The $[3+1]$ Formulation of Chemical Dynamics in Curved Spacetime under the Eulerian Observer

Abstract

Traditionally, gravity is generally considered to exert an extremely weak effect in chemistry because the Newtonian gravitation is typically negligible compared to the dominant Coulomb potentials in a molecular system. In this work, we porpose a primitive framework of chemical dynamics in curved spacetime through fiducial-observer $[3+1]$ formulation by revising the nuclear Hamiltonian operator through the metric tensor of configuration space rather than by adding Newtonian gravitation in the potential energy term, where the absolute-sapce and universal-time viewpoint of Galileo is adopted. Using frames fixed on normal observers in the $[3+1]$ formalism ensures possibility of this treatment. Taking spherically symmetric curved spacetime ({\it i.e.} Schwarzschild spacetime) as numerical demonstration, we explore (1) the H + H$_2$ reaction dynamics, (2) the H$_2$ + H$_2$ scattering dynamics, (3) dynamics of dissociative chemsorption of H$_2$O on Cu(111), (4) the spectrum band of anthracene cation, and (5) the Berry phase in the nuclear wave function of a 98D surface scattering model. These calculations predict that (i) reaction or scattering probability and (ii) spectrum band decrease abruptly to zero as the spacetime curvature increases; meanwhile, the geometric phase is unaffected by the spacetime curvature. Finally, discussions on these numerical results, together with perspectives on the applications of quantum field theory to chemical dynamics in curved spacetime are given.