From Smooth Curves to Universal Metrics

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.

10 pages, 1 figure. Discussions extended

References in corpus (6)

• Metrics With Vanishing Quantum Corrections
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• New Exact Solutions of Quadratic Curvature Gravity
• AdS-plane wave and pp-wave solutions of generic gravity theories
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Cited by in corpus (7)

• Classical Double Copy: Kerr-Schild-Kundt metrics from Yang-Mills Theory
• Generating exact solutions to Einstein's equation using linearized approximations
• Kerr-Schild--Kundt Metrics are Universal
• Wave Metrics in the Cotton and Conformal Killing Gravity Theories
• Non-Einsteinian Black Holes in Generic 3D Gravity Theories
• Almost Universal Metrics
• Generalized Vaidya Spacetime in Cotton and Conformal Killing Theories