Abstract
In this paper we will discuss how to localise a quantum wave-packet due to self-gravitating meso-scopic object by taking into account gravitational self-interaction in the Schrödinger equation beyond General Relativity. In particular, we will study soliton-like solutions in infinite derivative ghost free theories of gravity, which resolves the gravitational 1/r singularity in the potential. We will show a unique feature that the quantum spread of such a gravitational system is larger than that of the Newtonian gravity, therefore enabling us a window of opportunity to test classical and quantum properties of such theories of gravity in the near future at a table-top experiment.
Highlights
Introduction and motivationsEinstein’s general relativity (GR) has been widely accepted theory of gravity on large scales and late times, i.e. in the infrared (IR) regime, where it has been tested to a very high pre-L
We will obtain the same non-linear Schrödinger equation which has two completely different interpretations in the two cases: in 1) it is seen as a fundamental equation describing the dynamics of a self-gravitating one-particle system; while in 2) it is derived as the large N limit (N → ∞) of a linear Schrödinger equation for an N -particle state by applying a mean-field approximation, so that the self-gravitational potential will be given by the sum of an infinite number of mutual gravitational interaction-contributions
By minimizing the energy in Eq (24), we have found approximate solitonic solutions for the ground-state of a self-gravitating system in the non-relativistic regime, where the gravitational interaction is described by infinite derivative theories of gravity (IDG)
Summary
Einstein’s general relativity (GR) has been widely accepted theory of gravity on large scales and late times, i.e. in the infrared (IR) regime, where it has been tested to a very high pre-. While in the second case, one can study the dynamics of a condensate in a mean-field approximation by taking into account all internal mutual gravitational interaction which contribute to the selfpotential It has been known for a while that a quadratic curvature gravity (4 derivatives in the metric) is a renormalizable theory of gravity, but contains massive spin-2 ghost, signalling instability in the vacuum and lacking predictions [6]. We will be exploring for the first time quantum localization of a wave-packet in such non-local theories of gravity Such theories can resolve cosmological singularity as pointed out in [12,5,15], and possibly even blackhole singularity [16], due to the fact that the physical effect of non-locality can be spread out on macroscopic scale in spacetime. We will find the fundamental equations describing the dynamics of a quantum meso-scopic system whose self-gravitational interaction is taken into account
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