Quantum Gravitational Force Between Polarizable Objects

Abstract

Since general relativity is a consistent low energy effective field theory, it is possible to compute quantum corrections to classical forces. Here we compute a quantum correction to the gravitational potential between a pair of polarizable objects. We study two distant bodies and compute a quantum force from their induced quadrupole moments due to two graviton exchange. The effect is in close analogy to the Casimir-Polder and London-van der Waals forces between a pair of atoms from their induced dipole moments due to two photon exchange. The new effect is computed from the shift in vacuum energy of metric fluctuations due to the polarizability of the objects. We compute the potential energy at arbitrary distances compared to the wavelengths in the system, including the far and near regimes. In the far distance, or retarded, regime, the potential energy takes on a particularly simple form: $V(r)=-3987\hslash c{G}^2{\alpha }_{1S}{\alpha }_{2S}/(4\pi r^{11})$, where ${\alpha }_{1S},{\alpha }_{2S}$ are the static gravitational quadrupole polarizabilities of each object. We provide estimates of this effect.

5 pages, 1 figure, in double column format. V2: Fixed Eq. (16); added Feynman diagram to figure; other minor changes. V3: Updated to resemble version published in PRL

References in corpus (4)

• Relativistic theory of tidal Love numbers
• Casimir forces between arbitrary compact objects
• Current status of the Dynamical Casimir Effect
• Casimir effect for curved boundaries in Robertson-Walker spacetime

Cited by in corpus (21)

• Quantum gravitational interaction between a polarizable object and a boundary
• Effective field theories for van der Waals interactions
• Analytical On-shell Calculation of Low Energy Higher Order Scattering
• Quantum correction to classical gravitational interaction between two polarizable objects
• General Relativistic Decoherence with Applications to Dark Matter Detection
• Quantum interaction between two gravitationally polarizable objects in presence of boundaries
• Interaction between two gravitationally polarizable objects induced by thermal bath of gravitons
• One-loop quantum gravitational corrections to the scalar two-point function at fixed geodesic distance
• Spontaneous excitation of an accelerated atom coupled with quantum fluctuations of spacetime
• Quantum gravitational interaction between two objects induced by external gravitational radiation fields
• Resonance interaction between two entangled gravitational polarizable objects
• Dipole-dipole dispersion interactions between neutrons
• Quantum fluctuations of spacetime generate quantum entanglement between gravitationally polarizable subsystems
• Atom-field dynamics in curved spacetime
• Nonadditive quantum gravitational interaction for three nonpointlike objects
• Induced quantum gravitational interaction between two objects with permanent quadrupoles in external gravitational fields
• Towards the merger of Hawking radiating black holes
• Quantum gravitomagnetic interaction
• Quantum Corrections to Gravitational Potential of Scalarized Neutron Star Binary
• Few-neutron systems with the long-range Casimir-Polder force
• Repulsive quantum gravitoelectric-gravitomagnetic interaction