Quantum gravity in JNW spacetime

TL;DR

This paper investigates scalar field behavior coupled to gravitons in Janis-Newman-Winicour spacetime, revealing a complex, position-dependent mass matrix that cannot be simultaneously diagonalized with the kinetic energy, highlighting unique quantum effects in this background.

Contribution

It introduces the analysis of scalar-graviton coupling in JNW spacetime and uncovers the non-commuting, position-dependent mass and kinetic operators, a novel feature compared to standard models.

Findings

Discovered a 17-dimensional position-dependent mass matrix.

Found the mass matrix is non-diagonal in the kinetic energy basis.

Identified a basis where the mass matrix is diagonal but kinetic energy is not.

Abstract

In this paper we study the behavior of a scalar field coupled to gravitons on the Janis-Newman-Winicour background, which somewhat interpolates between Minkowski and Schwarzschild space-times. The most important physical effect we find is that there is a 17-dimensional position-dependent mass matrix YABpxq which happens to be non-diagonal in the basis in which the kinetic energy term is diagonal. There is a different basis with a mixing between the scalar field and the graviton trace in which the mass matrix is diagonal, but this basis fails to diagonalize the kinetic energy piece. This is at variance with what happens in the Standard Model with the quark mixing, and is of course due to the fact that the mass matrix here is position dependent and thus it does not commute with the kinetic energy operator, so that both operators cannot be diagonalized simultaneously.