Ivan Arraut

We show that black-hole remnant scenario naturally arises in the original computations of Hawking without extra assumptions.

We demonstrate that the observed parameters, related to the flavor oscillation of the neutrinos, are consistent with a system with three degenerate ground states. These ground states must have the same energy and they are connected by a symmetry with its corresponding generator. This symmetry is not spontaneously broken because the neutrino never selects a specific vacuum state. Instead, the neutrino keeps oscillating between the three ground states as it moves through spacetime. The order parameter in this case is the neutrino flavor and then the superposition of all the possible vacuum flavor states for one neutrino gives a trivial (zero) result. From this trivial condition, we can find constraints over the observed mixing angles θ _ij . By using these constraints we make the predictions of the mixing angles which are in agreement with the observations. Subsequently, complementing these arguments with a triangular formulation of the neutrino oscillation, we find relations between the the mass eigenvalues and the mixing angles, making again predictions consistent with the observations and consistent with a normal order in hierarchy with m ₃ >> m ₂ ≈ m ₁ . Finally, we analyze the symmetry related to the flavor oscillation.

In this paper, we demonstrate that the effects of Dark-Matter, partially in the way proposed by the Modified Newtonian Dynamics (MOND), emerge naturally from the standard theory of General Relativity (without any modification) under a new proposed vacuum solution. There is a family of metric solutions able to reproduce the galaxy rotation curves and the relevant scales where the Dark-Matter effects are supposed to appear in a galaxy. This family of solutions deviate from the standard spherically symmetric solution. The proposed formulation, being relativistic by nature, opens the scenario where we can test the relativistic effects attributed to Dark-Matter and having relevance in cosmology. Among such effects, we have gravitational lensing, effects on the CMB scenario and effects on the formation of galaxies.

We derive the vacuum energy from the zero-point quantum fluctuations after imposing a natural constraint emerging from the rotational symmetry inside the de-Sitter metric. The constraint imposes a maximum azimuthal angle for each frequency mode emerging from the vacuum. In this way, the shorter the wavelength of the mode, the larger will be its suppression. The same result is derived subsequently by using the Friedmann–Lemaitre–Robertson–Walker (FLRW) metric. We then make a physical interpretation of the physical effects from the perspective of pair creations over the vacuum, where the mentioned constraint emerges, limiting then the maximum angle which each pair generated from the vacuum can rotate with respect to each other during their short existence.

It has been previously demonstrated that stochastic volatility emerges as the gauge field necessary to restore local symmetry under changes in stock prices in the Black–Scholes (BS) equation. When this occurs, a Merton–Garman-like equation emerges. From the perspective of manifolds, this means that the Black–Scholes and Merton–Garman (MG) equations can be considered locally equivalent. In this scenario, the MG Hamiltonian is a special case of a more general Hamiltonian, here referred to as the gauge Hamiltonian. We then show that the gauge character of volatility implies a specific functional relationship between stock prices and volatility. The connection between stock prices and volatility is a powerful tool for improving volatility estimations in the stock market, which is a key ingredient for investors to make good decisions. Finally, we define an extended version of the martingale condition, defined for the gauge Hamiltonian.

The information paradox suggests that the black hole loses information when it emits radiation. In this way, the spectrum of radiation corresponds to a mixed (non-pure) quantum state even if the internal state generating the black hole is expected to be pure in essence. In this paper we propose an argument solving this paradox by developing an understanding of the process by which spontaneous symmetry breaks when a black hole selects one of the many possible ground states and emits radiation as a consequence of it. Here, the particle operator number is the order parameter. This mechanism explains the connection between the density matrix, corresponding to the pure state describing the black hole state, and the density matrix describing the spectrum of radiation (mixed quantum state). From this perspective, we can recover black hole information from the superposition principle, applied to the different possible order parameters (particle number operators).

The cosmological constant is normally introduced as an additional term entering the Einstein-Hilbert (EH) action. In this letter we demonstrate that instead, it appears naturally from the standard EH action as an invariant term emerging from spacetime symmetries. We then demonstrate that the same constraint emerging from this invariant, suppresses the short wavelength modes and it favors the long wavelength ones. In this way, inside the proposed formulation, the observed value for the vacuum energy density is obtained naturally from the zero-point quantum fluctuations.

It was demonstrated previously that the stochastic volatility emerges as the gauge field necessary for restoring the local symmetry under changes of the prices of the stocks inside the Black-Scholes (BS) equation. When this occurs, then a Merton-Garman-like equation emerges. From the perspective of manifolds, this means that the Black-Scholes equation and the Merton-Garman (MG) one can be considered as locally equivalent. In this scenario, the MG Hamiltonian is a special case of a more general Hamiltonian, here called gauge-Hamiltonian. We then show that the gauge character of the volatility implies some specific functional relation between the prices of the stock and the volatility. The connection between the prices of the stocks and the volatility, is a powerful tool for improving the volatility estimations in the stock market, which is a key ingredient for the investors to make good decisions. Finally, we define an extended version of the martingale condition, defined for the gauge-Hamiltonian.