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We study the constraint equations for a class of scalar-tensor effective field theories of gravity, including the operators up to $4$ derivatives in the action ($4\partial$ST).
1904
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D. M. Walsh, Non-uniqueness in conformal formulations of the Einstein constraints
1926
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J. W. York, Jr., Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial value problem of general relativity
1973
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G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space
1974
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M. Cantor, The existence of non-trivial asymptotically flat initial data for vacuum spacetimes
1977
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R. M. Wald, General Relativity · 1984
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R. Gregory and R. Laflamme, Black strings and p-branes are unstable
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E. E. Flanagan and R. M. Wald, Does back reaction enforce the averaged null energy condition in semiclassical gravity?
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P. Kanti, N. E. Mavromatos, J. Rizos, K. Tamvakis, and E. Winstanley, Dilatonic black holes in higher curvature string gravity
1996
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S. Brandt and B. Bruegmann, A Simple construction of initial data for multiple black holes
1997
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J. York, James W., Conformal ’thin sandwich’ data for the initial-value problem
1999
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G. B. Cook, Initial data for numerical relativity
2000
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Y. Choquet-Bruhat, J. Isenberg, and J. W. York, Einstein constraints on asymptotically euclidean manifolds
2000
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Courant lecture notes. American Mathematical Society, Providence, RI, 2001
L. Nirenberg, Topics in nonlinear functional analysis · 2001
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2002
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Á. D. Kovács and H. S. Reall, Well-posed formulation of scalar-tensor effective field theory
2003
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Á. D. Kovács and H. S. Reall, Well-posed formulation of Lovelock and Horndeski theories
2003
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H. P. Pfeiffer and J. York, James W., Extrinsic curvature and the Einstein constraints
2003
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W. Tichy, B. Bruegmann, M. Campanelli, and P. Diener, Binary black hole initial data for numerical general relativity based on post-Newtonian data
2003
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C. P. Burgess, Quantum gravity in everyday life: General relativity as an effective field theory
2004
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2009
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2009
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2011
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B. Kleihaus, J. Kunz, and E. Radu, Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory
2011
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2004
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G. B. Cook and H. P. Pfeiffer, Excision boundary conditions for black hole initial data
2004
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R. Cayuso and L. Lehner, Nonlinear, noniterative treatment of EFT-motivated gravity
2005
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H. P. Pfeiffer and J. W. York, Jr., Uniqueness and non-uniqueness in the Einstein constraints
2005
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M. A. Scheel, H. P. Pfeiffer, L. Lindblom, L. E. Kidder, O. Rinne, and S. A. Teukolsky, Solving Einstein’s equations with dual coordinate frames
2006
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2006
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T. W. Baumgarte, N. O. Murchadha, and H. P. Pfeiffer, The Einstein constraints: Uniqueness and non-uniqueness in the conformal thin sandwich approach
2007
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2011
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Springer, Berlin, Heidelberg, 01, 2012
E. Gourgoulhon, 3+1 Formalism in General Relativity · 2012
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2014
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2016
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2016
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2017
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W. Tichy, The initial value problem as it relates to numerical relativity
2017
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2018
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2018
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F.-L. Julié and E. Berti, d + 1 d+1 formalism in einstein-scalar-gauss-bonnet gravity
2020
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J. M. Bowen and J. York, James W., Time asymmetric initial data for black holes and black hole collisions
2056
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