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Corrections to general relativity that introduce long-ranged scalar fieldswhich are non-minimally coupled to curvature typically predict that neutronstars possess a non-trivial scalar field profile. An observer far from a staris most sensitive to the spherically-symmetric piece of this profile thatdecays linearly with the inverse of the distance, the so-called scalar charge,which is related to the emission of dipolar radiation from compact binaries.The presence of dipolar radiation has the potential to very strongly constrainextended theories of gravity. These facts may lead people to believe thatgravitational theories with long-ranged scalar fields have already beenconstrained strongly from binary pulsar observations. Here we challenge this"lore" by investigating the decoupling limit of Gauss-Bonnet gravity as anexample, in which the scalar field couples linearly to the Gauss-Bonnet densityin the action. We prove a theorem that neutron stars in this theory cannotpossess a scalar charge. Thus Gauss-Bonnet gravity evades the strong binarypulsar constraints on dipole radiation. We discuss the astrophysical systemsyielding the best constraints on Gauss-Bonnet gravity and related quadraticgravity theories. To achieve this we explicitly compute the scalar charge forslowly-rotating neutron stars in quadratic gravity theories. In generic case,either neutron star-binary or neutron star-black hole systems can be used toconstrain the theory, but Gauss-Bonnet gravity evades the neutron star-binaryconstraints. However, black holes in Gauss-Bonnet gravity do anchor scalarcharge. The best constraints on Gauss-Bonnet gravity will thus come from blackhole observations, for example via pulsar-black hole binaries. We estimatethese constraints to be ten times better than the current estimated bound, andalso include estimated constraints on generic quadratic gravity theories.

Challenging the Presence of Scalar Charge and Dipolar Radiation in Binary Pulsars