Abstract
Quantum equations for massless particles of any spin are considered in stationary uncharged axially symmetric spacetimes. It is demonstrated that up to a normalization function, the angular wave function does not depend on the metric and practically is the same as in the Minkowskian case. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms, which depend in a unique way on time and space curvatures. In agreement with the principle of equivalence, these terms vanish locally, and the radial equations reduce to the same homogeneous equations as in Minkowski spacetime.
Highlights
In a sufficiently small region of spacetime, no experiment can distinguish between gravity and uniform acceleration
We have demonstrated that the wave function Φ can be factorized into a normalization function N(r,θ) and a reduced function ψ, which depends on diagonal elements of the metric
We have considered quantum equations of free massless particles of any spin in a flat Minkowski spacetime and in curved spacetimes in an attempt to unveil how the space curvature affects the physics of these particles
Summary
In a sufficiently small region of spacetime, no experiment can distinguish between gravity and uniform acceleration. Minkowski spacetime is flat and uniform throughout, and takes no account of gravitation It serves merely as a static background for whatever physical phenomena are present. Our main objective in what follows is to study how curvature of a spacetime influences the dynamics of free massless particles. To this aim, we consider quantum equations for free massless particles of any spin in a flat Minkowski spacetime and in axially symmetric spacetimes, namely, the static Schwarzschild, Friedmann–Robertson–Walker (FRW) and the stationary rotating Kerr spacetimes. Though expected to be quantized, the spacetimes are taken to be continuous
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