Gravitational non linearity: the glue of Black Holes

[Naty1]

Any comments on the following description from Kip Thorne, BLACK HOLES AND TIME WARPS, 1994, Box 10.1 would be appreciated. It seems odd to me that at some given curvature, gravity would become self sustaining...if that is what he is saying.

...When spacetime curvature is weak [as in the solar system]... [gravity] is weak...Einsteins general relativistic laws predict the curvature ...of BH and at the Big Bang.. should be among the most non linear phenomena in the Universe...as yet we possesses almost no experimental or observational data to show us the effects of gravitational non linearity [GNL] and we are so inept at solving Einsteins equation that our solutions have taught us about the non linearity only in simple situations...for example around a quiescent spinning BH.

A quiescent BH owes its existence to gravitational non linearity [GNL]; without the GNL the hole could not hold itself together just as without gaseous non linearities the great red spot on the plant Jupiter could not hold itself together. When the imploding star that creates a BH disappears through the hole's horizon the star loses it ability to influence the hole in any way; most important, the star's gravity can no longer hold the hole together. The hole then continues to exist solely because of GNL without the aid of the star and the self generated curvature acts as a nonlinear glue to bind itself together.

We have previously discussed in these forums that the current causal event horizon is affected by any future growth of the black hole... and the causal event horizon grows in anticipation or a BH merger or in-falling mass-energy. Can those effects be reconciled with the above description or do you think Thorne's 'quiescent' discussion is too simple to account for any accretion?? [that's my take]

 

[PeterDonis]

It seems odd to me that at some given curvature, gravity would become self sustaining...if that is what he is saying.

It is. But note that it's not "at some given curvature", because the curvature at the hole's horizon varies inversely with its mass. For a large enough hole, curvature at the horizon is negligible, so the formation of a horizon, which I think is basically what Thorne means by "the hole holding itself together", can't be a function of curvature.

We have previously discussed in these forums that the current causal event horizon is affected by any future growth of the black hole... and the causal event horizon grows in anticipation or a BH merger or in-falling mass-energy. Can those effects be reconciled with the above description

Sure. Any time additional matter falls into the hole, it works similarly to the collapse of the matter that intially formed the hole. Once the matter falls through the horizon, it can't hold the hole together at its new, larger mass. So the hole holding together at its new, larger mass must be due to GNL, just as the hole holding together at its original, smaller mass was. It's the same thing.