# Embedding the stationary spacetimes into Brans-Dicke cosmology via conformal transformations

## TL;DR

This paper explores how conformal transformations of stationary spacetimes within Brans-Dicke theory can produce cosmological models with varying expansion behaviors, depending on the original spacetime's matter content.

## Contribution

It introduces solutions for conformally transformed stationary spacetimes in Brans-Dicke cosmology, linking expansion rates to the matter content of the original geometry.

## Key findings

- BD scalar field induces accelerated expansion in vacuum geometries.
- No acceleration occurs if the original spacetime contains matter or curvature.
- Different expansion rates are obtained for FLRW and Kerr-Newman black hole metrics.

## Abstract

A conformal transformation of a static or stationary spacetime by a time dependent conformal scale factor ${S(\tau )}^2$ is one of the methods of producing a cosmological spacetime. Using this knowledge and Brans-Dicke (BD) field equations, we investigate two time dependent metrics, including Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime and conformally transformed Kerr-Newman black hole, and we obtain solutions that allow different expansion rates for each geometry. These expansion rates depend on the matter content of the conformally transformed geometry. We state that the BD scalar field yields accelerated expansion of the conformal spacetime if the original metric has vacuum geometry, and no acceleration if the original spacetime has some curvature or matter content in it.