Relativistic Quantum Geometry Research Articles

On the interaction of Schwarzschild black-holes with gravitational waves

Within the framework of Relativistic Quantum Geometry, we explore a physical scenario involving the interaction of a gravitational wave with a Schwarzschild black hole. During this interaction, the black hole absorbs a fraction of the incoming energy, converting it into rotational and translational kinetic energies. The remaining energy is then carried away by the reflected gravitational wave. This article focuses on examining the characteristics of the reflected wave and analyzing the amount of energy absorbed by the black hole.

Quantum thermodynamics in the interior of a Schwarzschild black-hole

We study space-time back-reaction configuration in the interior of a Schwarzschild Black-Hole (B-H) using Relativistic Quantum Geometry described in (Ridao and Bellini 2015 Astrophys. Space Sci. 357 94) and (Ridao and Bellini 2015 Phys. Lett. B 751 565). We found discrete energy levels for a scalar field from a polynomial condition for Heun Confluent functions expanded around the Schwarzschild radius. From the solutions it is obtained that the uncertainty principle is valid for each energy level of space-time, in the form: E n r sh,n = ℏ/2. Temperature, entropy and the B-H mass are dependent on the number of states in the B-H, such that the Bekenstein-Hawking (BH) results are obtained in a limit case.

New preinflation

I propose a new model of preinflation, where the universe suffers a transition from an initial stable state [such that the universe is initially at the minimum of a ϕ-quartic potential: V(ϕ)∼ϕ4], to an unstable evolving state that drives the initial accelerated expansion. Using Relativistic Quantum Geometry (RQG), I demonstrate that back-reaction produced by the inflaton field fluctuations should be responsible for an additional term in the effective scalar potential. These fluctuations are very strong, and should cause the initial expansion of the universe when self-interactions of the inflaton fluctuations are included in its dynamics, even though it is initially in a stable state. The equation of state evolves from ω=−1∕3 to ω≲−1 and slow-roll conditions become naturally at the end of preinflation.

Quantum thermodynamics in the interior of a Reissner–Nordström black-hole

We study the interior of a Reissner-Nordstr\"om Black-Hole (RNBH) using Relativistic Quantum Geometry, which was introduced in some previous works. We found discrete energy levels for a scalar field from a polynomial condition for the Heun Confluent functions expanded around the effective causal radius $r_*$. From the solutions it is obtained that the uncertainty principle is valid for each energy level of space-time, in the form: $E_n\, r_{*,n}=\hbar/2$, and the charged mass is discretized and distributed in a finite number of states. The classical RNBH entropy is recovered as the limit case where the number of states is very large, and the RNBH quantum temperature depends on the number of states in the interior of the RNBH. This temperature, depending of the number of states of the RNBH, is related with the Bekeinstein-Hawking (BH) temperature: $T_{BH} \leq T_{N} < 2\,T_{BH}$.

Quantum thermodynamics in a static de Sitter space-time and initial state of the universe

Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around r=0. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energy’s level and the Bekenstein–Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy E_p=m_p,c^2, and a B–H temperature: T_{BH}=left( frac{hbar ,c}{2pi ,l_p,K_B}right) .

Towards unified spinor fields: confinement of gravitons on a de Sitter background

We propose a unified theory for spinor fields on extended Weyl manifolds taking into account self-interactions to obtain the relativistic dynamics on a general curved Riemannian background as a continuation of the relativistic quantum geometry program, recently introduced. We focus our attention separately on both massless and matter fields. We study an example of confined gravitons on a de Sitter background at Planckian scales.

Relativistic quantum geometry from a 5D geometrical vacuum: Gravitational waves from preinflation

Abstract In this work we introduce Relativistic Quantum Geometry (RQG) on a Modern Kaluza–Klein theory by studying the boundary conditions on a extended Einstein–Hilbert action for a 5D vacuum defined on a 5D (background) Riemannian manifold. We introduce a connection which describes a displacement from the background manifold to the extended one, on which the 5D vacuum Einstein equations with cosmological constant included, describes the dynamics of the scalar field σ , which is responsible of describing the mentioned displacement and complies with a relativistic quantum algebra that depends on the relativistic observers. In our formalism the extra dimension is considered as space-like, and therefore is a noncompact one. After considering a static foliation on the extra dimension, we obtain the dynamics for the gravitational waves that propagates on a 4D (curved) background, defined on the 4D induced curved Riemannian manifold. Finally, an example, in which we study a pre-inflationary model of the early universe is developed. We obtain some constraints from Planck2018 observations.

Large scale solitonic back-reaction effects in pre-inflation

Abstract Using Relativistic Quantum Geometry (RQG), we study the emergence of back-reaction modes with solitonic properties, on astrophysical and cosmological scales, in a model of pre-inflation where the universe emerge from a topological phase transition. We found that, modes of the geometrical field that describes back-reaction effects related to larger scales (cosmological scales), are more coherent than those related to astrophysical scales, so that they can be considered a coarse-grained soliton.

Pre-inflation: Origin of the Universe from a topological phase transition

I study a model which describes the birth of the universe using a global topological phase transition with a complex manifold where the time, τ, is considered as a complex variable. Before the big bang τ is a purely imaginary variable so that the space can be considered as Euclidean. The phase transition from a pre-inflation to inflation is examined by studying the dynamical rotation of the time on the complex plane. Back-reaction effects are exactly calculated using Relativistic Quantum Geometry.

Absorption of charged particles in a Reissner-Nordström black-hole: entropy evolution from relativistic quantum geometry

Using Relativistic Quantum Geometry we show that the entropy can decrease in very small BHs, under certain circumstances, but always increases in very massive Black-Holes.

Charged and Electromagnetic Fields from Relativistic Quantum Geometry

In the recently introduced Relativistic Quantum Geometry (RQG) formalism, the possibility was explored that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the dynamics of an auxiliary geometrical scalar field θ, in order that the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold. In this framework we study jointly the dynamics of electromagnetic fields produced by quantum complex vector fields, which describes charges without charges. We demonstrate that complex fields act as a source of tetra-vector fields which describe an extended Maxwell dynamics.

Geometric back-reaction in pre-inflation from relativistic quantum geometry

The pre-inflationary evolution of the universe describes the beginning of the expansion from a static initial state, such that the Hubble parameter is initially zero, but increases to an asymptotic constant value, in which it could achieve a de Sitter (inflationary) expansion. The expansion is driven by a background phantom field. The back-reaction effects at this moment should describe vacuum geometrical excitations, which are studied in detail in this work using relativistic quantum geometry.

Inflationary back-reaction effects from Relativistic Quantum Geometry

Abstract We study the dynamics of scalar metric fluctuations in a non-perturbative variational formalism recently introduced, by which the dynamics of a geometrical scalar field θ , describes the quantum geometrical effects on a Weylian-like manifold with respect to a background Riemannian space–time. In this letter we have examined an example in the framework of inflationary cosmology. The resulting spectral predictions are in very good agreement with observations and other models of inflation.

Towards relativistic quantum geometry

We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.