Newtonian Sources Research Articles

Effective metric outside bootstrapped Newtonian sources

We determine the complete space-time metric from the bootstrapped Newtonian potential generated by a static spherically symmetric source in the surrounding vacuum. This metric contains post-Newtonian parameters which can be further used to constrain the complete underlying dynamical theory. For values of the post-Newtonian parameters within experimental bounds, the reconstructed metric appears very close to the Schwarzschild solution of General Relativity in the whole region outside the event horizon. The latter is however larger in size for the same value of the mass compared to the Schwarzschild case.

On the mass of bootstrapped Newtonian sources

We show that the bootstrapped Newtonian potential generated by a uniform and isotropic source does not depend on the one-loop correction for the matter coupling to gravity. The latter, however, affects the relation between the proper mass and the Arnowitt–Deser–Misner (ADM) mass and, consequently, the pressure needed to keep the configuration stable.

Gravitational Waves from Generalized Newtonian Sources

AbstractI review the elementary theory of gravitational waves on a Minkowski background and the quadrupole approximation. The modified conservation laws for energy and momentum keeping track of the gravitational‐wave flux are presented. The theory is applied to two‐body systems in bound and scattering states subject to newtonian gravity generalized to include a force allowing for orbital precession. The evolution of the orbits is studied in the adiabatic approximation. From these results I derive the conditions for capture of two bodies to form a bound state by the emission of gravitational radiation.

Gravitational radiation in Hořava gravity

We study the radiation of gravitational waves by self-gravitating binary systems in the low-energy limit of Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity. We find that the predictions for the energy-loss formula of general relativity are modified already for Newtonian sources: the quadrupole contribution is altered, in part due to the different speed of propagation of the tensor modes; furthermore, there is a monopole contribution stemming from an extra scalar degree of freedom. A dipole contribution only appears at higher post-Newtonian order. We use these findings to constrain the low-energy action of Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity by comparing them with the radiation damping observed for binary pulsars. Even if this comparison is not completely appropriate---since compact objects cannot be described within the post-Newtonian approximation---it represents an order of magnitude estimate. In the limit where the post-Newtonian metric coincides with that of general relativity, our energy-loss formula provides the strongest constraints for Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity at low-energies.

Carter-like constants of motion in the Newtonian and relativistic two-center problems

In Newtonian gravity, a stationary axisymmetric system admits a third, Carter-like constant of motion if its mass multipole moments are related to each other in exactly the same manner as for the Kerr black-hole spacetime. The Newtonian source with this property consists of two point masses at rest a fixed distance apart. The integrability of motion about this source was first studied in the 1760s by Euler. We show that the general relativistic analog of the Euler problem, the Bach–Weyl solution, does not admit a Carter-like constant of motion, first, by showing that it does not possess a non-trivial Killing tensor, and secondly, by showing that the existence of a Carter-like constant for the two-center problem fails at the first post-Newtonian order.