From Smooth Curves to Universal Metrics

TL;DR

This paper introduces a new method to construct universal metrics in d-dimensional spacetime from constrained curves in lower-dimensional Minkowski or Euclidean spaces, aiding the understanding of quantum fields in curved backgrounds.

Contribution

It provides a novel construction technique for universal metrics based on curves in lower-dimensional spaces, addressing a longstanding challenge in gravity theory.

Findings

Explicit construction of universal metrics from constrained curves.

Facilitates analysis of quantum fields in curved spacetime.

Advances understanding of covariant gravity theories.

Abstract

A special class of metrics, called universal metrics, solve all gravity theories defined by covariant field equations purely based on the metric tensor. Since we currently lack the knowledge of what the full of quantum-corrected field equations of gravity are at a given microscopic length scale, these metrics are particularly important in understanding quantum fields in curved backgrounds in a consistent way. But, finding explicit universal metrics has been a hard problem as there does not seem to be a procedure for it. In this work, we overcome this difficulty and give a construction of universal metrics of d-dimensional spacetime from curves constrained to live in a (d-1)-dimensional Minkowski spacetime or a Euclidean space.