arXiv subjects

Douglas Singleton

Publications and source records attributed to Douglas Singleton.

At least 37 records · Page 2Linked to original sources

arXiv2023

Minimal Lengths in 3D via the Generalized Uncertainty Principle

We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the standard position-momentum commutators as possible. Moreover, we bound the physical momentum which leads to an effective minimal length in every coordinate direction. The physical consequences of these modified operators are explored in two scenarios: (i) when a spherically-symmetric wave function is `compressed' into the smallest possible volume; (ii) when the momentum is directed in a single direction. In case (ii), we find that the three dimensional GUP exhibits interesting phenomena that do not occur in one dimension: the minimal distance in the direction parallel to a particle's momentum is different from the minimal distance in the orthogonal directions.

quant-ph↗

arXiv2023

Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics

This paper systematically explores new classes of black hole (BH) solutions in nonassociative and noncommutative gravity by focusing on features that generalize to higher dimensions. The theories we study are modelled on (co) tangent Lorentz bundles (i.e. eight dimensional phase spaces) with a star product structure determined by R-flux deformations in string theory. The nonassociative vacuum Einstein equations involve real and complex effective sources with coefficients which are proportional to the Planck and string constants or their products. We develop the anholonomic frame and connection deformation method and prove that such systems of nonlinear partial differential equations can be decoupled and integrated in general form for a generic off-diagonal ansatz for symmetric and non-symmetric metrics. The coefficients of such metrics may depend on all phase space coordinates (space-time coordinates plus energy-momentum). Conditions are given when the generating and integration functions and effective sources define two classes of physically important exact and parametric solutions with R-flux sources related via nonlinear symmetries to effective cosmological constants: (1) 6D Tangherlini BHs, which are star product and R-flux distorted to quasi-stationary configurations and 8D black ellipsoids (BEs) and BHs; (2) nonassocitative space-time and co-fiber space double BH and/or BE configurations generalizing Schwarzschild - de Sitter metrics. We argue that the concept of Bekenstein-Hawking entropy is applicable only for very special classes of nonassociative BHs encoding conventional horizons and (anti) de Sitter configurations. Finally, we show how analogs of the relativistic G. Perelman geometric thermodynamic variables can be defined and computed for general classes of off-diagonal solutions encoding nonassociative R-flux deformations.

hep-th↗

arXiv2022

Comments on the cosmological constant in generalized uncertainty models

The existence of a small, non-zero cosmological constant is one of the major puzzles in fundamental physics. Naively, quantum field theory arguments would imply a cosmological constant which is up to 10$^{120}$ times larger than the observed one. It is believed a comprehensive theory of quantum gravity would resolve this enormous mismatch between theory and observation. In this work, we study the ability of generalized uncertainty principle (GUP) models, which are phenomenologically motivated models of quantum gravity, to address the cosmological constant problem. In particular, we focus on how these GUP models may change the phase space of QFT, and how this affects the momentum space integration of the zero-point energies of normal modes of fields. We point out several issues that make it unlikely that GUP models, in their current form, would be able to adequately address the cosmological constant problem.

physics.gen-ph↗

arXiv2022

The more things change the more they stay the same: Minimum lengths with unmodified uncertainty principle and dispersion relation

Broad arguments indicate that quantum gravity should have a minimal length scale. In this essay we construct a minimum length model by generalizing the time-position and energy-momentum operators while keeping much of the structure of quantum mechanics and relativity intact: the standard position-momentum commutator, the special relativistic time-position, and energy-momentum relationships all remain the same. Since the time-position and energy-momentum relationships for the modified operators remains the same, we retain a form of Lorentz symmetry. This avoids the constraints on these theories coming from lack of photon dispersion while holding the potential to address the Greisen-Zatsepin-Kuzmin (GZK) puzzle of ultra high energy cosmic rays.

gr-qc↗

arXiv2022

A Subtle Aspect of Minimal Lengths in the Generalized Uncertainty Principle

In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator, $[\hat{X},\hat{P}] = i \hbar (1+βp^2)$, may have different physical consequences such as having no minimal length at all. These differences depend on how the position and/or momentum operators are modified rather than only on the resulting modified commutator. This provides guidance when constructing GUP models since it distinguishes those GUPs that have a minimal length scale, as suggested by some broad arguments about quantum gravity, versus GUPs without a minimal length scale.

gr-qc↗

arXiv2021

Comment on "Massive electrodynamics and the magnetic monopoles"

In this paper we correct previous work on magnetic charge plus a photon mass. We show that contrary to previous claims this system has a very simple, closed form solution which is the Dirac string potential multiplied by a exponential decaying part. Interesting features of this solution are discussed, namely, (i) the Dirac string becomes a real feature of the solution, (ii) the breaking of gauge symmetry via the photon mass leads to a breaking of the rotational symmetry of the monopole's magnetic field, (iii) the Dirac quantization condition is potentially altered.

hep-th↗

arXiv2021

Reconciling a quantum gravity minimal length with lack of photon dispersion

Generic arguments lead to the idea that quantum gravity has a minimal length scale. A possible observational signal of such a minimal length scale is that photons should exhibit dispersion. In 2009 the observation of a short gamma ray burst seemed to bound the minimal length scale to distances smaller than the Planck length, implying that spacetime appeared continuous to distances below the Planck length. This poses a challenge for such minimal distance models. Here we propose a modification of the position and momentum operators, ${\hat x}$ and ${\hat p}$, which lead to a minimal length scale, but preserve the photon energy-momentum relationship $E = p c$. In this way there is no dispersion of photons with different energies. This can be accomplished without modifying the commutation relationship $[{\hat x}, {\hat p}] = i \hbar$.

hep-th↗

arXiv2020

Non-Abelian Firewall

A simple, closed-form solution to the Yang-Mills field equations is presented which has a non-Abelian firewall - a spherical "horizon" where the energy density diverges. By the gravity/gauge duality, this non-Abelian firewall implies the existence of a gravitational firewall. Gravitational firewalls have been proposed as a way of resolving the information loss paradox, but at the cost of violating the equivalence principle.

gr-qc↗

arXiv2020

Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames

The duality of gravitational dynamics (projected on a null hypersurface) and of fluid dynamics is investigated for the scalar tensor (ST) theory of gravity. The description of ST gravity, in both Einstein and Jordan frames, is analyzed from fluid-gravity viewpoint. In the Einstein frame the dynamical equation for the metric leads to the Damour-Navier-Stokes (DNS) equation with an external forcing term, coming from the scalar field in ST gravity. In the Jordan frame the situation is more subtle. We observe that finding the DNS equation in this frame can lead to two pictures. In one picture, the usual DNS equation is modified by a Coriolis-like force term, which originates completely from the presence of a non-minimally coupled scalar field ($ϕ$) on the gravity side. Moreover, the identified fluid variables are no longer conformally equivalent with those in the Einstein frame. However, this picture is consistent with the saturation of Kovtun-Son-Starinets (KSS) bound. In the other picture, we find the standard DNS equation (i.e. without the Coriolis-like force), with the fluid variables conformally equivalent with those in Einstein frame. But, the second picture, may not agree with the KSS bound for some values of $ϕ$. We conclude by rewriting the Raychaudhuri equation and the tidal force equation in terms of the relevant parameters to demonstrate how the expansion scalar and the shear-tensor evolve in the spacetime. Although, the area law of entropy is broken in ST gravity, we show that the rewritten form of Raychaudhuri's equation correctly results in the generalized second law of black hole thermodynamics.

hep-th↗

arXiv2020

Modified commutators are not sufficient to determine a quantum gravity minimal length scale

In quantum gravity it is generally thought that a modified commutator of the form $[{\hat x}, {\hat p}] = i \hbar (1 + βp^2)$ is sufficient to give rise to a minimum length scale. We test this assumption and find that different pairs of modified operators can lead to the same modified commutator and yet give different or even no minimal length. The conclusion is that the modification of the operators is the main factor in determining whether there is a minimal length. This fact - that it is the specific form of the modified operators which determine the existence or not of a minimal length scale - can be used to keep or reject specific modifications of the position and momentum operators in theory of quantum gravity.

gr-qc↗

arXiv2019

Modified commutation relationships from the Berry-Keating program

Current approaches to quantum gravity suggest there should be a modification of the standard quantum mechanical commutator, $[{\hat x} , {\hat p}] = i \hbar$. Typical modifications are phenomenological and designed to result in a minimal length scale. As a motivating principle for the modification of the position and momentum commutator, we assume the validity of a version of the Bender-Brody-Müller variant of the Berry-Keating approach to the Riemann hypothesis. We arrive at a family of modified position and momentum operators, and their associated modified commutator, which lead to a minimal length scale. Additionally, this larger family generalizes the Bender-Brody-Müller approach to the Riemann hypothesis.

hep-th↗

arXiv2018

Interaction between gravitational radiation and electromagnetic radiation

In this review paper we investigate the connection between gravity and electromagnetism from Faraday to the present day. The particular focus is on the connection between gravitational and electromagnetic radiation. We discuss electromagnetic radiation produced when a gravitational wave passes through a magnetic field. We then discuss the interaction of electromagnetic radiation with gravitational waves via Feynman diagrams of the process $graviton + graviton \to photon + photon$. Finally we review recent work on the vacuum production of counterpart electromagnetic radiation by gravitational waves.

gr-qc↗

arXiv2018

Matter-antimatter asymmetry and other cosmological puzzles via running vacuum cosmologies

Current astronomical observations are successfully explained by the present cosmological paradigm based on the concordance model ($Λ_0$CDM + Inflation). However, such a scenario is composed of a heterogeneous mix of ingredients for describing the different stages of cosmological evolution. Particularly, it does not give an unified explanation connecting the early and late time accelerating inflationary regimes which are separated by many aeons. Other challenges to the concordance model include: a singularity at early times or the emergence of the Universe from the quantum gravity regime, the "graceful" exit from inflation to the standard radiation phase, as well as, the coincidence and cosmological constant problems. We show here that a simple running vacuum model or a time-dependent vacuum may provide insight to some of the above open questions (including a complete cosmic history), and also can explain the observed matter-antimatter asymmetry just after the initial deflationary period.

gr-qc↗

arXiv2018

Dirac and non-Dirac conditions in the 2-potential theory of magnetic charge

We investigate the Cabbibo-Ferrari, two potential approach to magnetic charge coupled to two different complex scalar fields, $Φ_1$ and $Φ_2$, each having different electric and magnetic charges. The scalar field, $Φ_1$, is assumed to have a spontaneous symmetry breaking self interaction potential which gives a mass to the "magnetic" gauge potential and "magnetic" photon, while the other "electric" gauge potential and "electric" photon remain massless. The magnetic photon is hidden until one reaches energies of the order of the magnetic photon rest mass. The second scalar field, $Φ_2$, is required in order to make the theory non-trivial. With only one field one can always use a duality rotation to rotate away either the electric or magnetic charge, and thus decouple either the associated electric or magnetic photon. In analyzing this system of two scalar fields in the Cabbibo-Ferrari approach we perform several duality and gauge transformations, which require introducing non-Dirac conditions on the initial electric and magnetic charges. We also find that due to the symmetry breaking the usual Dirac condition is altered to include the mass of the magnetic photon. We discuss the implications of these various conditions on the charges.

physics.gen-ph↗

arXiv2018

Gravity's light in the shadow of the Moon

In this essay we look at the possibility of vacuum production of very low frequency electromagnetic radiation from a gravitational wave background (i.e. gravity's light). We also propose that this counterpart electromagnetic radiation should be detectable by a lunar orbiting satellite which is periodically occulted by the Moon (i.e. in the shadow of the Moon). For concreteness we consider the possibility of detection of both the gravitational wave and hypothesized electromagnetic radiation counterpart from the supernova core collapse of Betelgeuse.

gr-qc↗

arXiv2018

Scalar field vacuum expectation value induced by gravitational wave background

We show that a {\it massless} scalar field in a gravitational wave background can develop a non-zero vacuum expectation value. We draw comparisons to the generation of a non-zero vacuum expectation value for a scalar field in the Higgs mechanism and with the dynamical Casimir vacuum. We propose that this vacuum expectation value, generated by a gravitational wave, can be connected with particle production from gravitational waves and may have consequences for the early Universe where scalar fields are thought to play an important role.

gr-qc↗

arXiv2018

Magnetic Charge and Photon Mass: Physical String Singularities, Dirac Condition, and Magnetic Confinement

We find exact, simple solutions to the Proca version of Maxwell's equations with magnetic sources. Several properties of these solutions differ from the usual case of magnetic charge with a massless photon: (i) the string singularities of the usual 3-vector potentials become real singularities in the magnetic fields; (ii) the different 3-vector potentials become gauge inequivalent and physically distinct solutions; (iii) the magnetic field depends on $r$ and $θ$ and thus is no longer rotationally symmetric; (iv) a combined system of electric and magnetic charge carries a field angular momentum even when the electric and magnetic charges are located at the same place i.e. for dyons); (v) for these dyons one recovers the standard Dirac condition despite the photon being massive. We discuss the reason for this. We conclude by proposing that the string singularity in the magnetic field of an {\it isolated} magnetic charge suggests a confinement mechanism for magnetic charge, similar to the flux tube confinement of quarks in QCD.

physics.gen-ph↗

arXiv2017

Low frequency electromagnetic radiation coming from gravitational waves generated by neutron stars

We investigate the possibility of observing very low frequency (VLF) electromagnetic radiation produced from the vacuum by gravitational waves. We review the calculations leading to the possibility of vacuum conversion of gravitational waves into electromagnetic waves and show how this process evades the well-known prohibition against particle production from gravitational waves. Using Newman-Penrose scalars, we estimate the luminosity of this proposed electromagnetic counterpart radiation coming from gravitational waves produced by neutron star oscillations. The detection of electromagnetic counterpart radiation would provide an indirect way of observing gravitational radiation with future spacecraft missions, especially lunar orbiting probes.

gr-qc↗