Abstract
The Laser Interferometer Space Antenna1, LISA, will detect gravitational wave signals from extreme mass-ratio inspirals2, where a stellar mass compact object orbits a supermassive black hole and eventually plunges into it. Here we report on LISA’s capability to detect whether the smaller compact object in an extreme mass-ratio inspiral is endowed with a scalar field3,4, and to measure its scalar charge—a dimensionless quantity that acts as a measure of how much scalar field the object carries. By direct comparison of signals, we show that LISA will be able to detect and measure the scalar charge with an accuracy of the order of per cent, which is an unprecedented level of precision. This result is independent of the origin of the scalar field and of the structure and other properties of the small compact object, so it can be seen as a generic assessment of LISA’s capabilities to detect new fundamental fields.
This is a preview of subscription content, access via your institution
Relevant articles
Open Access articles citing this article.
-
New horizons for fundamental physics with LISA
Living Reviews in Relativity Open Access 30 June 2022
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 per month
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$119.00 per year
only $9.92 per issue
Rent or buy this article
Get just this article for as long as you need it
$39.95
Prices may be subject to local taxes which are calculated during checkout




Data availability
The data that support the plots within this paper and the other findings of this study are available from the corresponding author upon request.
Code availability
The codes used to create the plots within this paper and support the other findings of this study are available from the corresponding author upon request. Flux calculations have been performed using the numerical routines of the Black Hole Perturbation Toolkit (http://bhptoolkit.org).
References
Amaro-Seoane, P. et al. Laser Interferometer Space Antenna. Preprint at https://arxiv.org/abs/1702.00786 (2017).
Babak, S. et al. Science with the space-based interferometer LISA. V: extreme mass-ratio inspirals. Phys. Rev. D 95, 103012 (2017).
Berti, E. et al. Testing general relativity with present and future astrophysical observations. Class. Quantum Gravity 32, 243001 (2015).
Barausse, E. et al. Prospects for fundamental physics with LISA. Gen. Relativ. Gravit. 52, 81 (2020).
Copeland, E. J., Sami, M. & Tsujikawa, S. Dynamics of dark energy. Int. J. Mod. Phys. D 15, 1753–1936 (2006).
Essig, R. et al. Working group report: new light weakly coupled particles. In Proc. Community Summer Study 2013: Snowmass on the Mississippi (eds Bernstein, R. H. et al.) 1311.0029 (2013).
Hui, L., Ostriker, J. P., Tremaine, S. & Witten, E. Ultralight scalars as cosmological dark matter. Phys. Rev. D 95, 043541 (2017).
Barack, L. et al. Black holes, gravitational waves and fundamental physics: a roadmap. Class. Quantum Gravity 36, 143001 (2019).
Damour, T. & Esposito-Farese, G. Nonperturbative strong field effects in tensor—scalar theories of gravitation. Phys. Rev. Lett. 70, 2220–2223 (1993).
Kanti, P., Mavromatos, N. E., Rizos, J., Tamvakis, K. & Winstanley, E. Dilatonic black holes in higher curvature string gravity. Phys. Rev. D 54, 5049–5058 (1996).
Yunes, N. & Stein, L. C. Non-spinning black holes in alternative theories of gravity. Phys. Rev. D 83, 104002 (2011).
Sotiriou, T. P. & Zhou, S.-Y. Black hole hair in generalized scalar–tensor gravity. Phys. Rev. Lett. 112, 251102 (2014).
Zel'dovich, Y. B. Generation of waves by a rotating body. JETP Lett. 14, 180 (1971).
Brito, R., Cardoso, V. & Pani, P. Superradiance: New Frontiers in Black Hole Physics Vol. 971 (Springer, 2020).
Arvanitaki, A., Dimopoulos, S., Dubovsky, S., Kaloper, N. & March-Russell, J. String axiverse. Phys. Rev. D 81, 123530 (2010).
Cardoso, V., Chakrabarti, S., Pani, P., Berti, E. & Gualtieri, L. Floating and sinking: the imprint of massive scalars around rotating black holes. Phys. Rev. Lett. 107, 241101 (2011).
Silva, H. O., Sakstein, J., Gualtieri, L., Sotiriou, T. P. & Berti, E. Spontaneous scalarization of black holes and compact stars from a Gauss–Bonnet coupling. Phys. Rev. Lett. 120, 131104 (2018).
Doneva, D. D. & Yazadjiev, S. S. New Gauss–Bonnet black holes with curvature-induced scalarization in extended scalar–tensor theories. Phys. Rev. Lett. 120, 131103 (2018).
Maselli, A., Franchini, N., Gualtieri, L. & Sotiriou, T. P. Detecting scalar fields with extreme mass ratio inspirals. Phys. Rev. Lett. 125, 141101 (2020).
Flanagan, E. E. & Hughes, S. A. Measuring gravitational waves from binary black hole coalescences: 2. the waves’ information and its extraction, with and without templates. Phys. Rev. D 57, 4566–4587 (1998).
Lindblom, L., Owen, B. J. & Brown, D. A. Model waveform accuracy standards for gravitational wave data analysis. Phys. Rev. D 78, 124020 (2008).
Chatziioannou, K., Klein, A., Yunes, N. & Cornish, N. Constructing gravitational waves from generic spin-precessing compact binary inspirals. Phys. Rev. D 95, 104004 (2017).
Julié, F.-L. & Berti, E. Post-Newtonian dynamics and black hole thermodynamics in Einstein-scalar-Gauss–Bonnet gravity. Phys. Rev. D 100, 104061 (2019).
Warburton, N. & Barack, L. Self force on a scalar charge in Kerr spacetime: eccentric equatorial orbits. Phys. Rev. D 83, 124038 (2011).
Warburton, N. Self force on a scalar charge in Kerr spacetime: inclined circular orbits. Phys. Rev. D 91, 024045 (2015).
Nasipak, Z., Osburn, T. & Evans, C. R. Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: evidence from frequency-domain scalar self-force calculations on generic Kerr orbits. Phys. Rev. D 100, 064008 (2019).
Cardoso, V. & Maselli, A. Constraints on the astrophysical environment of binaries with gravitational-wave observations. Astron. Astrophys. 644, A147 (2020).
Katz, M. L., Chua, A. J. K., Speri, L., Warburton, N. & Hughes, S. A. Fast extreme-mass-ratio-inspiral waveforms: new tools for millihertz gravitational-wave data analysis. Phys. Rev. D 104, 064047 (2021).
Baghi, Q. et al. Gravitational-wave parameter estimation with gaps in LISA: a Bayesian data augmentation method. Phys. Rev. D 100, 022003 (2019).
Chase, J. E. Event horizons in static scalar-vacuum space-times. Commun. Math. Phys. 19, 276–288 (1970).
Bekenstein, J. D. Novel ‘no-scalar-hair’’ theorem for black holes. Phys. Rev. D 51, R6608 (1995).
Hawking, S. W. Black holes in the Brans–Dicke theory of gravitation. Commun. Math. Phys. 25, 167–171 (1972).
Sotiriou, T. P. & Faraoni, V. Black holes in scalar–tensor gravity. Phys. Rev. Lett. 108, 081103 (2012).
Hui, L. & Nicolis, A. No-hair theorem for the galileon. Phys. Rev. Lett. 110, 241104 (2013).
Cardoso, V. & Gualtieri, L. Testing the black hole ‘no-hair’ hypothesis. Class. Quantum Gravity 33, 174001 (2016).
Sotiriou, T. P. & Zhou, S.-Y. Black hole hair in generalized scalar–tensor gravity: an explicit example. Phys. Rev. D 90, 124063 (2014).
Yunes, N., Pani, P. & Cardoso, V. Gravitational waves from quasicircular extreme mass-ratio inspirals as probes of scalar–tensor theories. Phys. Rev. D 85, 102003 (2012).
Hannuksela, O. A., Wong, K. W. K., Brito, R., Berti, E. & Li, T. G. F. Probing the existence of ultralight bosons with a single gravitational-wave measurement. Nat. Astron. 3, 447–451 (2019).
Annulli, L., Cardoso, V. & Vicente, R. Stirred and shaken: dynamical behavior of boson stars and dark matter cores. Phys. Lett. B 811, 135944 (2020).
Eardley, D. M. Observable effects of a scalar gravitational field in a binary pulsar. Astrophys. J. Lett. 196, L59–L62 (1975).
Damour, T. & Esposito-Farese, G. Tensor multiscalar theories of gravitation. Class. Quantum Gravity 9, 2093–2176 (1992).
Julié, F.-L. Reducing the two-body problem in scalar–tensor theories to the motion of a test particle : a scalar–tensor effective-one-body approach. Phys. Rev. D 97, 024047 (2018).
Julié, F.-L. On the motion of hairy black holes in Einstein–Maxwell-dilaton theories. J Cosmol. Astropart. Phys. 01, 026 (2018).
Steinhoff, J. & Puetzfeld, D. Influence of internal structure on the motion of test bodies in extreme mass ratio situations. Phys. Rev. D 86, 044033 (2012).
Teukolsky, S. A. Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations. Astrophys. J. 185, 635–647 (1973).
Hawking, S. W. & Hartle, J. B. Energy and angular momentum flow into a black hole. Commun. Math. Phys. 27, 283–290 (1972).
Hughes, S. A. The evolution of circular, nonequatorial orbits of Kerr black holes due to gravitational wave emission. Phys. Rev. D 61, 084004 (2000); erratum 63, 049902 (2001); erratum 65, 069902 (2002); erratum 67, 089901 (2003); erratum 78, 109902 (2008); erratum 90, 109904 (2014).
Gralla, S. E., Friedman, J. L. & Wiseman, A. G. Numerical radiation reaction for a scalar charge in Kerr circular orbit. Preprint at http://arxiv.org/abs/gr-qc/0502123v1 (2005).
Warburton, N. & Barack, L. Self force on a scalar charge in Kerr spacetime: circular equatorial orbits. Phys. Rev. D 81, 084039 (2010).
Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (W. H. Freeman, 1973).
Bonga, B., Yang, H. & Hughes, S. A. Tidal resonance in extreme mass-ratio inspirals. Phys. Rev. Lett. 123, 101103 (2019).
Barack, L. & Cutler, C. LISA capture sources: approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy. Phys. Rev. D 69, 082005 (2004).
Huerta, E. A. & Gair, J. R. Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals. Phys. Rev. D 84, 064023 (2011).
Canizares, P., Gair, J. R. & Sopuerta, C. F. Testing Chern–Simons modified gravity with gravitational-wave detections of extreme-mass-ratio binaries. Phys. Rev. D 86, 044010 (2012).
Babak, S., Fang, H., Gair, J. R., Glampedakis, K. & Hughes, S. A.‘Kludge’ gravitational waveforms for a test-body orbiting a Kerr black hole. Phys. Rev. D 75, 024005 (2007); erratum 77, 04990 (2008).
Apostolatos, T. A., Cutler, C., Sussman, G. J. & Thorne, K. S. Spin induced orbital precession and its modulation of the gravitational wave forms from merging binaries. Phys. Rev. D 49, 6274–6297 (1994).
Cutler, C. Angular resolution of the LISA gravitational wave detector. Phys. Rev. D 57, 7089–7102 (1998).
Huerta, E. A., Gair, J. R. & Brown, D. A. Importance of including small body spin effects in the modelling of intermediate mass-ratio inspirals. II. Accurate parameter extraction of strong sources using higher-order spin effects. Phys. Rev. D 85, 064023 (2012).
Piovano, G. A., Brito, R., Maselli, A. & Pani, P. Assessing the detectability of the secondary spin in extreme mass-ratio inspirals with fully-relativistic numerical waveforms. Phys. Rev. D 104, 124019 (2021).
Ori, A. & Thorne, K. S. The transition from inspiral to plunge for a compact body in a circular equatorial orbit around a massive, spinning black hole. Phys. Rev. D 62, 124022 (2000).
Robson, T., Cornish, N. J. & Liu, C. The construction and use of LISA sensitivity curves. Class. Quantum Gravity 36, 105011 (2019).
Poisson, E. & Will, C. M. Gravitational waves from inspiraling compact binaries: parameter estimation using second postNewtonian wave forms. Phys. Rev. D 52, 848–855 (1995).
Vallisneri, M. Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects. Phys. Rev. D 77, 042001 (2008).
Milne-Thomson, L. M. The Calculus of Finite Differences Vol. 15 (Cambridge Univ. Press, 1936).
Gair, J. R., Vallisneri, M., Larson, S. L. & Baker, J. G. Testing general relativity with low-frequency, space-based gravitational-wave detectors. Living Rev. Relativ. 16, 7 (2013).
Perkins, S. E., Nair, R., Silva, H. O. & Yunes, N. Improved gravitational-wave constraints on higher-order curvature theories of gravity. Phys. Rev. D 104, 024060 (2021).
Barausse, E., Yunes, N. & Chamberlain, K. Theory-agnostic constraints on black-hole dipole radiation with multiband gravitational-wave astrophysics. Phys. Rev. Lett. 116, 241104 (2016).
Acknowledgements
We thank S. Bhagwat, J. Harms, C. Pacilio, G. Piovano, L. Speri and N. Warburton for useful discussions and having carefully read the manuscript. A.M. acknowledges support from the Amaldi Research Center funded by the MIUR programme ‘Dipartimento di Eccellenza’ (CUP: B81I18001170001). N.F. acknowledges financial support provided under the European Union’s H2020 ERC Consolidator Grant ‘GRavity from Astrophysical to Microscopic Scales’ grant agreement No. GRAMS-815673. P.P. acknowledges financial support provided under the European Union’s H2020 ERC Starting Grant agreement No. DarkGRA–757480. We acknowledge financial support provided under the European Union’s H2020 MSCA-RISE Grant GRU, grant agreement No. 101007855. T.P.S. acknowledges partial support from the STFC Consolidated Grants No. ST/T000732/1 and No. ST/V005596/1. We also acknowledge support under the MIUR PRIN and FARE programmes (GW-NEXT, CUP: B84I20000100001). We also acknowledge networking support by the COST Action GW-verse Grant No. CA16104. All computations were performed on the Vera cluster of the Amaldi Research Center.
Author information
Authors and Affiliations
Contributions
A.M. and T.P.S. conceived the idea of probing the detectability of scalar charge by LISA with the approach developed in this manuscript. A.M. led the waveform modelling and statistical analysis and contributed to all aspects of the project. N.F. contributed significantly to the numerical calculations, the error analysis and the interpretation of the results. L.G. and T.P.S. made a major contribution to the development of the theoretical framework. S.B. made an important contribution to the computation of gravitational and scalar fluxes. L.G., T.P.S. and P.P. contributed strongly to the interpretation of the results and to overcoming technical difficulties in the analysis.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Astronomy thanks Alvin Chua, Kostas Tzanavaris and Katy Clough for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Further details on the waveform generation and discussion of the numerical procedure adopted for the EMRI parameter estimation and the accuracy of the calculations.
Rights and permissions
About this article
Cite this article
Maselli, A., Franchini, N., Gualtieri, L. et al. Detecting fundamental fields with LISA observations of gravitational waves from extreme mass-ratio inspirals. Nat Astron 6, 464–470 (2022). https://doi.org/10.1038/s41550-021-01589-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41550-021-01589-5
This article is cited by
-
New horizons for fundamental physics with LISA
Living Reviews in Relativity (2022)