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The recently reported gravitational wave events GW$150914$ and GW$151226$caused by the mergers of binary black holes[arXiv:1602.03841],[arXiv:1606.04855],[arXiv:1606.04856] provide a formidableway to set constraints on alternative metric theories of gravity in the strongfield regime. In this paper, we develop an approach where an arbitrary theoryof gravity can be parametrised by an effective coupling $G_{eff}$ and aneffective gravitational potential $\Phi(r)$. The standard Newtonian limit ofGeneral Relativity is recovered as soon as $G_{eff}\rightarrow G_N$ and$\Phi(r)\rightarrow \Phi_{N}$. The upper bound on the graviton mass and thegravitational interaction length, reported by the LIGO-VIRGO collaboration, canbe directly recast in terms of the parameters of the theory which allows ananalysis where the gravitational wave frequency modulation sets constraints onthe range of possible alternative models of gravity. Numerical results based onpublished parameters for the binary black hole mergers are also reported.Comparison of the observed phase of the GW$150914$ and GW$151226$ with themodulated phase in alternative theories of gravity does not give reasonableconstraints due the large uncertainties in the estimated parameters for thecoalescing black holes. In addition to these general considerations, we obtainlimits for the frequency dependence of the $\alpha$ parameter in scalar tensortheories of gravity.

Constraining alternative theories of gravity using GW$150914$ and GW$151226$