A new synthesis of matter and gravity: A nongravitating scalar field

We present a new manifestation of the nonlinearity of the gravity-matter interactions. We show explicitly that there exists a nongravitating dynamical scalar-field solution in Eddington-inspired Born-Infeld gravity. This kind of solution has not been found in previous literatures based on general relativity, or other modified-gravity theories. The nongravitating solution obtained in this work is unstable to perturbations.