Geometrodynamics in a spherically symmetric, static crossflow of null dust

TL;DR

This paper explores the geometrodynamics of a spherically symmetric, static null dust spacetime, revealing a new Hamiltonian formulation that simplifies quantization and constraint algebra, with implications for quantum gravity models.

Contribution

It introduces a novel Hamiltonian constraint linear in the conjugate momentum to an internal time in null dust spacetimes, facilitating quantization.

Findings

New Hamiltonian constraint linear in momentum

Strongly commuting algebra of constraints

Functional Schrödinger equation derived

Abstract

The spherically symmetric, static spacetime generated by a crossflow of non-interacting radiation streams, treated in the geometrical optics limit (null dust) is equivalent to an anisotropic fluid forming a radiation atmosphere of a star. This reference fluid provides a preferred / internal time, which is employed as a canonical coordinate. Among the advantages we encounter a new Hamiltonian constraint, which becomes linear in the momentum conjugate to the internal time (therefore yielding a functional Schr\"{o}dinger equation after quantization), and a strongly commuting algebra of the new constraints.