Two diverse models of embedding class one

TL;DR

This paper explores embedding theorems for class one spacetimes, applying them to models of charged wormholes and galaxy rotation curves, offering new solutions without dark matter.

Contribution

It introduces a complete charged wormhole model with conformal motions and a novel explanation for galaxy rotation curves without dark matter.

Findings

Charged wormhole solution with conformal symmetry

Model explaining flat galaxy rotation curves without dark matter

Insights into embedding class one spacetimes in higher dimensions

Abstract

Embedding theorems have continued to be a topic of interest in the general theory of relativity since these help connect the classical theory to higher-dimensional manifolds. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. These ideas are applied to two diverse models, a complete solution for a charged wormhole admitting a one-parameter group of conformal motions and a new model to explain the flat rotation curves in spiral galaxies without the need for dark matter.