying Einstein's general theory of relativity by observing gravitational waves, or by observing the behavior of objects very close to black holes. Although general relativity has been well tested in the weak-gravity regime of the solar system and some binary star systems, it has not been well tested in the regime of dynamical waves or of black holes. General relativity predicts the existence of gravitational waves, and an array of Earth-based detectors may soon make regular detections of these waves. Alternative theories of gravity may predict waves with rather different characteristics from those predicted by Einstein's theory, and this project studied these differences in two specific classes of alternatives: scalar-tensor theories (generalizations of the classic Brans-Dicke theory), and theories that violate Lorentz invariance. We analyzed the constraints that could be placed on such theories using detailed analyses of gravitational-wave signals from inspiralling compact binary systems (binary black holes or neutron stars), that should be detected in the near future. We also calculated the equations of motion and the tensor gravitational radiation for compact binary systems (black hole or neutron stars) in a general class of scalar-tensor theories using the post-Newtonian formalism, which provides an approximation to such theories in an expansion in v/c, where v is a characteristic velocity of the binary system and c is the speed of light. The results were accurate to the order of (v/c)^5 for the motion and (v/c)^4 for the waves. We studied the behavior of matter very close to massive black holes, such as the one (SgrA*) at the center of our galaxy, as a way to test whether the spacetime geometry for such objects is really that predicted by general relativity. We continued to analyze the possibility that observations of the orbits of stars very close to SgrA* could provide such a test. We showed, using both analytic and numerical calculations that this would be feasible in spite of the possible perturbing effect of other stars and small black holes that might reside in a cluster close to the central black hole. We also studied of the effects of a possible distribution of dark matter near the central black hole using a fully general relativistic approach, and found significant differences in the dark matter density profile close to the black hole compared to earlier work that did not fully incorporate general relativity. We found that the gravitational effect of such dark matter on the orbits of stars targeted for testing the black hole geometry would be negligible. We investigated the proper way to take general relativistic effects into account in calculations of the dynamics of many-body systems, such as clusters of stars around a central black hole, or three-body systems where a third body orbits a close binary star system with significant relativistic effects. We argued that such effects had not been fully incorporated into earlier investigations, and that they could lead to potentially significant changes in the long-term evolutions of such dynamical systems.
