arXiv subjects

Octavio Obregón

Publications and source records attributed to Octavio Obregón.

14 recordsLinked to original sources

arXiv2025

Constructing allowed complex metrics from black holes

We use diffeomorphic mappings to connect black hole metrics with complex solutions allowed by the Kontsevich-Segal criterion. By swapping radial and time-like coordinates and applying complex mappings, we derive dynamic metrics suitable for a Quantum Field Theory. This is shown for static and rotating black holes, mapping their interiors into the Kantowski-Sachs and a specific Gowdy-type cosmological model. We offer interpretations of the period during which the Kontsevich-Segal criterion holds.

gr-qc↗

arXiv2025

Quantum Black Hole as a Harmonic Oscillator from the Perspective of the Minimum Uncertainty Approach

Starting from the eigenvalue equation for the mass of a black hole derived by Mäkelä and Repo, we show that, by reparametrizing the radial coordinate and the wave function, it can be rewritten as the eigenvalue equation of a quantum harmonic oscillator. We then study the interior of a Schwarzschild black hole using two quantization approaches. In the standard quantization, the area and mass spectra are discrete, characterized by a quantum number $n$, but the wave function is not square-integrable, limiting its physical interpretation. In contrast, a minimal-uncertainty quantization approach yields an area spectrum that grows as $n^2$, and consequently the mass $M$ also increases. In this framework, the wave function is finite and square-integrable, with convergence requiring that the deformation parameter $β$ be regulated by a discrete quantum number $m$. The wave function exhibits quantum tunneling connecting the black hole interior with both its exterior and a white hole region, effects that disappear in the limit $β\to 0$. These results demonstrate how minimal-length effects both regularize the wave function and modify the semiclassical structure of the black hole.

gr-qc↗

arXiv2025

Energy-time uncertainty relation from entropy measures

In a previous study, it was shown that the Generalized Uncertainty Principle (GUP) can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as $S_\pm$ in the literature. This finding reveals an intriguing connection between non-extensive statistics and quantum gravity. In the present work, we extend our previous result and derive a generalized energy-time uncertainty relation based on a measure of non-extensive entropies. Consequently, the dispersion relation undergoes modifications consistent with those obtained in other approaches to quantum gravity. We interpret these modifications as evidence of the non-extensive behavior of spacetime fluctuations at scales close to the Planck scale. While these effects are significant in this regime, they become negligible in the classical one, i.e. at low energies where the spacetime is smooth. As a consequence of the non-extensive behavior exhibited by spacetime at very small scales, the black hole radiation temperature undergoes quantum-level corrections, increasing in the case of $ S_{-} $ and decreasing for the case of $ S_{+} $. Moreover, the modified uncertainty relation derived here predicts a maximum uncertainty in energy, of the order of Planck energy, and a minimum time interval, of the order of the Planck time, offering new insights into the fundamental structure of spacetime in the quantum regime.

hep-th↗

arXiv2024

Black hole interior quantization: a minimal uncertainty approach

In a previous work we studied the interior of the Schwarzschild black hole implementing an effective minimal length, by applying a modification to the Poisson brackets of the theory. In this work we perform a proper quantization of such a system. Specifically, we quantize the interior of the Schwarzschild black hole in two ways: once by using the standard quantum theory, and once by following a minimal uncertainty approach. Then, we compare the obtained results from the two approaches. We show that, as expected, the wave function in the standard approach diverges in the region where classical singularity is located and the expectation value of the Kretschmann scalar also blows up on this state in that region. On the other hand, by following a minimal uncertainty quantization approach, we obtain 5 new and important results as follows. 1) All the interior states remain well-defined and square-integrable. 2) The expectation value of the Kretschmann scalar on the states remains finite over the whole interior region, particularly where used to be the classical singularity, therefore signaling the resolution of the black hole singularity. 3) A new quantum number is found which plays a crucial role in determining the convergence of the norm of states, as well as the convergence and finiteness of the expectation value of the Kretschmann scalar. 4) A minimum for the radius of the (2-spheres in the) black holes is found 5) By demanding square-integrability of states in the whole interior region, an exact relation between the Barbero-Immirzi parameter and the minimal uncertainty scale is found.

gr-qc↗

arXiv2022

Modified entropies as the origin of generalized uncertainty principles

The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with $S_{+}$ and $S_-$ entropies are negative and positive respectively. This allows us to explore various possibilities in the search of physical implications. We conclude that non-extensive statistics constitutes a signature of quantum gravity.

quant-ph↗

arXiv2021

Deformed algebra and the effective dynamics of the interior of black holes

We consider the classical Hamiltonian of the interior of the Schwarzschild black hole in Ashtekar-Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform the classical canonical algebra and derive the effective dynamics of the model under this modification. We show that such a deformation leads to the resolution of the singularity of the black hole and a minimum nonzero radius for the infalling 2-spheres, provided that the deformation parameters are chosen to be negative.

gr-qc↗

arXiv2021

On how generalised entropies without parameters impact information optimisation processes

As an application of generalised statistical mechanics, it is studied a possible route toward a consistent generalised information theory in terms of a family of non-extensive, non-parametric entropies $H^\pm_D(P)$. Unlike other proposals based on non-extensive entropies with a parameter dependence, our scheme is asymptotically equivalent to the one formulated by Shannon, while it differs in regions where the density of states is reasonably small, which leads to information distributions constrained to their background. Two basic concepts are discussed to this aim. First, we prove two effective coding theorems for the entropies $H^\pm_D(P)$. Then we calculate the channel capacity of a binary symmetric channel (BSC) and a binary erasure channel (BEC) in terms of these entropies. We found that processes such as data compression and channel capacity maximisation can be improved in regions where there is a low density of states, whereas for high densities our results coincide with Shannon's formulation.

cs.IT↗

arXiv2021

A superstatistical formulation of complexity measures

It is discussed how the superstatistical formulation of effective Boltzmann factors can be related to the concept of Kolmogorov complexity, generating an infinite set of complexity measures (CMs) for quantifying information. At this level, the information is treated according to its background, which means that the CM depends on the inherent attributes of the information scenario. While the basic Boltzmann factor directly produces the standard complexity measure (SCM), it succeeds in the description of large-scale scenarios where the data components are not interrelated with themselves, thus adopting the behaviour of a gas. What happens in scenarios in which the presence of sources and sinks of information cannot be neglected, needs of a CM other than the one produced by the ordinary Boltzmann factor. We introduce a set of flexible CMs, without free parameters, that converge asymptotically to the Kolmogorov complexity, but also quantify the information in scenarios with a reasonable small density of states. We prove that these CMs are obtained from a generalised relative entropy and we suggest why such measures are the only compatible generalisations of the SCM.

cs.CC↗

arXiv2020

Minimal Length Effects on Quantum Cosmology and Quantum Black Hole Models

A Kantowski-Sachs model with a modified quantization prescription is considered. Such quantization rules, inspired by the so-called Generalized Uncertainty Principle (GUP), correspond to a modified commutation relation between minisuperspace variables and their conjugate momenta. For a wide range of the modification parameter, this approach differentiates from the standard results by the presence of a potential well in the corresponding Wheeler-DeWitt equation. This then produces the appearance of a set of wave functions, with corresponding discrete energy spectrum.

gr-qc↗

arXiv2019

Quantum implications of non-extensive statistics

Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the semiclassical approximation as $K=F(T) \exp\left(i S_{cl}/\hbar\right)$. We determine also propagators associated to different non-additive statistics; those are the entropies depending only on the probability $S_{\pm}$ [2] and Tsallis entropy $S_q$ [3]. For $S_{\pm}$ we obtain a power series solution for the probability vs. the energy, which can be analytically continued to the complex plane, and employed to obtain the propagators. Our work is motivated by [4] where a modified q-Schrödinger equation is obtained; that provides the wave function for the free particle as a q-exponential. The modified q-propagator obtained with our method, leads to the same q-wave function for that case. The procedure presented in this work allows to calculate q-wave functions in problems with interactions; determining non-linear quantum implications of non-additive statistics. In a similar manner the corresponding generalized wave functions associated to $S_{\pm}$ can also be constructed. The corrections to the original propagator are explicitly determined in the case of a free particle and the harmonic oscillator for which the semi-classical approximation is exact.

cond-mat.stat-mech↗

arXiv2017

Modified entropies, their corresponding Newtonian forces, potentials, and temperatures

Assuming the hypothesis of the entropic nature of gravity, we calculate generalized Newtonian forces, their associated potentials and field equations, when other, in general non-extensive, entropies are considered instead of the usual Boltzmann entropy. Some comments about the nature of the correction terms presented are given, and a calculation of corrections to the Bekenstein-Hawking temperature is performed using the arguments which lead to what can be called a Michell-Laplace black hole.

gr-qc↗

arXiv2016

Newtonian black holes: Particle production, "Hawking" temperature, entropies and entropy field equations

Newtonian gravitation with some slight modifications, along with some highly simplified ideas from quantum field theory allow us to reproduce, at least at the level of back-of-the-envelope calculations, many results of black hole physics. We consider particle production by a black hole, the Newtonian equivalent of the Hawking temperature, and the Bekenstein entropy. Also, we are able to deduce Newtonian field equations from entropy. We finally study higher-order Newtonian theories under the same assumptions used for ordinary Newtonian theory. In a companion article we will look at entropic forces for various entropies and make contact with our analysis of higher-order Newtonian theories.

gr-qc↗

arXiv2016

H-theorem and Thermodynamics for generalized entropies that depend only on the probability

We consider a previously proposed non-extensive statistical mechanics in which the entropy depends only on the probability, this was obtained from a f(β) distribution and its corresponding Boltzmann factor. We show that the first term correcting the usual entropy also arises from several f(β) distributions, we also construct the corresponding H-function and demonstrate that a generalized H-theorem is fulfilled. Furthermore, expressing this H-function as function of the simplest Maxwellian state we find, up to a first approximation some modified thermodynamic quantities for an ideal gas. In order to gain some insight about the behavior of the proposed generalized statistics, we present some simulation results for the case of a square-well and Lennard-Jones potentials, showing that an effective repulsive interaction is obtained with the new formalism.

cond-mat.stat-mech↗

arXiv2015

Generalized entanglement entropy and holography

In this work, we first introduce a generalized von Neumann entropy that depends only on the density matrix. This is based on a previous proposal by one of us modifying the Shannon entropy by considering non-equilibrium systems on stationary states, and an entropy functional depending only on the probability. We propose a generalization of the replica trick and find that the resulting modified von Neumann entropy is precisely the previous mentioned entropy that was obtained by other assumptions. Then, we address the question whether alternative entanglement entropies can play a role in the gauge/gravity duality. Our focus are 2d CFT and their gravity duals. Our results show corrections to the von Neumann entropy $S_0$ that are larger than the usual $UV$ ones and also than the corrections to the length dependent $AdS_3$ entropy which result comparable to the $UV$ ones. The correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT and the gravitational $AdS_3$ entropies.

hep-th↗