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Register a new userEffective metric outside bootstrapped Newtonian sources
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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.
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We study equilibrium configurations of a homogenous ball of matter in a bootstrapped description of gravity which includes a gravitational self-interaction term beyond the Newtonian coupling. Both matter density and pressure are accounted for as sources of the gravitational potential for test particles. Unlike the general relativistic case, no Buchdahl limit is found and the pressure can in principle support a star of arbitrarily large compactness. By defining the horizon as the location where the escape velocity of test particles equals the speed of light, like in Newtonian gravity, we find a minimum value of the compactness for which this occurs. The solutions for the gravitational potential here found could effectively describe the interior of macroscopic black holes in the quantum theory, as well as predict consequent deviations from general relativity in the strong field regime of very compact objects.
We analyse the classical configurations of a bootstrapped Newtonian potential generated by homogeneous spherically symmetric sources in terms of a quantum coherent state. We first compute how the mass and mean wavelength of these solutions scale in terms of the number of quanta in the coherent state. We then note that the classical relation between the ADM mass and the proper mass of the source naturally gives rise to a Generalised Uncertainty Principle for the size of the gravitational radius in the quantum theory. Consistency of the mass and wavelength scalings with this GUP requires the compactness remains at most of order one even for black holes, and the corpuscular predictions are thus recovered, with the quantised horizon area expressed in terms of the number of quanta in the coherent state. Our findings could be useful for analysing the classicalization of gravity in the presence of matter and the avoidance of singularities in the gravitational collapse of compact sources.
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We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second Post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second Post-Newtonian order equations of motion in harmonic gauge in a straightforward manner.
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