An Embedding for General Relativity and its Implications for New Physics

Abstract

We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological "constant" that is a specific function of the extra coordinate. For unified theories of the forces in higher dimensions, this has major physical implications.

References in corpus (19)

• The Cosmological Constant and Dark Energy
• Cosmological Constant - the Weight of the Vacuum
• The Cosmological Constant
• Gravitational Lorentz Violations and Adjustment of the Cosmological Constant in Asymmetrically Warped Spacetimes
• Application of the Campbell-Magaard theorem to higher-dimensional physics
• $D$-Dimensional Gravity from $(D+1)$ Dimensions
• Equivalence Between Space-Time-Matter and Brane-World Theories
• On Applications of Campbell's Embedding Theorem
• Null Geodesics in Five Dimensional Manifolds
• Extra Force in Brane Worlds
• Gauge-Dependent Cosmological "Constant"
• Null Geodesics in Brane World Universe
• Why do we observe a small but non zero cosmological constant ?
• The Effective Energy-Momentum Tensor in Kaluza-Klein Gravity With Large Extra Dimensions and Off-Diagonal Metrics
• The Cosmological Constant Problem and Kaluza-Klein Theory
• Classical and quantized aspects of dynamics in five dimensional relativity
• On Higher-Dimensional Dynamics
• Cosmological constant and gravitational theory on D-brane
• The Equivalence Principle as a Symmetry

Cited by in corpus (8)

• Vacuum Waves
• Mach's Principle and Higher-Dimensional Dynamics
• Embeddings for General Relativity
• Dark matter and cosmic acceleration from Wesson's IMT
• Scaling Relations for the Cosmological "Constant" in Five-Dimensional Relativity
• The seed of magnetic monopoles in the early inflationary universe from a 5D vacuum state
• Embeddings for 4D Einstein equations with a cosmological constant
• Scale invariant scalar metric fluctuations during inflation: non-perturbative formalism from a 5D vacuum