The existence of super massive black hole (BH) in the center of the giant elliptical galaxy M87 was demonstrated by the Horizon Telescope Collaboration (EHT) that produced a first image of the dark shadow caused by gravitational light bending and photon capture at the event horizon [1] . The EM radio-wave observations provide powerful evidence for the presence of supermassive Kerr black holes in centers of galaxies that act as the central engines of the active galactic nuclei (AGN).

According to Corley and Jacobson [2] , BHs that have ergoregions with an inner and an outer event horizon where a superluminal dispersion relation exists in their ergoregions, enhance exponentially in time the creation of boson particles in their ergoregions. The rotating BH ergoregions act like laser cavities that enhance exponentially the otherwise extremely weak Hawking radiation [3] . The Hawking process for a bosonic field becomes self-amplifying and the radiated flux grows exponentially in time, where the negative energy partner of the Hawking particle, after falling to the inner horizon, “bounces” and returns to the outer horizon ergosphere on a superluminal trajectory, where it stimulates more Hawking radiation bosons. Corley and Jacobson suggested that a bound state trapped between the ergoregion horizons is created and the particle creation increases monotonically with time, diverging as t → ∞ for a discrete set of frequencies.

Radiating Kerr black hole and Hawking radiation is studied by Chou [4] that estimated the Hawking-radiation temperature of black holes with the angular momentum and the same mass of Pluto to be 9.42 K. Brito et al. [5] [6] studied the Superradiance instability of black holes immersed in a magnetic field. Superradiance in BH ergoregions allows for energy, charge and angular momentum extraction at the classical GR level where Hawking radiation can be interpreted as a quantum version of black-hole Superradiance. Negative energy-states are dumped in the ergoregions and amplification of outgoing waves occurs on the ergosphere boundary surface in both the classical GR equation Superradiance solution and the black hole laser process based on Hawking radiation.

Superradiant pion clouds around primordial black holes are studied by Ferraz et al. [7] that showed that highly spinning primordial black holes may produce clouds of pions in their vicinity via the superradiant instability with densities up to that of nuclear matter. Superradiant amplification of low-frequency wave modes results from the dissipative nature of a black hole’s event horizon, combined with rotation in the Kerr case, and it is the trapping of such modes in the black hole’s vicinity that leads to continuous amplification of the pion production.

Since the u d ˜ d u ˜ exotic meson [8] is its own antimatter boson particle and assuming that superluminal dispersion relation exists in SMBH ergoregions where the QCD gas density is extremely high, we suggest here a method to determine if its density is further amplified and radiated to space by the Corley and Jacobson ergoregion laser process [2] or similarly by Superradiance [5] [6] .

The following pseudo-first order β decay (Equation (1)), the β decay rate (Equation (2)), the QCD gas atmospheric density (Equation (3)), the QCD gas mass formula (Equation (4)) and the equation of state parameter, w [8] , derived in a previous paper [9] proposed an alternative explanation for the observed β decay rate variability [10] [11] .

u d d ( n ) + u d ˜ d u ˜ ( exoticmeson ) → u d u ( p + ) + d u ˜ d d ˜ (1)

t 1 / 2 = 1 k β ρ ( h ) (2)

ρ ( h ) = ρ ( h 0 ) e − m Q C D   g a s G M s u n ( h − h 0 ) h 0 2 k b T (3)

m Q C D   g a s = − k b T h p e r i h e l i o n 2 ln ( t 1 2 , p e r i h e i l i o n t 1 2 , a p h e i l i o n ) G M s u n ( h a p h e l i o n − h p e r i h e l i o n ) (4)

w = G M s u n ( h a p h e l i o n − h p e r i h e l i o n ) − h p e r i h e l i o n 2 ln ( t 1 2 , p e r i h e i l i o n t 1 2 , a p h e i l i o n ) c 2 (5a)

w ~ − 3.4091 − 10 t 1 2 , a p h e i l i o n Δ t , Δ t = t 1 2 , a p h e i l i o n − t 1 2 , p e r i h e i l i o n (5b)

Here, we generalize this approach to galactic SMBH systems. The sun trajectory is not an exact ellipse; however, an eccentricity on the order of about 5% in the range of e = 0.02 - 0.08 is assumed. The perihelion and aphelion of the sun trajectory are estimated to be about 26,000 and 28,000 light years and the sun period is about 230 million years around the galaxy center SMBH, Sagittarius A. We propose performing the β decay rate measurement and the distance to Sagittarius A measurement at the earth’s aphelion day every year in a sequence for several years, for 10 - 20 years for example, and fitting the measured data by a linear curve. The inputs for the fit are the β decay rate t 1 / 2 and the distance to Sagittarius A, h S M B H .

We assume that the galactic QCD gas density drops from the SMBH ergosphere as a function of elevation according to Equation (6) below and propose to fit the data with the linear plot of the logarithm of the measured β decay rates as a function of the distance of earth at aphelion to the galaxy SMBH given by Equation (7). The linear fit parameters, a and b, are given by Equations (8) and (9).

ρ ( h S M B H ) = ρ ( h e r g o s p h e r e ) e − m Q C D   g a s G M B H ( h S M B H − h e r g o s p h e r e ) h e r g o s p h e r e 2 k b T (6)

− ln t 1 / 2 = a h S M B H + b (7)

a = − m Q C D   g a s G M B H h e r g o s p h e r e 2 k b T (8)

b = m Q C D   g a s G M B H h e r g o s p h e r e k b T + ln k β ρ ( h e r g o s p h e r e ) (9)

From the slope parameter, a (Equation (8)), we can calculate the SMBH ergosphere radii h e r g o s p h e r e and from it we can calculate further the Kerr spin parameter a s p i n , which is hard to determine experimentally [12] [13]

h e r g o s p h e r e = G M B H c 2 ( 1 + 1 − a s p i n 2 ) (10)

From the free parameter, b (Equation (9)), we can determine if the QCD gas density on the ergosphere remains constant in time, or alternatively, grows in time as predicted by Corley and Jacobson Kerr BH laser cavity process [2] . In the latter case, a deviation from the linear fit will be seen since the second term in Equation (9), e.g. ln k β ρ ( h e r g o s p h e r e ) , will change with time.

We proposed in the previous paper [9] that the u d ˜ d u ˜ exotic mesons condense into a new strongly bound peculiar positronium/quarkonium state introduced by Crater and Wong’s Two Body Dirac Equation (TBDE) approximate solution [14] [15] . We further assume here that in SMBH ergoregions the pressure is extremely high such that 2 u d ˜ d u ˜ exotic mesons may combine and form the following short-lived octaquark and a 16-quark exotic mesons:

2 u d ˜ d u ˜ ( exoticmeson ) → u d ˜ d u ˜ d d ˜ u ˜ u ( octaquarkmeson ) (11)

2 u d ˜ d u ˜ d d ˜ u ˜ u ( octaquarkmeson ) → u d ˜ d u ˜ d d ˜ u ˜ u u d ˜ d u ˜ d d ˜ u ˜ u ( 16-quarkmeson ) (12)

Octaquarks exotic mesons may decay to neutrons, protons, and short-lived pions where the antimatter particles, antineutrons d ˜ u ˜ d ˜ ( n ˜ ) (Equation (16)) and antiprotons d ˜ u ˜ u ˜ ( p ˜ ) (Equation (18)), are trapped in the BH ergoregions and the matter particles are emitted to space by Hawking radiation as described by Equations (13)-(16) below.

u d ˜ d u ˜ d d ˜ u ˜ u ( octaquarkmeson ) → u d d u ˜ u ( n ∗ ) + d ˜ u ˜ d ˜ ( n ˜ ) (13)

u d d u ˜ u ( n ∗ ) → u d u ( p + ) + d u ˜ ( π − ) → u d u ( p + ) + e − + ν ˜ e (14)

u d ˜ d u ˜ d d ˜ u ˜ u ( octaquarkmesom ) → u d u d ˜ d ( p + ∗ ) + d ˜ u ˜ u ˜ ( p ˜ ) (15)

u d u d ˜ d ( p + ∗ ) → u d d ( n ) + u d ˜ ( π + ) → u d d ( n ) + e + + ν e (16)

Note that in Equations (16) and (18) the excited neutron n ∗ and proton p + ∗ are exotic pentaquarks that include a u ˜ u and d ˜ d mesons that may trigger the quark and antiquark pair exchanges inside the nucleons.

16-quark exotic mesons may decay into deuterons and compact tetraquark u d ˜ d u ˜ ( bosons ) where the antideuterons d ˜ u ˜ d ˜ u ˜ d ˜ u ˜ ( n ˜ + p ˜ − ) (Equation (20)) are trapped in the BH ergoregions and the deuterons and u d ˜ d u ˜ ( exoticmeson ) are emitted to space by Hawking radiation.

u d ˜ d u ˜ d d ˜ u ˜ u u d ˜ d u ˜ d d ˜ u ˜ u ( 16-quarkmeson ) → u d d u u d ( deuteron ) + d ˜ u ˜ d ˜ u ˜ d ˜ u ˜ ( antideutron ) + u d ˜ d u ˜ ( boson ) (17)

Thus, if the QCD gas density is extremely high in the AGN SMBHs’ ergoregion, octaquark and 16-quark short-lived exotic mesons may be produced and decay into protons, electrons, neutrons and deuterons on the ergospheres and emitted to space by Hawking radiation. The BH laser amplification process of the proposed QCD gas exotic mesons in BH ergoregions suggests that matter and antimatter symmetry may be broken by the Hawking processes (note Equations (13)-(16)), where the antimatter particles remain trapped in the BHs’ ergoregions.

We propose to measure the β decay rate, t 1 / 2 , and the earth distances to Sagittarius A, h S M B H , at the earth aphelion for several years and fit the data with a linear curve: − ln t 1 / 2 = a h S M B H + b . The slope parameter, a, and the free parameter, b, may be used to calculate the Kerr spin parameter and determine if the QCD gas density on the ergosphere remains constant in time or alternatively grows in time.

Corley and Jacobson showed that boson particle creation may be amplified exponentially in time in rotating BH ergoregions and ergospheres [2] . Brito et al. showed that a BH immersed in a magnetic field has classical Superradiance instability [5] [6] . Ferraz et al. showed that highly spinning primordial black holes may produce clouds of pions via their superradiant instability [7] . Romero et al. showed that AGNs’ SMBHs may act under certain conditions as matter creator engines emitted to space by relativistic jets [13] . Kaburaki et al. showed that rotating black holes in strong magnetic fields may act as Carnot engines, where work is extracted from the BH in the form of electric current that flows along the poloidal field [16] . If the proposed linear fit of the β decay rate measurements [10] will indicate that the QCD gas density on the Sagittarius A ergosphere grows in time, SMBH ergoregions act as matter reactors that break matter and antimatter symmetry by trapping the antimatter particles in their ergoregions and may act as matter sources for a Quasi-Steady State Cosmology (QSSC) model [17] [18] .

The author declares no conflicts of interest regarding the publication of this paper.

Rom, R. (2023) Matter Reactors. Journal of High Energy Physics, Gravitation and Cosmology, 9, 455-460. https://doi.org/10.4236/jhepgc.2023.92033