Recently, a unicentric model of our observable universe was proposed. Accordingly, the big bang was neither a singular event nor invoked by external forces, but rather a frequent event in cosmic life cycles that occur sequentially or in parallel at the same and/or in different locations of our infinitely large, flat, homogeneous, and isotropic parent universe. The progenitor of our big bang is predicted to have been of a measurable size and happened to be in our neighbourhood. Based on theoretical arguments and general relativistic numerical calculations, it is argued that: 1) The surface of the progenitor is most appropriate for the hadron flash to run away; 2) The structure of the progenitor is immune to self-collapse into a hyper-massive black hole; and 3) The power and acceleration of high-redshift galaxies may be connected to the BB-explosion. We conclude that the currently observed high-redshift galaxies must have been old and inactive in older times, but turned into life through matter and momentum transfer from the fireball and the collision of the locally curved spacetime embedding the galaxy with the expanding one embedding the fireball. With the present scenario, the origin of the monstrous black hole candidates with MBH ≥109Me , that are believed to have resided at the centre of galaxies when the observable universe was 400 Myr old, could be straightforwardly explained. This implies that QSOs with ever higher redshifts should exist, though their detection becomes increasingly harder.
The state of matter inside the cores of massive neutron stars is probably one of the greatest secrets of the universe [
Indeed, careful inspection of the recent astronomical observations of high-redshift quasars, dark matter-dominated galaxies, mergers of neutron stars, glitch phenomena in pulsars, the missing first generation of massive neutron stars, the missing stellar mass black holes with M B H ≤ 6 M ⊙ , the cosmic microwave background radiation and experimental data from hadronic colliders, may not rule out this hypothesis, but they may support it indirectly [see [
Numerical modeling of the interiors of Ultra-Compact Objects (UCOs), such as massive Neutron Stars (NSs), pulsars, and magnetars, predict the central density, ρ c , to be much higher than the nuclear density ρ 0 [
Here, the sound speed is expected to regulate the communications between their constituents, which, in a supranuclear dense regime, should be equal roughly to the speed of light. The related consequence here is that the cores of massive NSs are well-equipped to resist all possible external perturbations, including compression by external forces. Indeed, recent theoretical and observational studies of the merger of neutron stars in GW170817 may support this hypothesis, as to date, there is no conclusive observational evidence that pinpoints a collapse of the remnant into a stellar black hole [
Further inevitable consequences are: 1) Formation of black holes in the classical sense may turn out to be just a mathematical solution, though not necessarily physical. This may support Einstein’s objection to the existence of BHs [
These indicate that our observable universe is a unicentric one, and that the cosmological principle may still hold, though not locally, but for the parent universe [
In this paper, we suggest possible answers to certain questions related to this scenario, namely: 1) Why hadronization of the progenitor must start at the surface and proceed inwards, rather than from the center outwards; 2) Without invoking inflation, how it was possible for the progenitor to escape collapse into a Supermassive Black Hole (SMBH); and 3) Could the power and acceleration of high-redshift galaxies be connected to the explosion of the BB-progenitor triggered by the hadronization process?
Based on the theoretical and observational arguments, it was argued in [
• The embedding spacetime of incompressible supranuclear dense matter with zero entropy must be flat.
• The supranuclear dense matter inside the cores of dead and massive NSs should be in an incompressible super-conducting superfluid state, termed SuSu-matter, which corresponds to the lowest quantum energy state.
• Similar to the cores of massive glitching pulsars, the interaction between the progenitor and the ambient media occurs at the interface between the enclosed flat and the ambient curved spacetime.
We note that there are at least four counterarguments opposing the conjecture that the hadron flash would have started the runaway process precisely at the center of the progenitor:
• The geometrical center of the progenitor, say r = 0 , in a perfectly homogenous and isotropic environment is ill-defined. Unlike in normal stars, where ∇ P = ∇ ρ = 0 at r = 0 , in perfectly homogenous and isotropic environment the physical properties at any point are identical.
• The topology of spacetime inside SuSu-matter cannot be communicated to the outside world by construction, as otherwise, gluon-quark superfluid would be transparent to outside observers.
• In the absence of theoretical mechanisms, such as inflation [
• In the absence of inflation and in a supranuclear dense and cold environment, it is not clear, why the hadron flash should run away rather than stifling by the weight of the overlying matter.
• Exploring the internal structure of hadrons in labs is based on violently shaking their confining membranes from outside, rather than from inside.
To study how the topology of spacetime embedding the progenitor evolves with time relative to our preferred observer, H 0 at the center of the progenitor, a new time-dependent H -metric was proposed [
d s 2 = g μ ν d x μ d x ν = g 00 d t 2 + g 11 d r ¯ 2 + g 22 d θ 2 + g 33 d φ 2 (1)
where
g 00 = e 2 V ( r , t ) = 1 − χ ( r , t ) , g 11 = e 2 λ ( r , t ) = − 1 1 − χ ( r , t ) g 22 = − e 2 C ( t ) r 2 , g 33 = − e 2 C ( t ) r 2 sin 2 θ . (2)
Here, we term V ( r , t ) as the “gravitational potential”, r is the comoving radius and t is the time relative to our preferred observer H 0 located at r = 0 , while C ( t ) is a function of time only.
In the present study, we employ Equation (19) in [
1 2 r [ ∂ ∂ t ( e − 2 V ) + e − 2 λ e − 2 V ∂ ∂ r ( e − 2 V ) + ∂ ∂ r e − 2 λ ] = − 1 2 κ ( E + p ) [ Γ 2 ( g 00 − V 2 g 11 ) ] = − 1 2 κ ( E + p ) Γ ¯ ¯ , (3)
where Γ is the Lorentz factor in curved dynamically varying spacetime and Γ ¯ ¯ is termed the modified Lorentz factor, which reads:
Γ ¯ ¯ 2 = { g 00 + V 2 g 11 g 00 − V 2 g 11 : Generalform 1 : Hydrostaticcoresembeddedincurvedspacetimes 1 + β 2 1 − β 2 : Flatspacetime . (4)
In the case of slowly contacting matter-configurations or in hydrostatic equilibrium, Γ ¯ ¯ 2 was verified to be physically more indicative than the classical Lorentz factor [
The in above-mentioned study χ ( r , t ) is a time-dependent function of the following form:
X ( r , t ) = α b b ( m n ( r , t ) r ) , (5)
where m n ( r , t ) is the enclosed mass of normal matter and α b b is the so-called compactness parameter.
Based on various theoretical and observational studies of glitching pulsars, it was argued that incompressible and entropy-free SuSu-matter inside the cores of massive pulsars and neutron stars decouples from the embedding spacetime [
Hence, the total mass content, m t o t ( r , t ) that determines the curvature of the embedding spacetime reduces to that of normal matter, m n ( r , t ) , which we classify as compressible and dissipative matter. In the stationary case, the curvature function χ ( r , t ) → χ ( r ) and therefore the metric d s 2 reduces to the Schwarzschild, Minkowski and/or to Friedmann metric, depending on the underlying type and spatial distribution of matter, namely:
X ( r ) ~ { r 2 : Schwarzschild & Friedmann ToM : incompressiblenormal fluids & dust r α : Schwarzschild ( α < 2 ) . ToM : Normalcompressible 0 : Flat ToM : Vacuum ( energy-free-space- ) time , incompressibleSuSu-matter , (6)
where “ToM” stands for “Type of Matter”.
Prior to BB-explosion, the progenitor was levitating in flat spacetime as m n ( r , t ≤ 0 ) = 0 . During the hadronization process, m n ( r , t ) was continuously increasing, thereby curving the embedding spacetime. The hadronization process is associated with four fronts that form at the surface of the progenitor and start propagating in different directions with different speeds (see
• The hadronization front, f h a d − , which propagates inwards with the speed of light.
• The rarefaction/decompression front, f r a r − which set to propagate inwards through the newly created normal compressible and dissipative matter with V s − < c .
• The expansion front f e x p + , which separates the ambient flat spacetime from the enclosed curved one, is set to propagate outwards with the speed of light and would last forever, though its intensity decreases both with time and distance from the center of the progenitor.
• A shock front, f s h + , that propagate ultra-relativistically outwards with V s h + → ≈ c .
In
The one-to-one correspondence between matter and spacetime in GR may also be used to extract the mass content by measuring the curvature of the embedding spacetime. Recalling that the spacetime at the background of the progenitor prior explosion was perfectly flat and that at t = 1 τ d y n , the volume enclosing normal matter is well-defined and calculable, using the causality condition. Outside the volume boundaries, there is no matter, and therefore χ ( r , t ) as well as the derivatives of the matric coefficients are set to vanish. The spherically symmetric surface bounding the curved spacetime at t = τ d y n reads:
S ( t = τ d y n ) = ∫ S 2 d S = 4 π R 2 ( t = τ d y n ) = 16 π c 2 t d y n 2 (7)
We may use the minimum energy theorem to calculate the ADM-mass [
M A D M = a 0 ∫ 0 τ d y n ∫ S 2 ( t ) n i g k l ( g l i , k − g l k , i ) d S d t + ∫ τ d y n ∞ ∫ S 2 ( t ) n i g k l [ ... ] d S d t ↗ 0 = M n + [ 0 ] = M n , (8)
where n i = ( 1 − χ ( r , t ) , 0 , 0 ) is the 3-normal vector to the dynamically varying spherical surface. The second integral vanishes as for t ≥ τ d y n , the ambient spacetime contains no matter and therefore the derivatives of the metric coefficients must vanish. On the other hand, during the hadronization phase, i.e. [ 0 ≤ t ≤ τ d y n ] , the mater generation rate reads [
M n o r = 3 t − 3 t 2 + t 3 . (9)
In this case, the curvature function increases almost linearly with time, but starts decreasing immediately thereafter as follows:
χ ( r , t ) = α B B m ( r , t ) r ~ { t t ≤ τ d y n 1 1 + t t > τ d y n (10)
In
In normal stars, the negative gradient of the energy density in the radial direction is necessary for ensuring dynamical stability. In the present case, however, the progenitor is made of incompressible SuSu-matter and therefore, the center becomes loosely defined, as ∇ E vanishes everywhere. For our geometrically preferred observer, H 0 , the interior of the progenitor is homogenous and isotropic. Moreover, as SuSu-matter is entropy-free, then the entire content of the progenitor must occupy just one single quantum energy state, which corresponds to the lowest possible one. This implies that the entire content of the progenitor is maximally coupled and behaves collectively as a single quantum entity.
On the other hand, following [
Recalling that the spacetime inside and outside the progenitor is flat, then both ∇ E and ∇ μ g μ ν must vanish everywhere, save at the boundary, where the former becomes almost singular, whereas the latter becomes negligibly small. However, such an imbalance is unlikely, as the superfluid cores in massive NSs would explode rather than glitch. Consequently, the pressure across the surface transforms into a two-dimensional surface tension that confines the ocean of the SuSu-fluid and keeps it hidden from the outside world.
We conjecture that such a configuration may maintain dynamical stability, if the coupling information of all its constituents are mirrored and encoded onto the 2D-like surfaces in a holographic manner as proposed by the holographic principle [
Based thereon and in the absence of macroscopic repulsive forces between stellar-mass DEOs, we expect clusters of DEOs to be extraordinarily tight, mimicking thereby the tightly packed nucleons in atomic nuclei. Also, recalling that SuSu-objects occupy the lowest possible energy state, then tightly packed SuSu-objects may merge smoothly without violently hadronizing their contents as it seems to be the case in the NS-merger event GW170817 [
Irrespective of whether 10 24 M ⊙ massive progenitor was made of tightly packed or merged normal matter objects, the corresponding event horizon, H B H would be larger than the currently measured cosmic horizon H C o s . This becomes even crasser if the progenitor was made of supranuclear dense normal matter embedded in Schwarzschild spacetime. In the latter case, the radius of the progenitor would be approximately fifteen orders of magnitude smaller than the corresponding event horizon, and therefore there will be no universe to evolve.
In the present case, the Birkhoff theorem has limited applications, as for t ≤ 0 the progenitor was made of SuSu-matter, and therefore incapable of communicating with or affecting the topology of the ambient spacetime.
This gives rise to the possibility that communications between matter and spacetime may doom to stagnate in entropy-free systems [
In
According to the here-presented scenario, BBs are actually local events that take off from time to time sequentially or in parallel at the same and/or in different locations of an infinitely large, flat, homogeneous, and isotropic universe.
Based thereon, it is tempting to explore how such giant explosions could affect the activities and dynamics of distant galaxies.
Consider an old and inactive galaxy, G, at a distance r G = 10 28 cm from the H 0 observer. Without loss of generality, let the mass and size of G be M G = 10 10 M ⊙ and volume V G v o l = l G 3 = k p c 3 and consisting of 1010 old and faint stars (see
Prior the BB-explosion, the partial mass of the progenitor enclosed inside the cone confining G reads:
M P G = M p 16 ( l G r G ) 2 ≈ 10 9 M ⊙ , (11)
where M p = 10 24 M ⊙ .
Note that if M P G were the only source of normal matter, then, due to the verified homogeneity and isotropy of the observable universe, no galaxy with M > 10 9 M ⊙ would ever form inside the G-cone, contrary to observations. This may justify our assertion, which these old inactive galaxies were behind the particle horizon, but got re-activated through the collision with the matter of the expanding fireball. Similar to spherical accretion, let A c a p be the effective capturing area of particles originating from the fireball. In the present case, A c a p should dramatically decrease, as the incoming velocity of particles from the fireball propagates with ultra-relativistic speeds. Hence A c a p may become comparable to the sum of the cross-sections of the objects of G, i.e. only those particles that collide face-to-face with the objects would be captured. In this case, we may generously set the average capturing area of an individual object to be:
〈 A c a p 〉 = ∑ i N A i , c a p N = π 〈 R c a p 〉 2 ≈ 10 22 cm 2 (12)
where N = 10 10 is the number of objects of G. This yields a total capturing area of approximately A c a p G = 10 10 × 〈 A c a p 〉 = 10 32 cm 2 , which is roughly ten orders of magnitude less than the cross-section of the galaxy A c s ~ l G 2 = 10 42 cm 2 .
To estimate the amount of normal matter and momentum transferred to the galaxy, we integrate the continuity and momentum equations over the volume of the galaxy confined by the cone with the solid angle d Ω = sin θ d θ d φ , where θ runs from zero to l G / r G . i.e.:
∫ V o l ( 1 − g ∂ ∂ t ( − g D ) + 1 − g ∂ ∂ r − g ( D V ) ) d V o l = 0, (13)
and where V , D are the transport velocity and relativistic density, i.e. the normal rest density times the Lorentz factor u t = 1 / ( g t t + V 2 g r r ) . Here − g ( = r 2 R 3 sin ( θ ) / G W ) is the determinant of the metric.
The integration yields:
δ M δ t + ( M ˙ o − M ˙ i n ) = 0, (14)
where δ M , M ˙ i n ( = A c o n e G D V ) and M ˙ o stand for the total mass absorbed by the galaxy, mass injection, and ejection rates, respectively. Note that as r G ≫ r p , the spacetime surrounding G may be safely considered as flat.
Let us assume M ˙ o = α M ˙ i n , where α < 1 . For the above-mentioned galaxy with A c a p G / A c s = 10 − 10 , we obtain: α = 1 − 10 − 10 .
In this case, the mass growth of the galaxy due to capturing of normal matter from the fireball reads:
δ M = ( 1 − α ) β 1 − β 2 × t , (15)
where β = V / c . Mass and time here are in units of M p c o n e and τ d = r p / c , respectively.
Note that δ M ≤ 1 , as the supply of normal matter is upper-limited by the progenitor’s mass content inside the cone.
Prior to hitting by the fireball’s matter, the galaxy with its locally curved spacetime, is assumed to be motionless with respect to H 0 , though embedded in an infinitely large flat spacetime. When the ultra-relativistically propagating matter from the fireball hits the galaxy, the transferred momentum is expected to set the galaxy into an outwardly accelerating motion.
Noting that the topology of the expanding spacetime embedding the fireball doesn’t allow velocity-crossover of normal matter, i.e. ∇ ⋅ V > 0 , which also implies that the normal matter’s particles may be considered as non-interacting or dust, and therefore the pressure gradient, | ∇ P | may be safely neglected. In this case, the collision between the motionless galaxy and the incoming and captured matter of the fireball can be treated as an inelastic collision in a two-body system. Under these conditions, we may volume-integrate the momentum equation:
1 − g ∂ ∂ t ( − g M r ) + 1 R 1 − g ∂ ∂ r ( − g M r V ) = − 1 R ∂ P ∂ r + M t 2 R ( g t t , r + V 2 g r r , r ) , (16)
where M σ ( ≐ D h u σ ) and u σ stand for the four-momenta and four-velocity in σ = { t , r , θ , φ } coordinates, respectively. h here is the enthalpy.
Requiring conservation of momentum and setting the second terms on the LHS and RHS to be equal, we obtain:
δ M β i n + M G β G = ( δ M + M G ) β f ↗ 0 ⇒ β f = ( δ M M G + δ M ) β i n , (17)
where β i n , β G , β f are the inflow velocity of normal matter through the left boundary of the galaxy (see
β f β i n = ( 1 − α ) β 1 − β 2 t M G + ( 1 − α ) β 1 − β 2 t . (18)
Obviously, for any positive mass of a galaxy, M G > 0 , the causality condition is safely satisfied.
Based thereon, we show in
Consequently, motionless galaxies are capable of accelerating their outward-oriented motions from rest up to ultrarelativistic velocities, depending on the amount and duration of the injection rate.
By means of GR-numerical calculations, the newly proposed H -metric has been employed to study the time-evolution of the topology of spacetime embedding the progenitor of the BB. Prior to the explosion, the progenitor was levitating in an infinitely large spacetime.
The hypothesis here is that incompressible superconducting gluon-quark superfluids (SuSu-matter) with zero entropy are incapable of affecting the curvature of the embedding spacetime. Spacetime-matter coupling is established only in the presence of normal matter, i.e. compressible and dissipative one. In our case, this matter is created via a hadronization process through which SuSu-matter is converted into hadrons.
Our calculations confirm that during the hadronization process, the fireball forms a curved spacetime, whilst the newly created normal matter is jettisoned into the surrounding flat spacetime with ultrarelativistic velocities. The driving force here is ∇ P , which remains constant during the hadronization process. ∇ P is effective at the hadronization front only. The background of the here-calculated varying spacetime dictates that the velocity of outflowing particles satisfies ∇ V > 0 , which forbids crossing over of particles, and therefore may be treated as non-interacting.
Our calculations also confirm that due to the finite mass of the progenitor, the spacetime embedding the fireball expands, and the enclosed spacetime flattens, thereby asymptotically converging into a flat spacetime.
We have argued that the surface of the progenitor is most appropriate for the hadron flash to run away and reach its center after roughly 46 minutes.
It is also shown that incompressibility in general relativity requires this type of matter to be embedded in flat spacetime, making the progenitor immune to collapse into a supermassive BH, even when the compactness parameter of order one. On the other hand, incompressibility and flatness ensure that the interior of the progenitor is perfectly homogenous and isotropic and that these properties must hold for at least 13.8 Gyr later.
It is also shown that in the absence of theoretical mechanisms, such as inflation, hadronizing the progenitor through a runaway hadron flash that starts precisely at the center of a 10 24 M ⊙ and not at r = 0 ∓ ε , is a vague assertion that cannot be supported by observations. Among others, this approach implicitly prioritizes r = 0 as a special location, which must be imposed by an already existing spacetime of unknown topology, which embeds an object made of quantum matter of an unknown energy state.
Our scenario predicts the progenitor to have a measurable size and its explosion should have taken off in our neighborhood. Both the formation and explosion of a progenitor are neither invoked by extra forces nor singular events, but rather: they are vital parts in a universal life-cycle that occur from time to time sequentially or in parallel at the same and/or in different locations in our infinitely large, flat, homogeneous, and isotropic parent universe. In this life cycle, massive pulsars are born with embryonic SuSu-cores, which are set to grow in mass and dimension as pulsars cool down on the cosmic time scale and become old NSs. These in turn continue to cool down to finally metamorphose entirely into invisible Dark Energy Objects (DEOs). In our parent universe, DEOs have ample time to conglomerate into tight clusters, where they merge to form giant progenitors. At certain times, these progenitors decay and hadronize promptly enter promptly and end up forming fireballs. These in turn cool down via expansion, thereby giving rise to the formation of the first generation of stars, which subsequently collapse to form massive pulsars, and so the cosmic life cycle starts anew (see
In this paper, a new model for powering and accelerating high-redshift galaxies has been presented. Accordingly, through the collision of the BB-matter with
high-redshift galaxies, matter and momentum are transferred to the galaxy, which appears to be capable of turning these galaxies into active mode and setting them into outward accelerating motions. As a consequence, the distance between two arbitrary galaxies on the same line of sight relative to the observer H 0 , must increase with cosmic time (see
The author acknowledges the financial support of the IWR and KAUST. Max Camenzind, Mario Livio, and Adi Nasser are acknowledged for their valuable comments, and Dr. M. Umar for his valuable assistance both in solving software and mathematical problems during his stay at the IWR.
The author declares no conflicts of interest regarding the publication of this paper.
Hujeirat, A.A. (2022) The Origin of Power and Acceleration of High-Redshift Galaxies in the Unicentric Model of the Universe. Journal of Modern Physics, 13, 1581-1597. https://doi.org/10.4236/jmp.2022.1312096