Why are black holes stable against their own gravity?

Neutron stars are time-like matter, with a maximum mass of about 2.34 solar masses in quantum chromodynamics (the strong color force). Black holes are space-like matter, which have no maximum mass, but a minimum mass of 2.35 solar masses. Indeed, black holes have been identified as having millions or billions of solar masses.

All time-like matter is causal, whereas the space-like matter of black holes is acausal. Acausal space-like matter has no identifiable particle states (everything is off-mass in the space-like region), no Pauli principle, no equations of motion, no hydrostatic stability equation, no equations of state, no entropy, no temperature, no Planck constant, no Boltzmann constant, no finite-temperature quantum field theory.

The only quantities a black hole has are gravitational invariants, which are observable at infinity, and the scalar curvature R. Functions of gravitational invariants are also gravitational invariants such as its volume, area, radius, etc.

Gravitational manifolds are metric spaces that have isometric symmetries, and these gravitational invariants are invariants under these symmetries. If the metric space is Minkowski space, the isometric symmetries are just the well-known Poincaré group.

Black holes are stable objects with no maximum mass

Black Hole Pressures — P_Sthe external pressure that keeps it inflated because of the negative scalar curvature, and P_M the internal pressure of self-gravity trying to compress it — are gravitational invariants. In the proof that P_S = -P_M it is shown that the equilibrium is also stable and that a universal black hole constant appears F = 3c⁴/4G = 9.077…x10⁴³ N.

All black holes have the same force constant F that inflates them, regardless of their mass. It is this new universal constant of black holes that explains why black holes have no maximum mass.

This universal force constant has two immediate consequences:

(1) The greatest pressure in the universe, P_universeis a physical and computable observable. The smallest black hole has the highest pressure in the universe. Using the estimated minimum of 2.35 solar masses mentioned earlier, we obtain P_universe = 1.5183…x 10³⁵ N/m²This is an incomprehensibly large value, so we can compare it to Jupiter’s estimated central pressure P_Jupiter = 650 x 10⁶ pounds/inch² (NASA website — uses British units), which gives P_universe/P_Jupiter = 3.3878…x10²²still beyond human understanding.

(2) There is an area law for black hole coalescence, but it is not a Hawking assumption and has nothing to do with entropy. For two coalescing black holes to form with pressures P₁ and P₂ in the volume, leaving a residue with a pressure P₃it is necessary that P₁+P₂ > P₃otherwise the rest cannot exist. Since the pressures are P = F/area, with a universal force constant F, this gives the real law for the black hole coalescence area, involving reciprocal areas 1/A₁ + 1/A₂ > 1/A₃The available gravitational wave data are consistent with this reciprocal coalescence zone law. The existence of the universal black hole constant controls the coalescence of black holes.

The question of black hole singularities

Applying causality to acausal space-like matter always leads to contradictions. The widely cited claim that black holes have a singularity is based on a misapplication of Einstein’s causal equations of motion to acausal black holes, producing a false singularity, see Figure 2.

This equation is a contradiction, because scalar curvature is gravitationally invariant on the left side, but the right side has spherical coordinates, which are not gravitationally invariant. In the paper published in Reports on progress in physical sciencesIt is thus proven that black holes do not have singularities.

Contradictions always arise if causal physics is applied to black hole-like matter.

Contradictions arise if causal finite-temperature quantum field theory is diverted to spacelike acausal black holes: in a frequently cited reference, Hawking made exactly this diversion and stated that black holes have a temperature and evaporate their mass, reaching the vacuum state.

Where is the contradiction we expect when causal physics is applied to spacelike acausal black holes? If black holes really radiated, their mass would indeed approach zero, but as Figure 1 shows, their negative scalar curvature R does not tend to zero, but rather to negative infinity: the final state of the black hole is not the required vacuum state R = 0. This is the contradiction that arises from the mistaken appropriation of the causal theory of finite temperature fields to spacelike acausal matter.

Renormalization of the scalar curvature R

One of the goals of general relativity is the renormalization of R in four-dimensional spacetime. It is shown in a 2018 paper that the renormalization of R in finite-temperature quantum field theory satisfies the same theorem as the renormalization of the thermodynamic potential.

Both of these quantities are physical observables that have no “legs” (i.e., no external Green functions) in Feynman diagrams. The “infamous” prediction of quantum field theory that the energy density of the electroweak vacuum is 10¹²⁰ orders of magnitude higher than the experimental vacuum energy density is a false statement, because this constant term vanishes in the renormalization theorem of the thermodynamic potential.

Finally, it can be said that the planet Jupiter, due to causality, is undoubtedly a much more complex object than an acausal black hole.

This article is part of Science X Dialog, where researchers can present the results of their published research papers. Visit this page for information about Science X Dialog and how to participate.

Dr. Peter Morley is a theoretical physicist. A partial list of his papers is available here: inspirehep.net/authors/996788