EXPERIMENTAL TESTS OF GENERAL RELATIVITY 
Testing ScalarTensor Gravity We studied the motion and gravitationalwave generation from compact binary systems in a general class of massless scalartensor theories, using the formalism of the Direct Integration of the Relaxed Einstein Equations (DIRE) adapted to scalartensor theory, coupled with an approach pioneered by Eardley for incorporating the internal gravity of compact, selfgravitating bodies. We calculated the explicit equations of motion for nonspinning compact objects through 2.5 postNewtonian (PN) order, including the 1.5 PN and 2.5 PN contributions to gravitational radiation reaction, the former corresponding to the effects of dipole gravitational radiation (Mirshekari and Will, 2013). For binary black holes we showed that the motion through 2.5 PN order is observationally identical to that predicted by general relativity. For mixed blackhole neutronstar binary systems, the motion deviates from that of general relativity by terms that depend on a single parameter involving the scalartensor coupling constant and the structure of the neutron star. Postdoc Ryan Lang then obtained the tensor contribution to the gravitational waveform through 2 PN order, and the scalar contribution to 1.5 PN order, as well as the energy flux to 1 PN order beyond the GR quadrupole approximation (Lang 2014, 2015). For binary black holes, the gravitational radiation is also observationally identical to that predicted by general relativity. With Lang and MarieCurie Postdoctoral fellow Anna Heffernan we are working to complete the energy flux through 2PN order. This actually requires computation of certain scalarfield multipole moments to 3PN order and knowing the equations of motion to 3PN order. 
Testing the "Nohair" Theorems with the Galactic Center Black Hole SgrA* We showed that future highprecision observations of the orbits of stars very close to the galactic center black hole could test whether the hole's quadrupole moment matches the nohair requirement that Q=J^2/M (Will 2008). Whether such a test is feasible depends in part on whether perturbations of the orbit of a target star due to other stars in the central cluster will mask the relativistic effects. We studied this using both numerical simulations (Merritt, Alexander, Mikkola and Will 2009) and semianalytic orbit perturbation theory (Sadegian and Will, 2011), and showed that, given reasonable assumptions about the distribution and number of stars in the central cluster, and for a target star within a few tenths of a milliparsec of the black hole, the relativistic precessions would be larger than those induced by stars.

Testing general relativity with compactbody orbits: A modified EinsteinInfeldHoffmann framework We described a general framework for analyzing orbits of systems containing compact objects in a class of Lagrangianbased alternative theories of gravity that also admit a global preferred reference frame (Will 2018). The framework is based on a modified EinsteinInfeldHoffmann (EIH) formalism that uses a postNewtonian Nbody Lagrangian with arbitrary parameters that depend on the theory of gravity and on ``sensitivities'' that encode the effects of the bodies' internal structure on their motion. We determined the modified EIH parameters for the EinsteinAether and Khronometric vectortensor theories of gravity. We obtained the effects of motion relative to a preferred universal frame on the orbital parameters of binary systems containing neutron stars, such as a class of ultracircular pulsarwhite dwarf binaries; the amplitudes of the effects depend upon ``strongfield'' preferredframe parameters which we related to the fundamental modified EIH parameters. 

Bounding the Mass of the Graviton We studied the possibility of placing a bound on the mass of the graviton using gravitationalwave data from inspiralling compact binaries (Will 1998). The potential bounds were refined by incorporating better LISA noise curves, the effects of spins and the contributions of higher harmonics in the waveforms [see Will and Yunes (2004), Berti, Buonanno and Will (2005a,2005b), Arun and Will (2009), Stavridis and Will (2009)]. This idea came to fruition in 2015 with the first detection of gravitational waves by LIGO, where they placed a lower bound of 10^13 km on the graviton Compton wavelength! 
A new general relativistic contribution to Mercury's perihelion advance We pointed out the existence of a new general relativistic contribution to the perihelion advance of Mercury that, while smaller than the contributions arising from the solar quadrupole moment and angular momentum, is 100 times larger than the secondpostNewtonian contribution (Will 2018). It arises in part from relativistic ``crossterms'' in the postNewtonian equations of motion between Mercury's interaction with the Sun and with the other planets, and in part from an interaction between Mercury's motion and the gravitomagnetic field of the moving planets. At a few parts in 10^6 of the leading general relativistic precession of 42.98 arcseconds per century, these effects are likely to be detectable by the BepiColombo mission to place and track two orbiters around Mercury, scheduled for launch around 2018. 
The Multiple Deaths of Whitehead's Theory of Gravity In a jab at some philosophers of science, who continue to love Whitehead's theory, despite evidence presented in 1971 that it violates experiment, Gary Gibbons and I (2006) became serial killers, and showed that the theory violates 5 different kinds of experiments. 

Review
Articles on Tests of GR 

Articles by Clifford Will: The Confrontation between General Relativity and Experiment. A Living Review (here) Was Einstein right? A centenary assessment (here) The 1919 measurement of the deflection of light (here) Resource Letter on Precision Tests of Gravity (here)

Other Review articles:

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