A black hole in space is, just, a collapsed star. So there shouldn’t be any surprise that it can do work on objects in its vicinicity in space. A star doesn't ``disappear'', upon collapsing, it remains, albeit in another guise-that's how ``real'' black holes can be sought after and found.

On the other hand, it’s a classical object, so the relevance of the Casimir force, or any quantum effects, isn’t obvious. It is true that the vacuum of quantum fluctuations, in the presence of a black hole, isn't uniquely defined, so a quantum probe of the vicinity of a black hole would detect a thermal bath. And such a quantum probe,, will, of course, feel pressure, due to this thermal bath. That shouldn't be surprising, either. I think the popular account of the technical paper is misleading, unfortunately.

But the temperature of this bath is very low, for astrophysical black holes, and it is relevant at distances so close to the black hole (as a collapsed star) to be irrelevant for astrophysical objects. That's why the classical work done by an astrophysical black hole, on objects in its vicinity, that are quite ``far'' from it (in Planck units), isn't sensitive to these fluctuations.

What is interesting is that, while, for an ordinary star, the corresponding calculation does depend on its equation of state, for a collapsed star (i.e. a black hole), it doesn't.

Dear Mr. Stam Nicolis,

Thanks for the extensive answer. However, my proposed black-hole-associated Casimir force (bhaCF) isn't directly generated by the (thermal bath-like) vicinity of that black-hole (bh), but by the gradient in the number of virtual pairs (VPs) (which are predicted to be in a much larger number per unit of volume outside that black-hole than inside it, as the appearance of those VPs inside that bh is predicted to be strongly and partially inhibited by the very large density of that bh, thus by the much less availability of "free space/volume" inside that bh). It is this large positive gradient in the number of VPs (per unit of volume, outside vs inside) which is predicted to generate that bhaCF (acting from outside-to-inside) which also generates a reactional force (acting from inside-to-outside, on the surrounding space) which manifests as a pressure exerted by that bh on its surrounding space (which surrounding space primarily exerts that bhaCF on that bh).

I hope that I have made myself more clear now.

Best regards and best health possible!

Andrei

Dear Andrei,

Thanks-it's clearer, but there do remain some issues that require further thought, I think.

One problem that I can see is the statement about the high density of the black hole. That would be true for the star-and that's where the known quantum properties of matter lead to conditions, under which collapse is even possible (what Chandrasekhar found, for instance). Once the collapse has taken place, however, the statement about the density isn't that obvious and just what is ``the interior'' is not at all clear. This paper: Preprint The elastic vacuum

I'd also like to point out that the idea about a Casimir force and about the relevance of virtual pairs was the idea of Hawking-which is nice to know, since you have understood something correctly, however it would be a good idea to be careful with the details. This paper: Article ENTANGLEMENT AND THERMODYNAMICS OF BLACK HOLE ENTROPY

might be of interest, also.

Regarding the fluctuations, this: Article Stochastically Fluctuating Black-Hole Geometry, Hawking Radi...

A very nice review is this one: Article A primer for black hole quantum physics

Indeed a ``puzzle'' is that, once it's recognized that a black hole does have a temperature, it's expected to have a pressure; but the pressure depends, apparently, on the equation of state, which, for a black hole, isn't at all obvious. That's what Calmet and Kuipers actually study.

The pressure, apparently, can be identified with the cosmological constant of the spacetime geometry, described by the black hole metric:

These papers: Article Benchmarking Black Hole Heat Engines

Article Benchmarking Black Hole Heat Engines, II

It's a huge subject, so, of course, it's nice, on the one hand, to understand things by yourself and, on the other, to see how these are related to what others have understood!

Best regards and best wishes for good health to you, too!

Stam

Dear Mr. Stam Nicolis,

Thanks for the extensive answer and reference.

However, there is no strong evidence that rest masses of the absorbed particles aren't conserved inside a black hole (BH) (which keeps its 3D volume relatively constant when absorbing those particles) thus the density of BH progressively increases (at least in what is measured from outside that BH, as my bhCF is also an outer phenomenon). This is a fact: the other ideas on what happens inside that BH are mainly speculations (as the reference frame of measurements remains outside, as also detailed next). Furthermore, even the big G may vary at the BH horizon.

In the case of various elementary particles (EPs) nature can reach massic densities much higher than a BH: for example, in the case of the electron (which has a rest mass of about 10^(-31)kg concentrated in a volume under r_x^3, with r_x=10^(-22) being the electron mass radius upper bound as determined by Penning traps) nature can reach massic densities up to 10^35kg/m^3 (and that is only the lower bound!). My proposed bh-associated Casimir Force (bhCF) theory predicts that, in the case of an electron for example, the apparition of virtual pairs (VPs) inside that r_x^3 volume is so strongly inhibited that bhCF should be huge (and should exert a huge pressure from outside to inside that micro-volume in which the electron confines). That bhCF may actually explain why the shape of the VP cloud from around that electron is almost perfectly spherical (see URL: https://www.bbc.com/news/science-environment-13545453) and doesn’t deform even in relativistic regime. What do you think about that? Do you have another explanation on the spherical shape of the VP cloud surrounding an electron? Furthermore, this perfect spherical shape of the VP cloud suggests that the electron is also most probably a spherical object (possibly an extreme micro/quantum BH) and that the spherical-shaped VP cloud is its “mold” (see URL: https://en.wikipedia.org/wiki/Black_hole_electron)

I think that my hypothetic bhCF offers a unified view on both macrocosmic and micro-BH and suggests that all elementary particles with non-zero rest masses (nzrm) (not just the electron) may be actually extreme (but stable!) quantum BHs.

What is more interesting about the electron (a kind of BH-like attribute)

is that the electron (/positron) the lightest known electromagnetically charged EP, with a special significance implicitly: the rest mass of the electron may have a profound significance on the minimum mass needed for any EP to can posses electromagnetic charge (emc), as if emc is “storable” only on a finite minimum “amount” of nzrm. I’ve extensively treated that observation in some older papers of mine:

No electromagnetic charge and no photon without gravity: the electromagnetic field (EMF) as an epiphenomenon caused by the gravitational field (GF)

https://www.researchgate.net/publication/341598164_EpiphenEMF_-_v10_-_23052020

A proposed set of relatively new conjectures and hypotheses in modern physics, mainly the concept of subquantum movement (SQM), the finite “elasticity” of spacetime hypothesis (FESTH), the self-repulsiveness of electromagnetic charge (SR-EMC) and the plausible gravitational significance of the fine structure constant (GS-FSC)

https://www.researchgate.net/publication/338983106_FESTH_-_v10_-_2022020

On a possible logarithmic connection between Einstein's constant and the fine-structure constant, in relation to an electro-gravitational resistivity of vacuum (EGRV) and to a zero-energy hypothesis (this paper is however NOT between the winning papers of this 2020 essays contest)

https://www.researchgate.net/publication/340132361

Integrating the speed of gravity in Newton's gravitational law, we're it probably… belongs: the universal gravitational constant (big G) is very plausibly not a true constant, but only a composite quasi-constant depending on a slightly variable speed of gravity and an electro-gravitational resistivity of (quantum) vacuum (EGRV)

https://www.researchgate.net/publication/339687819

A very short summary of my Amazon book called "SUSYA -a SUSY alternative based on a newly proposed electro-gravitational seesaw mechanism applicable to all elementary particles (and organizing them in boson-fermion pairs of 'mass-conjugates')"

https://www.researchgate.net/publication/355163505

SUSYA – a SUSY alternative based on a newly proposed electro-gravitational seesaw mechanism applicable to all elementary particles

https://www.researchgate.net/publication/353391432

A proposed electro-gravitational seesaw mechanism applicable to all elementary particles and offering an alternative to SUSY

https://www.researchgate.net/publication/350090267

A proposed electro-gravitational seesaw mechanism applicable to all elementary particles, offering a SUSY alternative and predicting the existence of two distinct types of massless right-handed Majorana neutrinos that may compose a fermionic aether

https://www.researchgate.net/publication/350089930

See also my ORCID page for the peer-reviewed article versions of some of the listed preprints:

www.orcid.dragoii.com

Best regards!

Andrei

Here is a new article that may have subtle connections with my bhCE hypothesis (as bhCE may mediate the coupling between the accelerated expansion of our universe and black holes compressed by my proposed bhCF).

https://phys.org/news/2021-11-expansion-universe-impacts-black-hole.html

If dark matter is actually the sum of all existing primordial black holes (pBHs) (https://scitechdaily.com/black-holes-could-be-dark-matter-and-may-have-existed-since-the-beginning-of-the-universe/), THEN my proposed bhCE would more plausibly explain the universal accelerated expansion of our universe (thus dark energy) by the pressure exerted by all these pBHs on their surrounding space (which pressure is the reaction force of my proposed BH-associated Casimir force).