Rafael A. Araya-Gochez

(nearly-)indistinghishable Fermi-Dirac occupation states of the TAPIR:

a.k.a. [0-1]

"...because the warrior, having chosen a path, has but one goal: to traverse its full length."

from "The Teachings of Don Juan" by Carlos Castaneda.

Welcome to Rafael's web page. I was a visitor at Caltech's Theoretical Astrophysics group (a.k.a. TAPIR) from about 2000 to 2005, working on various Magnetohydrodynamic and General Relativity problems in Astrophysics. More recently, I moved to mathematical physics driven primarily by a desire to understand "the dark mysteries of the Universe"; namely, Dark Matter and the cosmological constant problem (a.k.a. Dark Energy). In a nut-shell, for roughly the last ten years I have aimed to make sense of the mathematical structure of gravity in the modern language of symmetries. This exercise led me to formulate a theory of gravity at low energies that incorporates the most fundamental symmetries of spacetime in a geometrically intrinsic manner; literally building Universal space from its core foundational constituents. The first paper in a series of papers that expound this program is entitled ''On the Algebraic Structure of Spacetime and 3rd Quantization". In it, I conclude that quantization of spacetime endows it with matter content upon incorporation of the symmetries of the Standard Model of particle physics; in particular, a coupling to the Higgs Vacuum Expectation Value. The framework then naturally leads to a clear prediction for a Dark Matter particle in the form of a non--super-symmetric Majorana spinor..

The early years: 2000-2005

Nascent black holes are conjectured to occur at the cores of very massive stars to yield Gamma-ray Bursts. As I set out to understand the magnetic nature of accretion flows onto black holes, I was first to carry out a fully general relativistic analysis of the problem (in the Cowling approximation). In a subsequent paper, I make the prediction that the black hole may be driven into a strongly vibrating mode by heavy clumps of material falling in through the "event horizon" in unison with the hole's natural oscillating tempo. The energy of such vibrations would radiate away in a very uniform pattern of Gravitational Waves that may someday be observed by LIGO. Remarkably, the 2017 Nobel Prize in Physics was rightfully awarded to the LIGO collaboration for the monumental first detection of gravitational waves; this time from a very powerful collision black holes. The signal I proposed is much weaker than this first detection but would be very characteristic of the quasi-ringing modes in a hyper-accreting stellar mass black hole.

More recently: 2008-2017

After a rendezvous with mathematical finance and game theory, I was drawn back to the realm of theoretical physics by the cosmological constant problem. Standard fare in modern physics posits that empty space is endowed with quantum energy. Although quantum physics and general relativity are fundamentally inconsistent with each other, the mathematical framework invoked by Albert Einstein to construct the General Theory of Relativity admits an extra term--a.k.a. the cosmological term--that accounts for the "virtual" energy of the vacuum. Taken at face value, such conjecture leads to an outlandish dynamical effect: a "speeding up" in the expansion of the fabric of space-time associated with the growth of vacuum in the Universe. Astonishingly, today we know that the expansion of the Universe has indeed been accelerating for well over half of the time the Universe's been around! However, this effect is much too weak to fit into the standard model of particle physics; in particular, it seems to point towards our clear misunderstanding of the physical vacuum!

I am chiefly concerned with fundamentally geometric constructions of [quantum] gravity where a non-vanishing cosmological constant could arise naturally as a by product of interpreting gravity as a ``gauge theory" of an underlying symmetry principle; e.g., gauging the deSitter group in a quasi--Yang-Mills form. Yet, gravity as a gauge theory has a far richer mathematical structure than a standard Yang-Mills gauge theory. In particular, the gauge fields of gravity must account for the frames of general relativity in a very peculiar way. I have taken the faithful representation of the Lorentz group--more technically, its simply connected component--to constitute the core foundational symmetry of spacetime and combine this with some fancy math to accommodate for gravity's significantly more complex mathematical structure: algebraic, geometric and topological. This is the physical content of graviforms as postulated in my first paper. Rather amusingly, I start with general relativity and end up with a curious variant of a quantum field theory without explicit coordinate referents! More technically, my thesis sustains that the use of quotient algebras facilitates the most transparent interpretation of spin structure as a manifestly quantum phenomenon. The formal machinery goes by the name of quantum ring theory and it facilitates a transparent interpretation of spacetime as a quantized derivation algebra. The generalized frames of general relativity then encompass spin structure in the form of "singular geometric points" and this leads to the prediction for a Dark Matter particle at the electro-weak scale; i.e., with a mass within a factor of 2 from the mass of the Higgs particle. Status: this paper was submitted to Annals of Physics on December 8th, 2017.