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Generally speaking, the universe is electrically neutral and the universe abhors an unbalanced charge. Wherever there is a positively charged object, you can bet there is a negatively charged object not far away.

However, no laws of physics prevent the accumulation of positive charge, say, so long as the negative charge is sent somewhere else. This must be true on a cosmic scale as well.

Hence my question:

What is the most electrically charged celestial body in the universe, and what is its charge, i.e. positive or negative?

Dipoles don't count.

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You said that:

no laws of physics prevent the accumulation of positive charge, say, so long as the negative charge is sent somewhere else. This must be true on a cosmic scale as well.

This is not accurate. Charge conservation is important, but isn't everything - there is also the local forces that extra positive charges (for example) exert on one another. The problem is that the electromagnetic force is much, much, much, much stronger than gravity - the electric force between two electrons is is $2.4∗10^{43}$ times (24 million trillion trillion trillion times!) stronger than the gravitational force between these two electrons.

Other people asked whether we could have Electron or Proton stars, like we have Neutron starts - see Can there be Electron and/or Proton Stars? and Could electron "Stars" exist? and the answer is no: If a star had just one extra charge for each $1*10^{18}$ particles, the star would basically blow up instead of remaining gravitationally bound.

So for your question,

What is the most electrically charged celestial body in the universe, and what is its charge, i.e. positive or negative?

When it comes to stars, I guess the number $1 * 10^{-18}$ extra charges per particle above is an upper bound for the charge of a star made of matter and held together by gravity.

For charged black holes, the calculation is different - see https://en.wikipedia.org/wiki/Extremal_black_hole.

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You really can't make macroscopic bodies that have a (large) net charge. This is a consequence of the many orders of magnitude stronger nature of the electromagnetic force and the fact that "gravitational charge" comes with only one sign. You can to some extent end up with a charge on a body because the gravitational attraction felt by electrons and positive ions is different, whereas both feel a similar Coulomb force. (i.e. It is easier for a stellar wind to carry away electrons than protons).

You can however create large charge imbalances within macroscopic objects - i.e. you can separate positive and negative charge. The most extreme example of this is probaby at the magnetic poles of rapidly rotating neutron stars. The rapid rotation means that charges move relative to the field lines and thus there is a magnetic Lorentz force (opposite for opposite charges) that separates the charges until the consequent electric field builds up sufficently to match the magnetic Lorentz force. This leads to a charge build up at the poles and charge of the opposite sign at lower latitudes. The consequent electric fields are sufficient to accelerate charged particles outwards along the magnetic field lines. This is the Goldreich & Julian (1969) model of pulsar magnetospheres, which is still used as the basic picture.

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The only way to estimate the net charge of a star is to calculate its gravitational lensing and compare it to if the star was uncharged using GR.I dont think anyone has done this and we probably wouldnt learn anything new from the process except maybe validating GR once more.

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