1. Introduction

2. Kerr-Newman Black Hole

2.1. Boyer-Lindquist metric

The Boyer-Lindquist metric of the Kerr-Newman geometry is:

(1)

where R and are defined by:

(2)

And Δ is the horizon function defined by:

(3)

If M = Q = 0, so that Δ = 1, the Boyer-Lindquist metric (1) goes over to the metric of Minkowski space expressed in ellipsoidal coordinates

At large radius r, the Boyer-Lindquist metric is

(4)

The weak- field metric in Newtonian gauge, around an object of mass M and angular momentum L takes the form:

(5)

Where, the scalar ϕ, ψ and vector W potentials are:

(6)

The asymptotic Boyer-Lindquist metric (4) is not quite in the Newtonian form (5), but a transformation of the radial coordinate brings it to Newtonian form. Comparison of the two metrics establishes that M is the mass of the black hole and a = L/M is its angular momentum per unit mass. For positive a, the black hole rotates right-handedly about its polar axis ϕ = 0.

The Boyer-Lindquist line-element (1) defines not only a metric but also a tetrad. The Boyer-Lindquist coordinates and tetrad are carefully chosen to exhibit the symmetries of the geometry. In the locally inertial frame defined by the Boyer-Lindquist tetrad, the energy-momentum tensor (which is non-vanishing for charged Kerr-Newman) and the Weyl tensor are both diagonal. These assertions become apparent only in the tetrad frame and are obscure in the coordinate frame.

2.2. Oblate Spheroidal Coordinates

Boyer-Lindquist coordinates r, ϕ, θ are oblate spheroidal coordinates (not polar coordinates). Corresponding Cartesian coordinates are:

(7)

Surfaces of constant r, are confocal oblate spheroids, satisfying

(8)

Equation (39) implies that the spheroidal coordinate r is given in terms of x, y, z by the quadratic equation:

(9)

Figure 1, illustrates the spatial geometry of a Kerr black hole, and of a Kerr-Newman black hole, in Boyer-Lindquist coordinates.

2.3. Time and Rotation Symmetries

The Boyer-Lindquist metric coefficients are independent of the time coordinate t and of the azimuthal angle ϕ. This shows that the Kerr-Newman geometry has time translation symmetry, and rotational symmetry about its azimuthal axis. The time and rotation symmetries mean that the tangent vectors e(t) and e(ϕ) in Boyer-Lindquist coordinates are Killing vectors. It follows that their scalar products:

(10)

are all gauge-invariant scalar quantities. As will be seen below, gtt = 0 defines the boundary of ergospheres, gtϕ = 0 defines the turnaround radius, and gϕϕ = 0 defines the boundary of the sisytube, the toroidal region containing closed time like curves.

The Boyer-Lindquist time t and azimuthal angle ϕ are arranged further to satisfy the condition that e(t) and e(ϕ) are each orthogonal to both e(r) and e(θ).

2.4. Ring Singularity

The Kerr-Newman geometry contains a ring singularity where the Weyl tensor (9.26) diverges, ρ = 0, or equivalently at

(11)

The ring singularity is at the focus of the confocal ellipsoids of the Boyer-Lindquist metric. Physically, the singularity is kept open by the centrifugal force.

Figure 2, illustrates contours of constant in a Kerr black hole.

2.5. Horizons

The horizon of a Kerr-Newman black hole rotates, as observed by a distant observer, so it is incorrect to try to solve for the location of the horizon by assuming that the horizon is at rest. The worldline of a photon that sits on the horizon, battling against the in ow of space, remains at fixed radius r and polar angle θ, but it moves in time t and azimuthal angle ϕ. The photon's 4-velocity is , and the condition that it is on a null geodesic is:

(12)

This equation has solutions provided that the determinant of the 2 x 2 matrix of metric coefficients in t and ϕ is less than or equal to zero (why?). The determinant is:

(13)

where is the horizon function defined above, equation (34). Thus, if Δ ≥ 0, then there exist null geodesics such that a photon can be instantaneously at rest in r and θ, whereas if Δ < 0, then no such geodesics exist. The boundary

Δ = 0

(14)

defines the location of horizons. With Δ given by equation (3), equation (14) gives outer and inner horizons at:

(15)

Between the horizons Δ is negative, and photons cannot be at rest. This is consistent with the picture that space is falling faster than light between the horizons.

2.6. Angular Velocity of the Horizon

The angular velocity of the horizon as observed by observers at rest at infinity can be read o directly from the Boyer-Lindquist metric (1). The horizon is at dr = dθ = 0 and Δ = 0, and then the null condition ds² = 0 implies that the angular velocity is

(16)

The derivative is with respect to the proper time t of observers at rest at infinity, so this is the angular velocity observed by such observers

2.7. Ergospheres

There are finite regions, just outside the outer horizon and just inside the inner horizon, within which the worldline of an object at rest, dr = dθ = dϕ = 0, is spacelike. These regions, called ergospheres, are places where nothing can remain at rest (the place where little children come from). Objects can escape from within the outer ergosphere (whereas they cannot escape from within the outer horizon), but they cannot remain at rest there. A distant observer will see any object within the outer ergosphere being dragged around by the rotation of the black hole. The direction of dragging is the same as the rotation direction of the black hole in both outer and inner ergospheres.

The boundary of the ergosphere is at

(17)

which occurs where:

(18)

Equation (18) has two solutions, the outer and inner ergospheres. The outer and inner ergospheres touch respectively the outer and inner horizons at the poles, θ = 0 and π.

2.8. Turnaround Radius

The turnaround radius is the radius inside the inner horizon at which infallers who fall from zero velocity and zero angular momentum at infinity turn around. The radius is at:

(19)

which occurs where Δ = 1, or equivalently at:

(20)

In the uncharged Kerr geometry, the turnaround radius is at zero radius, r = 0, but in the Kerr-Newman geometry the turnaround radius is at positive radius.

2.9. Antiverse

The surface at zero radius, r = 0, forms a disk bounded by the ring singularity. Objects can pass through this disk into the region at negative radius, r < 0, the Antiverse.

The Boyer-Lindquist metric (1) is unchanged by a symmetry transformation that simultaneously flips the sign both of the radius and mass, r → -r and M → -M. Thus, the Boyer-Lindquist geometry at negative r with positive mass is equivalent to the geometry at positive r with negative mass. In effect, the Boyer-Lindquist metric with negative r describes a rotating black hole of negative mass

(21)

2.10. Sisytube

Inside the inner horizon there is a toroidal region around the ring singularity, which I call the sisytube, within which the light cone in t-ϕ coordinates opens up to the point that ϕ as well as t is a time like coordinate. In the Wormhole, the direction of increasing proper time along t is t increasing, and along ϕ is ϕ decreasing, which is retrograde. In the Parallel Wormhole, the direction of increasing proper time along t is t decreasing, and along ϕ is ϕ increasing, which is again retrograde. Within the toroidal region, there exist time like trajectories that go either forwards or backwards in coordinate time t as they wind retrograde around the toroidal tunnel. Because the ϕ coordinate is periodic, these time-like curves connect not only the past to the future (the usual case), but also the future to the past, which violates causality. In particular, as rst pointed out by Carter (1968), there exist closed time like curves (CTCs), trajectories that connect to themselves, connecting their own future to their own past, and repeating interminably, like Sisyphus pushing his rock up the mountain.

The boundary of the sisytube torus is at:

(22)

which occurs where:

(23)

In the uncharged Kerr geometry, the sisytube is entirely at negative radius, r < 0, but in the Kerr-Newman geometry the sisytube extends to positive radius, Figure 1.

2.11. Extremal Kerr-Newman Geometry

The Kerr-Newman geometry is called extremal when the outer and inner horizons coincide, r+ = r-, which occurs where:

(24)

Figure 3, illustrates the structure of an extremal Kerr (uncharged) black hole and an extremal Kerr-Newman (charged) black hole.

2.13. Energy-Momentum Tensor

The coordinate-frame Einstein tensor of the Kerr-Newman geometry in Boyer-Lindquist coordinates is a bit of a mess. The trick of raising one index, which for the Reissner-Nordström metric brought the Einstein tensor to diagonal form, equation (5), fails for Boyer-Lindquist (because the Boyer-Lindquist metric is not diagonal). The problem is endemic to the coordinate approach to general relativity. After tetrads it will emerge that, in the Boyer-Lindquist tetrad, the Einstein tensor is diagonal, and that the proper density ρ, the proper radial pressure p(r), and the proper transverse pressure p(Ʇ) in that frame are (do not confuse the notation ρ for proper density with the radial parameter ρ, equation (2), of the Boyer-Lindquist metric).

(25)

This looks like the energy-momentum tensor of the Reissner-Nordström geometry with the replacement r → ρ. The energy-momentum is that of an electric field produced by a charge Q seemingly located at the ring singularity.

2.14. Weyl Tensor

The Weyl tensor of the Kerr-Newman geometry in Boyer-Lindquist coordinates is likewise a mess. After tetrads, it will emerge that the 10 components of the Weyl tensor can be decomposed into 5 complex components of spin 0, ±1, and ±2. In the Boyer-Lindquist tetrad, the only non-vanishing component is the spin-0 component, the Weyl scalar C, but in contrast to the Schwarzschild and Reissner-Nordström geometries the spin-0 component is complex, not real:

(26)

2.15. Electromagnetic Field

The expression for the electromagnetic eld in Boyer-Lindquist coordinates is again a mess. After tetrads, it will emerge that, in the Boyer-Lindquist tetrad, the electromagnetic field is purely radial, and the electromagnetic potential has only a time component. For reference, the covariant electromagnetic potential Au in the Boyer-Lindquist coordinate (not tetrad) frame is:

(27)

2.16. Principal Null Congruences

The Kerr-Newman geometry admits a special set of space-filling, non-overlapping null geodesics called the principal outgoing and ingoing null congruences. These are the directions with respect to which the Weyl tensor and the electric field vector align. Photons that hold steady on the outer horizon are on the principal outgoing null congruence. The construction and special character of the principal null congruences will be demonstrated after tetrads.

Geodesics along the principal null congruences satisfy:

(28)

where w = a / R² is the azimuthal angular velocity of the geodesics through the coordinates. The Boyer Lindquist line-element (1) is specifically constructed so that it aligns with the principal null congruences.

2.17. Finkelstein Coordinates

Along the principal outgoing and ingoing null congruences, where equations (28) hold, the Boyer-Lindquist metric (32) reduces to:

(29)

A tortoise coordinate r* in the Kerr-Newman geometry may be defined analogously to that (16) in the Reissner-Nordström geometry,

(30)

which integrates to the same expressions in terms of horizon radii r± and surface gravities k± as in the Reissner-Nordström geometry. Principal outgoing and ingoing null geodesics follow

(31)

A Finkelstein time coordinate tF can be defined as in the Reissner-Nordström geometry. Likewise, Kruskal-Szekeres coordinates can be defined as in the Reissner-Nordström geometry. The Finkelstein and Kruskal spacetime diagrams for the Kerr-Newman geometry look identical to those of the Reissner-Nordström geometry (if the horizon radii r± are the same).

The behaviour of geodesics in the angular direction is more complicated in the Kerr-Newman than Reissner Nordström geometry, but this complexity is hidden in the Finkelstein and Kruskal diagrams

2.18. Doran Coordinates

For the Kerr-Newman geometry, the analogue of the Gullstrand-Painlevé metric is the Doran (2000) metric:

(32)

where the free-fall time t(H) and azimuthal angle ϕ(H) are related to the Boyer-Lindquist time t and azimuthal angle ϕ by:

(33)

The free-fall time t(H) is the proper time experienced by persons who free-fall from rest at infinity, with zero angular momentum. They follow trajectories of fixed θ and ϕ(H), with radial velocity dr / dt = βR² /ρ². The 4-velocity of such free-falling observers is:

(34)

For the Kerr-Newman geometry, the velocity β is:

(35)

Where the ± sign is - (infalling) for black hole solutions, and+ (outfalling) for white hole solutions.

Horizons occur where the magnitude of the velocity β equals the speed of light.

(36)

The boundaries of ergospheres occur where the velocity is:

(37)

The turnaround radius is where the velocity is zero

β = 0

(38)

The sisytube is bounded by the imaginary velocity:

(39)

3. Modelling of a Black Hole

4. Application of the Model And Results

4.1. Correlation between Kerr-Newman Black Hole vs. RLC Electrical Modelling of a Black Hole

• 1. We are going to perform an analysis for the condition: M² > Q² + a²

If we observe and compare Figure 14 and Figure 15, we see the following:

In both models the black holes rotate around their axial axis.

In Figure 14, we can see an ergosphere, an outer horizon and an inner horizon. We also observe that the outer and inner horizons are cofocal oblate spheroids whose focus is the ring singularity.

In Figure 15, we can also observe an event horizon and a ring singularity, we can assume that the event horizon is cofocal oblate spheroids and whose focus is the ring singularity.

Under this condition, M² > Q² + a²; The black hole is born and grows, we can say that it represents the first moments of the life time of a black hole.

As the black hole grows, the distance between the outer horizon and the inner horizon decreases.

The particles that enter the black hole pass through the ergosphere, cross the outer horizon and the inner horizon and finally fall into the ring singularity. Inside the ring singularity (r ≤ 0) the bosonic particles move at a speed greater than the speed of light, which generates an additional mass which we represent in our model as – iδ (see equation 41). This additional mass generates a gravitational force that is not attractive and is the gravitational force that gives rise to dark matter.

Let us remember that a black hole grows in the same way as the Tau constant of an RC circuit (equation 40).

We are going to represent the graphs and calculations that describe the growth of a black hole, the complete mathematical development can be found in the paper: RLC Electrical Modelling of Black Hole and Early Universe. Generalization of the Boltzmann constant in curved spacetime.

Now we are going to present the Penrose Diagram:

Now we are going to try to relate Figure 15 with Figure 17.

If we look at Figure 15, we see that the spheroid that represents a black hole can be divided into two parts, an upper part and a lower part.

If we look at Figure 17, if we consider the yellow vertical line, we can also divide the graph into two parts, a spatial part representing the right side and a spatial part representing the left side.

If we consider a test particle, we see in Figure 15 that it can enter the upper part, at the equator of the spheroid, cross the event horizon and head to the upper singularity. There is also another option in which the test particle could enter the lower part of the equator, in the spheroid, cross the event horizon and head to the lower singularity.

If we consider a test particle, we see in Figure 17, in analogy with Figure 15, that it can enter the left side of the black hole, in the ergosphere, cross the event horizon, pass through the wormhole region and end up in the antiverse region. There is also another option in which the test particle could enter on the right side of the black hole, in the ergosphere, cross the event horizon, cross the parallel wormhole region and end up in the parallel antiverse region.

If we look at Figure 15, both currents I₁ and I₂ have a positive charge and move in the opposite direction. We observe that current I₁ moves counter clockwise and generates an upward magnetic field (blue); Current I₂ moves clockwise and generates a downward magnetic field (orange).

Both the electric and magnetic force generated by currents I₁ and I₂ produce a repulsion force between the coils, this is counteracted only by the gravitational force.

If we look at Figure 17, if we consider a test particle, we see that there is a repulsion force between the left side of the graph and the right side, for example, if a test particle (1) that enters the black hole, enters the ergosphere, enter the wormhole and antiverse; If we consider Figure 15, by analogy the particle heads upward until it reaches the ring singularity. Now we consider the test particle (2) that enters the black hole, ergosphere, parallel wormhole, parallel antiverse, by analogy to Figure 15, the test particle heads downward until it reaches the ring singularity. The test particle (1) is directed upward, while the test particle (2) is directed downward, as if both positive particles were under opposite forces.

There is an analogy between graph 15 and graph 17, the upper part of graph 15, from the equator up, corresponds to the left symmetrical region of the vertical yellow line of graph 17; The lower part of graph 15, from the equator downwards, corresponds to the right symmetrical part of the vertical yellow line of graph 17.

Another important analogy that we must highlight is the ring singularity, above the equator in Figure 15, which corresponds to the antiverse in the left symmetry of graph 17; We must also highlight the ring singularity below the equator in Figure 15, which corresponds to the parallel antiverse in the right symmetry of graph 17.

Finally, it is important to note that the black hole grows and as it increases in size, the regions of the black hole that we call ergosphere, wormhole (parallel wormole) and antiverse (parallel antiverse) also grow.

Here, it is important to note that although the black hole grows, nothing material comes out of the black hole, therefore we can represent this in Figure 17 only with the yellow triangle. What is stated here is very important.

2.

>2. We are going to perform an analysis for the condition: M² = Q² + a²

The Kerr-Newman geometry is called extremal when the outer and inner horizons coincide:

We see that in this condition there is a single event horizon, which we are going to represent in the following Figure:

Figure 18 Spatial geometry of an extremal Kerr-Newman black hole with charge Q = 08M and spin parameter a = 06M.

We could express the relationship M² = Q² + a² in another way:

M² / (Q² + a²) = 1

This is telling us that the growth of a black hole has a limit, that the amount of matter it devours is limited and if it exceeds that limit it has to be expelled in some way; Therefore, the amount of matter that enters the interior of the ring singularity (antiverse) is limited by the mass M of the black hole.

For example, we could assume that this limit is generally exceeded when a stellar black hole devours a star, a quasar.

Here, it is important to note that although the black hole grows, nothing material comes out of the black hole, therefore we can represent this in Figure 17 only with the yellow triangle.

3.

We are going to perform an analysis for the condition: M² < Q² + a²

We could express the relationship M² < Q² + a² in another way:

M² / (Q² + a²) < 1

In this condition, the event horizon disappears and we say that we have a naked singularity.

In this condition, we can observe that the amount of matter (charge) that the black hole devours exceeds its mass.

We said that the growth of a black hole is limited by its mass M, therefore, the amount of matter that enters a black hole is limited by the mass M, that is, if the black hole devours a greater amount of matter that its mass M, then somehow the black hole has to eliminate the excess matter it is ingesting.

We are going to represent the statement in the following Figure:

Let's interpret what we said in a Penrose diagram.

Figure 20, Let's consider two sets of test particles, the two sets of test particles enter the black hole (ergosphere), one set through the horizon and the other set through the parallel horizon; Now let's look at Figure 15, one set of test particles enters above the equator of the spheroid and the other set of particles enters below the equator of the spheroid.

Let us remember that we are under the condition: M² < Q² + a²

Figure 20, the first set that was in the parallel universe, enters the black hole (ergosphere) through the parallel horizon, part of that set of particles is devoured by the black hole and ends up in the antiverse and the rest of the particles leave the black hole, crosses the inner antihorizon and ends in the new parallel universe. The second set of particles follows a similar path, it enters the black hole (ergosphere) through the horizon, part of that set of particles is devoured by the black hole and ends up in the parallel antiverse and the rest of the particles leave the black hole. It crosses the parallel inner antihorizon and ends in the new universe.

If we look at Figure 15, the first set of particles enters the black hole above the equator of the spheroid, part of the set of particles is devoured by the black hole and goes to the ring singularity and the rest of the particles are expelled out of the black hole, upwards. Similarly, the second set of particles enters the black hole through the lower part of the equator of the spheroid, part of the set of particles is devoured by the black hole and goes to the ring singularity and the rest of the particles are expelled from the hole black, down.

If we compare Figure 17 with Figure 20, we see that there is a difference between them.

Figure 17 represents a black hole that grows, under the condition M² ≥ Q² + a², which is telling us that no matter comes out of the black hole. This is represented by the inverted yellow triangle.

Figure 20 represents a black hole that grows and has an associated relativistic jet, under the condition M² < Q² + a², which is telling us that part of the matter that the black hole devours is expelled. This is represented by the two highlighted triangles; the yellow triangle representing the black hole devouring matter and the orange triangle (white hole) representing the amount of matter ejected from the black hole.

An example of the true meaning of what Figure 20 represents would be a quasar.

Reissner-Nordström Black Hole, the inflationary instability, under the condition Q > M, at point X, an inflationary instability occurs that produces feedback which generates the relativistic jets. The interior mass is not the only thing that increases exponentially during mass inflation. The proper density and pressure, and the Weyl scalar (all gauge-invariant scalars) exponentiate together.

This is analogous to what happens in a black hole with the Kerr-Newman geometry, part of the mass that enters the black hole ends up in the antiverse (ring singularity) and the rest of the mass is ejected in the form of a relativistic jet, is given for the condition M² < Q² + a².

Under this interpretation, the universe, the parallel universe, the new universe and the new parallel universe actually represent our only universe. See Figure 20.

Under this interpretation, the antiverse and the parallel antiverse in Figure 17 and 20, represent in Figure 15, the ring singularity that is at the top of the equator of the spheroid and the ring singularity that is at the bottom of the equator of the spheroid.

According to our description, the black hole model in Figure 15 perfectly emulates the black hole model represented in Figure 20, corresponding Penrose diagram of the Kerr-Newman geometry.

4.

We are going to perform an analysis for the condition: M = Mc

Here, we are going to analyse the condition in which the black hole reaches its critical mass Mc.

In the theory of the paper: RLC Electrical Modelling of Black Hole and Early Universe. Generalization of Boltzmann’s Constant in Curved Space-Time; we put forward the hypothesis of a black hole growth in analogy to an RC electrical circuit that grows according to a constant Tau being defined as:

$$\tau =RC$$

(48)

In a capacitor when its charge reaches the value of 5$\tau$, we say that the capacitor reached its maximum charge, in analogy to the capacitor, when the black hole reaches the value of 5$\tau$ it reaches its maximum mass value; Let us remember that a capacitor stores electrical energy and a black hole stores gravitational potential energy.

Let us remember that the mass of a black hole in the theory of the paper: Rlc Electrical Modelling of Black Hole and Early Universe. Generalization of Boltzmann’s Constant in Curved Space-Time; It is represented by the following equation:

$$M=m-i\delta$$

(49)

Where M is the total mass of a black hole, m is the baryonic mass; $\delta$ corresponds to dark matter and (i) is the irrational number $\sqrt{-1}$. This equation is in analogy to impedance of an RC circuit.

To calculate the total energy associated to the black hole, we can introduce its total mass (equation 49) into:

$$E^2=c^2{p}^2+c^4{M}^2$$

(50)

Where E is energy; c represents the speed of light and m represents the mass. This lead to:

$$E^2=c^2{p}^2+\left(m^2-{\delta }^2\right)c^4-2im\delta c^4.$$

(51)

We can assume that during the big bang inflation phase baryonic matter was overrepresented compared to dark matter together with an infinitesimal momentum, which would give us from equation (51) the following:

$$E^2=-{\delta }^2{c}^4 ; E=(+/-)\delta c^{2}i$$

(52)

As expected, this result corresponds to the total energy of the universe at the big bang if we consider it to be made of dark matter represented as a reactance in an RC circuit.

The positive value of E is determined by matter, there is no antimatter inside a black hole.

If we consider charge as a fundamental property of matter, $E=(+)\delta c^{2}i$, represents the amount of relativistic dark matter inside the black hole at the time of disintegration.

If we consider mass as a fundamental property of matter, $E=(-)\delta c^{2}i$, represents the amount of relativistic dark matter inside a black hole, which exerts a repulsive gravitational force at the moment of disintegration. This repulsive gravitational force is what generates the cosmic inflation and dark energy after the Big Bang.

At time T0, when the black hole disintegrates and the Big Bang occurs, roughly all matter was dark matter. Relativistic dark matter.

We could also consider a universe at infinity proper time in which baryonic matter is dominant over dark matter, which would transform equation (51) back into equation (50) but with baryonic matter.

$$E^2=c^2{p}^2+m^2{c}^4.$$

(53)

Here we put forward the hypothesis that the big bang is the convolution of the energy released by disintegration of the black hole with the space-time surrounding the black hole, being defined as:

$$(m-i\delta )\mathrm{*}\mathrm{Ɛ}$$

(54)

Where $m-i\delta ,$ is the total mass of a black hole, Ɛ is the space-time surrounding the black hole and * is the convolution symbol.

Equation (54) can be simplified and considered analogous to an RLC circuit.

Where RC represents a black hole and L represents the space-time around a black hole.

$$RC=m-i\delta$$

(55)

$$L=ℇ$$

(56)

the resolution of the quadratic equation of the RLC circuit will determine how space-time will expand after the Big Bang and the bandwidth of the equation will give us the spectrum of gravitational waves that originated during the Big Bang.

The growth of the black hole from its birth until it reaches the value of 5$\tau$ is represented in Table 2 and Figure 16.

a)

In item 1 of the Table 1, for the following parameters, T = 10¹³ K, Cɢ = C = 310⁸ m/s, calculating we get the following values:

m = 6 10³⁰ kg, baryonic mass.

δ = 0, dark matter mass.

M = m = 6 10³⁰ kg

Rs = 8.89 10³ m, Schwarzschild radius.

• b) In item 9 of the Table 1, for the following parameters, T = 5 10²⁶ K, Cɢ = 3 10²¹ m/s, C = 310⁸ m/s, calculating we get the following values:

m = 1.20 10⁵⁶ kg, baryonic mass.

δ = 1.20 10⁸² kg, dark matter mass.

M = δ = 1.20 10⁸² kg

Rs = 1.77 10²⁹ m, Schwarzschild radius.

c) It is important to emphasize, for the time t equal to 5τ, at the moment the disintegration of the black hole occurs, the big bang originates, the total baryonic mass of the universe corresponds to m = 10⁵⁶ kg.

d)

It is important to highlight, for time t equal to 5τ, at the moment in which the disintegration of the black hole occurs, the big bang originates, the total mass of the dark matter of the universe corresponds to δ = 10⁸² kg.

It is important to highlight the following, when scientists calculated the total baryon mass of the universe, they gave them the following value m = 10⁵⁴ kg, in our calculation, the total baryon mass of the universe gave the following value, m = 10⁵⁶ kg; 100 times greater, I think the difference between the calculations is in the order taking into account the complexity of the calculation.

Figure 16, shows the growth of the tau (τ) constant, as a function of speed vs. temperature.

If we look at Figure 15, we see that the upper and lower ring singularity are formed by positively charged bosons.

If we consider the electric field E, both (ring singularity) exert a repulsive force. If we consider the magnetic field B, both (ring singularity) exert a repulsive force. Therefore, the only force holding the black hole together is the gravitational force. Above the critical mass of the black hole, the force of repulsion of the electric field and the magnetic field Fr is greater than the force of gravitational attraction Fg, the disintegration of the black hole occurs, that is, a white hole is produced. What we call the Big Bang, this process gives rise to cosmic inflation.

Next, we are going to explain the process that gives rise to cosmic inflation.

Cosmic Inflation

Let's look at Figure 17 and 20, consider that we move only in the vertical Y time axis, the X axis of space is null. If we consider the instant of time To⁻, we observe that we are in a black hole; If we consider the instant of time To⁺, we observe that we are in a white hole. The instant of time To is an inflection point at which the transition from a black hole to a white hole occurs.

Now let's consider a test particle (1) that moves in the X axis, the Y time axis is null. We begin our movement on the right side through the parallel antiverse, we continue to the left and cross the region of the parallel wormhole, until we reach the inflection point.

Now let's consider a test particle (2) that moves in the X axis, the Y time axis is null. We begin our movement on the left side along the antiverse, we continue to the right, we cross the wormhole region, until we reach the inflection point X.

Let us observe that the test particles (1) and the test particle (2) are at the inflection point, but cannot exceed it.

Now, if we analyse the inflection point, we see that it is a space-type point, its trajectory is space-type, this implies that in order to cross it we need to move at a speed greater than the speed of light, v > c.

If we analyse section 2.9, Antiverse; We see that there is a region for negative radii, r < 0 which corresponds to a negative mass, M < 0.

Later we will analyse the importance of negative mass.

Now we will analyse Figure 15, we will use two test particles for our analysis, the test particle (1) and the test particle (2). We will consider that the test particle (1) is directed towards the upper singularity ring and the test particle (2) is directed towards the lower singularity ring.

The test particle (1) that is in the upper singularity ring cannot go to the lower singularity ring.

The test particle (2) that is in the lower singularity ring cannot go to the upper singularity ring.

Therefore, in the black hole model represented in Figure 15, there is also an inflection point.

Here, we are going to hypothesize that the black hole reaches its critical mass Mc, collapses, disintegrates and transforms into a white hole, this process generates cosmic inflation.

This is the only condition in which a test particle can cross the inflection point whose velocity v > c.

If we look at Figure 20, at time To, the amount of matter in the black hole is the same as that of the white hole. We can deduce this by comparing the orange triangle with the yellow triangle.

There is a second condition in which a test particle can cross the inflection point, it is when a black hole behaves like a quasar, generating relativistic jets. In this condition that we have already analyzed, the inflection point exhibits a feedback inflationary instability, which is what generates the relativistic jets and occurs for the condition M² < Q² + a²

Now we are going to analyse the importance of negative mass, M < 0 (Antiverse), in the origin of cosmic inflation.

We said that the mass of a black hole can be represented in analogy to that of an RC circuit as follows:

$$M=m-i\delta$$

(57)

Where M is the total mass of a black hole, m is the baryonic mass; δ corresponds to dark matter and (i) is the irrational number √(-1).

We can represent this equation in the following way:

$$M=m+i(-\delta )$$

(58)

In equation 58, we see that the mass of dark matter can be represented as a negative mass.

We said that a black hole grows like a capacitor, following the Tau constant.

$$\tau =RC$$

(59)

In item 9 of the Table 1, for the following parameters, T = 5 10²⁶ K, Cɢ = 3 10²¹ m/s, C = 310⁸ m/s, calculating we get the following values:

m = 1.20 10⁵⁶ kg, baryonic mass.

δ = 1.20 10⁸² kg, dark matter mass.

M = δ = 1.20 10⁸² kg

Rs = 1.77 10²⁹ m, Schwarzschild radius.

These values correspond to the moment of time To, in which the black hole reaches its critical mass Mc, collapses, disintegrates, transforming into a white hole.

We will use these values to calculate your Plank Length.

At instant To, the Planck length inside a black hole (white hole) corresponds to Lp = 1.28 10⁻⁵⁴ m.

If we consider the Planck length Lpɛ, the minimum length of space-time, like a spring and due to the action of v > c (300,000 km/s), this length decreases in values of Lpɢ, that is, Lpɢ < Lpɛ, allowing us to imagine the immense forces involved in compressing space-time of length Lpɛ into smaller values of space-time Lpɢ. The immense energy stored and released in the spring of length Lpɢ, to recover its initial length Lpɛ, is the cause of the exponential expansion of space-time in the first moments of the Big Bang.

At time T0, when the black hole disintegrates and the Big Bang occurs, roughly all matter was dark matter, relativistic dark matter. This is represented in equation (52).

5. Conclusions

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