Geometry of a Quantized Spacetime: The Quantum Potential Approach

Quantum dynamics in a curved spacetime can be studied using a modified Lagrangian approach directly in terms of the spacetime variables [Mirza, B.M., Quantum Dynamics in Black Hole Spacetimes, IC-MSQUARE 2012]. Here we investigate the converse problem of determining the nature of the background spacetime when quantum dynamics of a test particle is known. We employ the quantum potential formalism here to obtain the modifications introduced by the quantum effects to the background spacetime. This leads to a novel geometry for the spacetime in which a test particle modifies the spacetime via interaction through the quantum potential. We present here the case of a Gaussian wave packet, and a localized quantum soliton, representing the test particle, and determine the corresponding geometries that emerge.