Question: are there conditions under which a universe uniformly filled with charged matter will expand isotropically and is it allowed to take the shear of an expanding charged fluid to be zero?

Detail: I've been working to understand what happens to the cosmic scale factor if the universe is, on the large scale, a uniform fluid with gradually increasing charge. Even the constant charge case is of interest. In my research online I have found references to an early paper

H. Bondi and R. A. Lyttleton, Proc; Roy. Soc. 252A (1959), 313

in which, I believe, the authors find that the charge, if its density is sufficiently more than the mass density, drives isotropic expansion of space. I believe that the shear is assumed to be zero in this work.

Then I found

Raychaudhuri and De, 1970, Charged-dust distributions in general relativity

which includes a fairly general theorem that a charged dust cannot expand or contract without shear (and therefore does not expand isotropically).

And then

De, 1972, Collapse of a Charged Dust Distribution

in which the symmetry constraints seem to allow a universe filled with a uniform charged fluid and in which shear seems to be a prime culprit in guaranteeing a collapse no matter how great the charge density is.

Many more recent papers study shear-free expansion and collapse of charged matter, with an example having a formalism I personally liked being

Kouretsis & Tsagas, 2010, Raychaudhuri’s equation and aspects of charged collapse, https:/arxiv.org/abs/1010.4211v1

In eqs 30, 31 and 32 of this last paper, shear is set to zero and conditions for the charged matter driving isotropic expansion of space are once again presented.

So what's the deal? Is it unphysical to set the shear to zero? How would the cosmic scale factor of a uniformly charged universe actually behave?


1 Answer 1


Here's the answer I came up with. The charged dust universe of Bondi and Lyttleton contemplates a bounded charged dust expanding into empty space. This universe is obviously not homogeneous.

In a homogeneous universe filled with charged dust the Faraday tensor must be zero everywhere by symmetry (in spite of the charge) making the Einstein-Maxwell equation reduce to the standard Einstein field equation. Electromagnetism plays no role in determining the spacetime geometry.

  • 2
    $\begingroup$ I thought about the same problem and reached the same conclusion about 20 years ago when I was doing my undergraduate thesis. However, intuitively I still think it is strange that a uniformly charged universe is the same as one with no charge. $\endgroup$
    – DFJ
    Jan 6, 2021 at 4:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.