Effective metric for bootstrapped Newtonian sources

In this work, we address the problem of constructing an effective space-time picture for the gravitational field in the bootstrapped Newtonian theory (BNT). After a short review of the singularity problem and the corpuscular model of black holes, we present a detailed introduction to the BNT. This theory provides us with an exact formula for the gravitational potential felt by slowly-moving particles outside a static and spherically symmetric source. Our goal is to determine the most general metric tensor that reproduces this potential in the Newtonian limit and use it in relativistic or strong-gravity scenarios. After we make so that the effective space-time agrees with the experimental constraints and contains a black hole region, we study its properties in two opposite limits: the weak- and the strong-field regime. In the first case, we find departures from the predictions of General Relativity as early as order GNM=R2, where R is the characteristic length scale of a given system. In the second case, we discover that the BN black hole is different from the Schwarzschild one, and it generally violates the first law of black hole mechanics. In the end, we restore time-dependence to study the propagation of gravitational waves in the reconstructed space-time. The upshot is that we cannot exclude the existence of scalar waves.