Summations Only

Negative pressure is not 'anti gravity' in the technical sense (which may require negative mass) - only in a colloquial sense. It's easy to get confused on that, though.

You really do need to realise just how little you understand here, and just how much pure gibberish you are spouting.

Gravitation is not energy so the question makes no sense.

The gravitation field is described by a tensor field, and so cannnot be simply "negative".

No, it most certainly is not. Consider any of the vacuum solutions of General Relativity.

Abusive ad hominem (also called personal abuse or personal attacks) usually involves insulting or belittling one's opponent in order to attack his claim or invalidate his argument...

Part (b) shows how energy can be extracted as the shell is allowed to uniformly contract. Each piece of the shell is tied by a rope to an electrical generator, producing power as the piece is lowered toward its final position.

The basic idea is that gravity "wants" to pull things together. If no other forces counteract it, gravity will do so. In principle, this gravitational force could be harnessed to do work on an external device such as a generator. (Force times distance equals work or energy.). This extracts energy from the gravitational field.

But since energy is conserved, and positive energy has been extracted to the generator, the gravitational field must contain negative energy.

Why choose a convention where gravitational energy is negative?Gravitational potential is a scalar potential energy per unit mass at each point in space associated with the force fields. Notice at r tends to infinity, ϕ tends to 0 :.
As with all potential energies, only differences in gravitational potential energy matter for most physical purposes, and the choice of zero point is arbitrary. Given that there is no reasonable criterion for preferring one particular finite r over another, there seem to be only two reasonable choices for the distance at which U becomes zero: r = 0 and . The choice of U = 0 at infinity may seem peculiar, and the consequence that gravitational energy is always negative may seem counterintuitive, but this choice allows gravitational potential energy values to be finite, albeit negative.
The singularity at r = 0 in the formula for gravitational potential energy means that the only other apparently reasonable alternative choice of convention, with U = 0 for r = 0, would result in potential energy being positive, but infinitely large for all nonzero values of r, and would make calculations involving sums or differences of potential energies beyond what is possible with the real number system. Since physicists abhor infinities in their calculations, and r is always non-zero in practice, the choice of U = 0 at infinity is by far the more preferable choice, even if the idea of negative energy appears to be peculiar at first.
The negative value for gravitational energy also has deeper implications that make it seem more reasonable in cosmological calculations where the total energy of the universe can meaningfully be considered; see inflation theory for more on this.

Not only do you know nothing about the topic, you don't even know what an ad hominem is.

Calling you a twit for the sole purpose of alerting others to your twithood with no intent to attack your claim or invalidate your argument is not ad hominem...