1 - The gravitational oscillator
(Hole through the center of the Earth - http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/earthole.html)
gravitational potential energy - kinetic energy = 0
"If you drilled a hole through the axis of the Earth from pole to pole, and put a long thin vacuum chamber in it then dropped an object into one end of that chamber, it would fall down the hole, picking up speed. And it would be moving very fast when it reached the centre of the Earth so it would carry on going until it reached the other pole where it would stop, and then fall back down again. It would "bounce" back and to. If the density of the Earth was constant (rather than increasing as you go down) the body would exhibit simple harmonic motion." (Author - Bored chemist)
2 - The singularity avoidance
At x = 0 when the particle is going faster (don't rely on GIF for speed), its kinetic energy allows it not to fall into the singularity.
Kinetics of the particle at the bottom of the potential well, and avoidance of the singularity:
I must specify that the avoidance of the sigularity, by the kinetics of the particle at the bottom of the potential well, also occurs when the particle is at rest in the false vacuum, namely the ZPE; And which corresponds to the same celestial mechanics of the orbit of the planets around the star. In other words when the particle is at rest at the bottom of the well and it undergoes the ZPE disturbance of the false vacuum, then we understand that the particle orbiting around the gravitational singularity, rather than a vibratory disturbance. Indeed for an observer the reproduction of the path of the particle is expressed by a sinusoidal signal in time or elliptical by its magnitude. True vacuum is total collapse.
3 - The Higgs field
The kinetics of the particle make it possible to avoid the singularity through the Higgs field. The Higgs field corresponds to the path taken by the particle. In other words, the Higgs field corresponds to the path taken by the particle thanks to the kinetic energy and makes it possible to avoid the singularity. If the kinetic energy of the particle is sufficient and if the range of the energy condition allows to pass the potential barrier the singularity avoidance occurs, but during the attenuation of the kinetics of the particle, this causes by the quantity of lower energy to fall towards the singularity and to reach the true vacuum. In conclusion, the metastability of the vacuum is shifted and is represented in three parts. The first corresponds to the false vacuum of the Higgs field at the level of Spontaneous Symmetry Breaking, follows in two the true vacuum of the Higgs field which is in fact the Zero Point Energy and is therefore not the true vacuum since in three we have the true absolute vacuum which corresponds to the total collapse. Without any kinetic energy the contour of the potential barrier corresponds to the path of the orbit of the particle in Zero Point Energy in relation to its inertia.
Application of conventional physics. Namely the kinetic energy of the particle for the harmonic or anharmonic oscillator, and inertia to simulate the orbiting motion of the particle or mass around a more massive object. According to the oscillator model that I propose, the orbit(s) is located at approximately at x=0 in the potential well of the oscillator, and corresponds to the Zero Point Energy. The initial Zero Point Energy disturbance (ZPE) corresponds to the movement of the particle located in the false vacuum in orbit around the gravitational singularity.
The idea now is that the inertia of an orbiting body would correspond to the movement of its mass occurring by the force of gravity, but by an avoidance of the gravitational singularity thanks to the barrier of potential. In other words the particle slides along the barrier of potential and corresponds to the motion of inertia following the orbit in relation to the object with the greatest gravity at the center of the system. Indeed in the conventional illustration, the orbit is the closed curve representing the trajectory that a celestial object draws under the effect of gravitation and inertial forces. It should therefore be remembered that the own deformation by sinking of the celestial object in the curvature of spacetime creates all around it a barrier of energy potential from higher edges.
The Higgs field and potential are also used well to be able to represent the metastability of the universe, as well as the quantum particle. Being able to make the link between GR and QM through the gravitational oscillator by explaining the Higgs mechanism becomes very interesting, even important. If we were to make the jump of a massive object over the potential barrier and the gravitational singularity, then we would draw through the particle, the curve of the Higgs field. It is therefore understood that in order to do this, the kinetic energy must be accordingly. We would therefore tend to believe that for a quantum particle that the step of crossing a black hole would become easier. I guess that its avoidance is related to the electromagnetic force.
In a more speculative definition and given our knowledge of the gravitational sigularity followed by the time dilation, we could associate the center of the earth as such. Indeed for the quantum particle it becomes easier to imagine the avoidance of the singularity at the level of the terrestrial core through the gravitational oscillator.
4 - References:
Black Hole singularity avoidance by the Higgs scalar field Einstein gravitation is known to give rise to the formation of singularities at high densities unless the dominant energy condition is made invalid by the occurrence of new physics: we show that such a new physics can be the already present Higgs sector of the standard model of particle physics. https://arxiv.org/abs/1901.05295
Black holes and Higgs stability We study the effect of primordial black holes on the classical rate of nucleation of AdS regions within the standard electroweak vacuum. We find that the energy barrier for transitions to the new vacuum, which characterizes the exponential suppression of the nucleation rate, can be reduced significantly in the black-hole background. A precise analysis is required in order to determine whether the the existence of primordial black holes is compatible with the form of the Higgs potential at high temperature or density in the Standard Model or its extensions. https://arxiv.org/abs/1606.04018
Unification of gravity and the harmonic oscillator on a quantum black hole horizon II: Perturbative particle scattering and Feynman amplitudes n Article I, a harmonic-oscillator model of a universe of n quarks is infinitesimally modified to eliminate the background reference frame. As a result, quark trajectories exhibit the unification of gravity and the harmonic oscillator near the horizon of a quantum black hole, a region that is approximately flat in space-time. Constituent quarks are confined to composite particles by cluster decomposition rather than a binding force. Here, the composite-particles are input for a perturbation model of particle-exchange interactions. https://arxiv.org/abs/hep-th/0307136
Gravitational and harmonic oscillator potentials on surfaces of revolution In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with constant Gaussian curvature. The two potentials leading to closed orbits are suitable generalizations of the gravitational and harmonic oscillator potential. We also show that there could be surfaces admitting only one potential that leads to closed orbits. In this case, the potential is a generalized harmonic oscillator. In the special case of surfaces of revolution with constant Gaussian curvature, we prove a generalization of the well-known Bertrand theorem. https://arxiv.org/abs/1305.3930