An Unexpected Electrovac Solution with the Negative Cosmological Constant

TL;DR

This paper presents an exact Einstein-Maxwell solution with a negative cosmological constant, revealing a unique electromagnetic field-cosmological constant relationship and implications for universe modeling and measurement.

Contribution

It introduces a novel exact solution linking electromagnetic fields and the cosmological constant, expanding understanding of universe backgrounds with negative cosmological constant.

Findings

Electromagnetic field and cosmological constant are interdependent.

The solution suggests a lower value for the absolute cosmological constant.

Defines the universe's lifetime as a function of the negative cosmological constant.

Abstract

An exact solution of the current-free Einstein-Maxwell equations with the cosmological constant is presented. The solution is of Petrov type D, includes the negative cosmological constant, and could be a ``background addition'' to the present-day models of the universe. It has a surprising property such that its electromagnetic field and cosmological constant are interdependent (this constant is proportional to the energy density of this field), which may suggest a new way of measuring the constant in question. The solution describes a constant electromagnetic background with a preferred direction in the universe, and defines the entire lifetime of the universe as a simple function of the negative cosmological constant. According to our solution the absolute value of this constant should be considerably lower than that recently estimated, when astrophysical data are taken into account. Our solution is a special case of that published by Bertotti in 1959. His solution (in terms of which the cosmological constant and the background electromagnetic field are independent) and its two other special cases, i.e. the conformally flat Robinson solution (1959) and the one which is the counterpart of our solution with the positive cosmological constant, are briefly discussed.