Living Rev. Relativity, 16, (2013), 7 ,)6).' 2%6)%73 http://www.livingreviews.org/lrr-2013-7 doi:10.12942/lrr-2013-7 INRELATIVITY Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors Jonathan R. Gair Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, UK email: [email protected] http://www.ast.cam.ac.uk/~jgair Michele Vallisneri Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA email: [email protected] http://www.vallis.org Shane L. Larson Center for Interdisclipinary Research and Exploration in Astrophysics, Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA email: [email protected] John G. Baker Gravitational Astrophysics Lab, NASA Goddard Space Flight Center, 8800 Greenbelt Rd., Greenbelt, MD 20771, USA email: [email protected] Accepted: 19 August 2013 Published: 12 September 2013 Abstract We review the tests of general relativity that will become possible with space-based gravita- tional-wave detectors operating in the ∼ 10{5 { 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational- wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of as- trophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger. Keywords: general relativity, gravitational waves, LISA, eLISA, data analysis, black holes, gravitation This review is licensed under a Creative Commons Attribution-Non-Commercial 3.0 Germany License. http://creativecommons.org/licenses/by-nc/3.0/de/ Imprint / Terms of Use Living Reviews in Relativity is a peer reviewed open access journal published by the Max Planck Institute for Gravitational Physics, Am M¨uhlenberg 1, 14476 Potsdam, Germany. ISSN 1433-8351. This review is licensed under a Creative Commons Attribution-Non-Commercial 3.0 Germany License: http://creativecommons.org/licenses/by-nc/3.0/de/. Figures that have been pre- viously published elsewhere may not be reproduced without consent of the original copyright holders. Because a Living Reviews article can evolve over time, we recommend to cite the article as follows: Jonathan R. Gair, Michele Vallisneri, Shane L. Larson and John G. Baker, \Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors", Living Rev. Relativity, 16, (2013), 7. URL (accessed <date>): http://www.livingreviews.org/lrr-2013-7 The date given as <date> then uniquely identifies the version of the article you are referring to. Article Revisions Living Reviews supports two ways of keeping its articles up-to-date: Fast-track revision. A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here. Major update. 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Contents 1 Introduction 5 2 The Theory of Gravitation7 2.1 Will's \standard model" of gravitational theories................... 7 2.2 Alternative theories ................................... 10 2.2.1 Scalar-tensor theories .............................. 10 2.2.2 Vector-tensor theories .............................. 10 2.2.3 Scalar-vector-tensor theories ........................... 11 2.2.4 Modified-action theories ............................. 12 2.2.5 Massive-graviton theories ............................ 15 2.2.6 Bimetric theories of gravity ........................... 16 2.3 The black-hole paradigm ................................. 17 3 Space-Based Missions to Detect Gravitational Waves 19 3.1 The classic LISA architecture .............................. 19 3.2 LISA-like observatories .................................. 21 3.3 Mid-frequency space-based observatories ........................ 22 4 Summary of Low-Frequency Gravitational-Wave Sources 24 4.1 Massive black-hole coalescences ............................. 27 4.2 Extreme-mass-ratio inspirals ............................... 30 4.3 Galactic binaries ..................................... 33 5 Gravitational-Wave Tests of Gravitational Physics 35 5.1 The \classic tests" of general relativity with gravitational waves . 37 5.1.1 Tests of gravitational-wave polarization .................... 38 5.1.2 Tests of gravitational-wave propagation .................... 40 5.1.3 The quadrupole formula and loss of energy to gravitational waves . 42 5.2 Tests of general relativity with phenomenological inspiral template families . 45 5.2.1 Modifying the PN phasing coefficients ..................... 45 5.2.2 The parameterized post-Einstein framework . 46 5.2.3 Other approaches ................................. 49 5.3 Beyond the binary inspiral ................................ 49 6 Tests of the Nature and Structure of Black Holes 51 6.1 Current observational status ............................... 51 6.2 Tests of black-hole structure using EMRIs ....................... 52 6.2.1 Testing the \no-hair" property ......................... 52 6.2.2 Probing the nature of the central object .................... 55 6.2.3 Astrophysical perturbations: the influence of matter . 57 6.2.4 Astrophysical perturbations: distant objects . 60 6.2.5 Properties of the phase space of orbits ..................... 60 6.2.6 Black holes in alternative theories ....................... 63 6.2.7 Interpretation of observations .......................... 68 6.2.8 Extreme-mass-ratio bursts ............................ 69 6.3 Tests of black-hole structure using ringdown radiation: black-hole spectroscopy . 70 6.4 Prospects from gravitational-wave and other observations . 73 7 Discussion 76 References 78 List of Tables 1 Hierarchy of formulations of the equivalence principle. ................ 8 2 Leading-order effects of alternative theories of gravity, as represented intheppE framework. ........................................ 47 3 Accuracy with which a LISA observation could determine the multipole moments of a spacetime decreases as more multipoles are included in the model. 54 Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors 5 1 Introduction The first direct detection of gravitational waves (GWs), widely expected in the mid 2010swith advanced ground-based interferometers [219, 2], will represent the culmination of a fifty-year exper- imental quest [124]. Soon thereafter, newly plentiful GW observations will begin to shed light on the structure, populations, and astrophysics of mostly dark, highly relativistic objects such as black holes and neutron stars. In the low-frequency band that will be targeted by space-based detectors (roughly 10{5 to 1 Hz), GW observations will provide a census of the massive black-hole binaries at the center of galaxies, and characterize their merger histories; probe the galactic population of binaries that include highly evolved, degenerate stars; study the stellar-mass objects that spiral into the central black holes in galactic nuclei; and possibly detect stochastic GW backgrounds from the dynamical evolution of the very early universe. Thus, there are very strong astrophysical motivations to observe the universe in GWs, especially because the systems and phenomena that can be observed in this fashion are largely orthogonal to those accessible to traditional electromagnetic (EM) and astroparticle astronomy. The promise of GWs appears just as great for fundamental physics. Einstein's theory of gravity, general relativity (GR), has been confirmed by extensive experimental tests; but these have largely been confined to the solar system, where gravity is well approximated by Newtonian gravity with small corrections. A few tests, based on observations of binary compact-object systems, have confirmed the weakest (leading-order) effects of GW generation. By contrast, observation of strong GWs will providethe first direct observational probe of the dynamical, strong-field regime of GR, where the nature and behavior of gravity can be significantly different from the Newtonian picture. GWsare prima facie the perfect probe to investigate gravitation, since they originate directly from the bulk motion of gravitating matter, relieving the need to understand and model the physics of other intermediate messengers, typically photons from stellar surfaces or black-hole surroundings. Already today we can rely on a very sophisticated understanding of the analytical and numerical techniques required to model GW sources and their GW emission, including the post-Newtonian expansion [84, 190], black-hole perturbation theory [119], numerical relativity for vacuum space- times [368], spacetimes