We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order. We start by obtaining a Lagrangian for the gravitational potential coupled to a static matter source from the weak field expansion of the Einstein-Hilbert action. By analyzing a few classical solutions of the resulting field equation, we show that our construction leads to the expected post-Newtonian expressions. Next, we show that one can reproduce the classical Newtonian results very accurately by employing a coherent quantum state, and modifications to include the first post-Newtonian corrections are considered. Our findings establish a connection between the corpuscular model of black holes and post-Newtonian gravity, and set the stage for further investigations of these quantum models.
Quantum corpuscular corrections to the Newtonian potential / Casadio, Roberto; Giugno, Andrea; Giusti, Andrea; Lenzi, Michele. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - STAMPA. - 96:4(2017), pp. 1-15. [10.1103/PhysRevD.96.044010]
Quantum corpuscular corrections to the Newtonian potential
CASADIO, ROBERTO;GIUSTI, ANDREA;LENZI, MICHELE
2017
Abstract
We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order. We start by obtaining a Lagrangian for the gravitational potential coupled to a static matter source from the weak field expansion of the Einstein-Hilbert action. By analyzing a few classical solutions of the resulting field equation, we show that our construction leads to the expected post-Newtonian expressions. Next, we show that one can reproduce the classical Newtonian results very accurately by employing a coherent quantum state, and modifications to include the first post-Newtonian corrections are considered. Our findings establish a connection between the corpuscular model of black holes and post-Newtonian gravity, and set the stage for further investigations of these quantum models.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.