arXiv subjects

Matthew J. Lake

Publications and source records attributed to Matthew J. Lake.

At least 37 records · Page 2Linked to original sources

arXiv2020

Dark energy effects in the Schrödinger-Newton approach

The Schrödinger-Newton equation is a proposed model to explain the localization of macroscopic particles by suppressing quantum dispersion with the particle's own gravitational attraction. On cosmic scales, however, dark energy also acts repulsively, as witnessed by the accelerating rate of universal expansion. Here, we introduce the effects of dark energy in the form of a cosmological constant $Λ$, that drives the late-time acceleration of the Universe, into the Schrödinger-Newton approach. We then ask in which regime dark energy dominates both canonical quantum diffusion and gravitational self-attraction. It turns out that this happens for sufficiently delocalized objects with an arbitrary mass and that there exists a minimal delocalization width of about $67$ m. While extremely macroscopic from a quantum perspective, the value is in principle accessible to laboratories on Earth. Hence, we analyze, numerically, how the dynamics of an initially spherical Gaussian wave packet is modified in the presence of $Λ> 0$. A notable feature is the gravitational collapse of part of the wave packet, in the core region close to the center of mass, accompanied by the accelerated expansion of the more distant shell surrounding it. The order of magnitude of the distance separating collapse from expansion matches analytical estimates of the classical turnaround radius for a spherically symmetric body in the presence of dark energy. However, the time required to observe these modifications is astronomical. They can potentially be measured only in physical systems simulating a high effective cosmological constant, or, possibly, via their effects on the inflationary universe.

gr-qc↗

arXiv2019

A solution to the soccer ball problem for generalised uncertainty relations

We propose a new method for generating generalised uncertainty relations (GURs) including the generalised uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalised uncertainty principle (EGUP), previously proposed in the quantum gravity literature, without modifying the Heisenberg algebra. Our approach is compatible with the equivalence principle, and with local Poincar{\' e} invariance in the relativistic limit, thus circumventing many of the problems associated with GURs derived from modified commutation relations. In particular, it does not require the existence of a nonlinear additional law for momenta. This allows sensible multiparticle states to be constructed in which the total momentum is macroscopic, even if the momentum of an individual particle is bounded by the Planck momentum, thus providing a resolution of the "soccer ball problem" that plagues current approaches to GURs.

gr-qc↗

arXiv2019

Generalised uncertainty relations from superpositions of geometries

Phenomenological approaches to quantum gravity implement a minimum resolvable length-scale but do not link it to an underlying formalism describing geometric superpositions. Here, we introduce an intuitive approach in which points in the classical spatial background are delocalised, or `smeared', giving rise to an entangled superposition of geometries. The model uses additional degrees of freedom to parameterise the superposed classical backgrounds. Our formalism contains both minimum length and minimum momentum resolutions and we naturally identify the former with the Planck length. In addition, we argue that the minimum momentum is determined by the de Sitter scale, and may be identified with the effects of dark energy in the form of a cosmological constant. Within the new formalism, we obtain both the generalised uncertainty principle (GUP) and extended uncertainty principle (EUP), which may be combined to give an uncertainty relation that is symmetric in position and momentum. Crucially, our approach does not imply a significant modification of the position-momentum commutator, which remains proportional to the identity matrix. It therefore yields generalised uncertainty relations without violating the equivalence principle, in contradistinction to existing models based on nonlinear dispersion relations. Implications for cosmology and the black hole uncertainty principle correspondence are briefly discussed, and prospects for future work on the smeared-space model are outlined.

quant-ph↗

arXiv2019

Minimum length uncertainty relations in the presence of dark energy

We introduce a dark energy-modified minimum length uncertainty relation (DE-MLUR) or dark energy uncertainty principle (DE-UP) for short. The new relation is structurally similar to the MLUR introduced by K{\' a}rolyh{\' a}zy (1968), and reproduced by Ng and van Dam (1994) using alternative arguments, but with a number of important differences. These include a dependence on the de Sitter horizon, which may be expressed in terms of the cosmological constant as $l_{\rm dS} \sim 1/\sqrtΛ$. Applying the DE-UP to both charged and neutral particles, we obtain estimates of two limiting mass scales, expressed in terms of the fundamental constants $\left\{G,c,\hbar,Λ, e\right\}$. Evaluated numerically, the charged particle limit corresponds to the order of magnitude value of the electron mass ($m_e$), while the neutral particle limit is consistent with current experimental bounds on the mass of the electron neutrino ($m_{ν_e}$). Possible cosmological consequences of the DE-UP are considered and we note that these lead naturally to a holographic relation between the bulk and the boundary of the Universe. Low and high energy regimes in which dark energy effects may dominate canonical quantum behaviour are identified and the possibility of testing the model using near-future experiments is briefly discussed.

gr-qc↗

arXiv2018

The Compton-Schwarzschild relations in higher dimensions

In three spatial dimensions, the Compton wavelength $(R_C \propto M^{-1}$) and Schwarzschild radius $(R_S \propto M$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there is a fundamental link -- termed the Black Hole Uncertainty Principle or Compton-Schwarzschild correspondence -- between elementary particles in the $M < M_{P}$ regime and black holes in the $M > M_{P}$ regime. In the presence of $n$ extra dimensions, compactified on some scale $R_E$, one expects $R_S \propto M^{1/(1+n)}$ for $R < R_E$, which breaks this duality. However, it may be restored in some circumstances because the effective Compton wavelength depends on the form of the $(3+n)$-dimensional wavefunction. If this is spherically symmetric, then one still has $R_C \propto M^{-1}$, as in the $3$-dimensional case. The effective Planck length is then increased and the Planck mass reduced, allowing the possibility of TeV quantum gravity and black hole production at the LHC. However, if the wave function is pancaked in the extra dimensions and maximally asymmetric, then $R_C \propto M^{-1/(1+n)}$, so that the duality between $R_C$ and $R_S$ is preserved. In this case, the effective Planck length is reduced but the Planck mass is unchanged, so TeV quantum gravity is precluded and black holes cannot be generated in collider experiments. Nevertheless, the extra dimensions could still have consequences for the detectability of black hole evaporations and the enhancement of pair-production at accelerators on scales below $R_E$. Though phenomenologically general for higher-dimensional theories, our results are shown to be consistent with string theory via the minimum positional uncertainty derived from $D$-particle scattering amplitudes.

gr-qc↗

arXiv2018

Does Compton/Schwarzschild duality in higher dimensions exclude TeV quantum gravity?

In three spatial dimensions, the Compton wavelength $(R_C \propto M^{-1}$) and Schwarzschild radius $(R_S \propto M$) are dual under the transformation $M \rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests that there could be a fundamental link -- termed the Black Hole Uncertainty Principle or Compton-Schwarzschild correspondence -- between elementary particles with $M < M_{P}$ and black holes in the $M > M_{P}$ regime. In the presence of $n$ extra dimensions, compactified on some scale $R_E$ exceeding the Planck length $R_P$, one expects $R_S \propto M^{1/(1+n)}$ for $R_P < R < R_E$, which breaks this duality. However, it may be restored in some circumstances because the {\it effective} Compton wavelength of a particle depends on the form of the $(3+n)$-dimensional wavefunction. If this is spherically symmetric, then one still has $R_C \propto M^{-1}$, as in the $3$-dimensional case. The effective Planck length is then increased and the Planck mass reduced, allowing the possibility of TeV quantum gravity and black hole production at the LHC. However, if the wave function of a particle is asymmetric and has a scale $R_E$ in the extra dimensions, then $R_C \propto M^{-1/(1+n)}$, so that the duality between $R_C$ and $R_S$ is preserved. In this case, the effective Planck length is increased even more but the Planck mass is unchanged, so that TeV quantum gravity is precluded and black holes cannot be generated in collider experiments. Nevertheless, the extra dimensions could still have consequences for the detectability of black hole evaporations and the enhancement of pair-production at accelerators on scales below $R_E$. Though phenomenologically general for higher-dimensional theories, our results are shown to be consistent with string theory via the minimum positional uncertainty derived from $D$-particle scattering amplitudes.

gr-qc↗

arXiv2018

The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity

Though not a part of mainstream physics, Salam's theory of strong gravity remains a viable effective model for the description of strong interactions in the gauge singlet sector of QCD, capable of producing particle confinement and asymptotic freedom, but not of reproducing interactions involving $SU(3)$ colour charge. It may therefore be used to explore the stability and confinement of gauge singlet hadrons, though not to describe scattering processes that require colour interactions. It is a two-tensor theory of both strong interactions and gravity, in which the strong tensor field is governed by equations formally identical to the Einstein equations, apart from the coupling parameter, which is of order $1 \ \rm GeV^{-1}$. We revisit the strong gravity theory and investigate the strong gravity field equations in the presence of a mixing term which induces an effective {\it strong cosmological constant}, $Λ_{f}$. This introduces a {\it strong de Sitter radius} for strongly interacting fermions, producing a confining bubble, which allows us to identify $Λ_{f}$ with the `bag constant' of the MIT bag model, $B \simeq 2 \times 10^{14} \rm gcm^{-3}$. Assuming a static, spherically symmetric geometry, we derive the strong gravity TOV equation, which describes the equilibrium properties of compact hadronic objects. From this, we determine the generalised Buchdahl inequalities for a strong gravity `particle', giving rise to upper and lower bounds on the mass/radius ratio of stable, compact, strongly interacting objects. We show, explicitly, that the existence of the lower mass bound is induced by the presence of $Λ_f$, producing a mass gap, and that the upper bound corresponds to a deconfinement phase transition. The physical implications of our results for holographic duality in the context of the AdS/QCD and dS/QCD correspondences are also discussed.

hep-th↗

arXiv2018

Does space-time torsion determine the minimum mass of gravitating particles?

We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin-fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.

gr-qc↗

arXiv2017

Can Superconducting Cosmic Strings Piercing Seed Black Holes Generate Supermassive Black Holes in the Early Universe?

The discovery of a large number of supermassive black holes (SMBH) at redshifts $z > 6$, when the Universe was only 900 million years old, raises the question of how such massive compact objects could form in a cosmologically short time interval. Each of the standard scenarios proposed, involving rapid accretion of seed black holes or black hole mergers, faces severe theoretical difficulties in explaining the short-time formation of supermassive objects. In this work we propose an alternative scenario for the formation of SMBH in the early Universe, in which energy transfer from superconducting cosmic strings piercing small seed black holes is the main physical process leading to rapid mass increase. As a toy model, the accretion rate of a seed black hole pierced by two antipodal strings carrying constant current is considered. Using an effective action approach, which phenomenologically incorporates a large class of superconducting string models, we estimate the minimum current required to form SMBH with masses of order $M = 2 \times 10^{9}M_{\odot}$ by $z = 7.085$. This corresponds to the mass of the central black hole powering the quasar ULAS J112001.48+064124.3 and is taken as a test case scenario for early-epoch SMBH formation. For GUT scale strings, the required fractional increase in the string energy density, due to the presence of the current, is of order $10^{-7}$, so that their existence remains consistent with current observational bounds on the string tension. In addition, we consider an "exotic" scenario, in which an SMBH is generated when a small seed black hole is pierced by a higher-dimensional $F-$string, predicted by string theory. We find that both topological defect strings and fundamental strings are able to carry currents large enough to generate early-epoch SMBH via our proposed mechanism.

astro-ph.CO↗

arXiv2017

Is there a connection between "dark" and "light" physics?

In the early-mid 20$^{\rm th}$ century Dirac and Zel'dovich were among the first scientists to suggest an intimate connection between cosmology and atomic physics. Though a revolutionary proposal for its time, Dirac's Large Number Hypothesis (1937) adopted a standard assumption of the day, namely, the non-existence of the cosmological constant term ($Λ= 0$). As a result, its implementation necessitated extreme violence to the theory of general relativity -- something few physicists were prepared to sacrifice in favour of `numerology' -- requiring a time-dependent gravitational coupling of the form $G(t) \sim 1/t$. Zel'dovich's insight (1968) was to realise that a small but nonzero cosmological term ($Λ> 0$) allowed the present day radius of the Universe to be identified with the de Sitter radius, $r_{\rm U} \simeq l_{\rm dS} \simeq 1/{\sqrtΛ}$, which removed the need for time-dependence in the fundamental couplings. Thus, he obtained the formula $Λ\simeq m^6G^2/\hbar^4$, where $m$ is a mass scale characterising the relative strengths of the gravitational and electromagnetic interactions, which he identified with the proton mass $m_{\rm p}$. In this paper, we review a number of recent arguments which, instead, suggest the identification $m = m_{\rm e}/α_{\rm e}$, where $m_{\rm e}$ is the electron mass and $α_{\rm e} = e^2/\hbar c \simeq 1/137$ is the usual fine structure constant. We note that these are of a {\it physical} nature and, therefore, represent an attempt to lift previous arguments \emph{{\` a} la} Dirac from the realm of numerology into the realm of empirical science. If valid, such arguments suggest an intimate connection, not only between the macroscopic and microscopic worlds, but, perhaps even more surprisingly, between the very essence of "dark" and "light" physics.

gr-qc↗

arXiv2017

Dynamical behavior and Jacobi stability analysis of wound strings

We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of $\mathbb{R}^2$, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an $S^2$ of constant radius $\mathcal{R}$. We then use Kosambi-Cartan-Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective $(3+1)$-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.

hep-th↗

arXiv2016

The minimum mass of a charged spherically symmetric object in $D$ dimensions, its implications for fundamental particles, and holography

We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a $D$-dimensional space-time in the framework of general relativity, and in the presence of dark energy. The total energy, including the gravitational component, and the stability of objects with minimum mass/radius ratio is also investigated. The minimum energy condition leads to a representation of the mass and radius of the charged objects with minimum mass/radius ratio in terms of the charge and vacuum energy only. As applied to the electron in the four-dimensional case, this procedure allows one to re-obtain the classical electron radius from purely general relativistic considerations. By combining the lower mass bound, in four space-time dimensions, with minimum length uncertainty relations (MLUR) motivated by quantum gravity, we obtain an alternative bound for the maximum charge/mass ratio of a stable, gravitating, charged quantum mechanical object, expressed in terms of fundamental constants. Evaluating this limit numerically, we obtain again the correct order of magnitude value for the charge/mass ratio of the electron, as required by the stability conditions. This suggests that, if the electron were either less massive (with the same charge) or if its charge were any higher (for fixed mass), a combination of electrostatic and dark energy repulsion would destabilize the Compton radius. In other words, the electron would blow itself apart. Our results suggest the existence of a deep connection between gravity, the presence of the cosmological constant, and the stability of fundamental particles.

gr-qc↗

arXiv2016

Which quantum theory must be reconciled with gravity? (And what does it mean for black holes?)

We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic QFTs, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, such schemes give rise to quantum states obeying canonical dispersion relations, obtained by substituting the de Broglie relations into the relevant (classical) energy-momentum relation. In canonical QM, this yields a dispersion relation involving $\hbar$ but not $c$, whereas the canonical relativistic dispersion relation involves both. Extending this logic to the canonical quantization of the gravitational field gives rise to loop quantum gravity, and a map between classical variables containing $G$ and $c$, and associated commutators involving $\hbar$. This naturally defines a "wave-gravity duality", suggesting that a quantum wave packet describing {\it self-gravitating matter} obeys a dispersion relation involving $G$, $c$ and $\hbar$. We propose an ansatz for this relation, which is valid in the semi-Newtonian regime of both QM and general relativity. In this limit, space and time are absolute, but imposing $v_{\rm max} = c$ allows us to recover the standard expressions for the Compton wavelength $λ_C$ and the Schwarzschild radius $r_S$ within the same ontological framework. The new dispersion relation is based on "extended" de Broglie relations, which remain valid for slow-moving bodies of {\it any} mass $m$. These reduce to canonical form for $m \ll m_P$, yielding $λ_C$ from the standard uncertainty principle, whereas, for $m \gg m_P$, we obtain $r_S$ as the natural radius of a self-gravitating quantum object. Thus, the extended de Broglie theory naturally gives rise to a unified description of black holes and fundamental particles in the semi-Newtonian regime.

gr-qc↗

arXiv2016

Mass bounds for compact spherically symmetric objects in generalized gravity theories

We derive upper and lower bounds on the mass-radius ratio of stable compact objects in extended gravity theories, in which modifications of the gravitational dynamics via-{\' a}-vis standard general relativity are described by an effective contribution to the matter energy-momentum tensor. Our results include the possibility of a variable coupling between the matter sector and the gravitational field and are valid for a large class of generalized gravity models. The generalized continuity and Tolman-Oppenheimer-Volkoff equations are expressed in terms of the effective mass, density and pressure, given by the bare values plus additional contributions from the total energy-momentum tensor, and general theoretical limits for the maximum and minimum mass-radius ratios are explicitly obtained. As an applications of the formalism developed herein, we consider compact bosonic objects, described by scalar-tensor gravitational theories with self-interacting scalar field potentials, and charged compact objects, respectively. For Higgs type models, we find that these bounds can be expressed in terms of the value of the potential at the surface of the compact object. Minimizing the energy with respect to the radius, we obtain explicit upper and lower bounds on the mass, which admits a Chandrasekhar type representation. For charged compact objects, we consider the effects of the Poincaré stresses on the equilibrium structure and obtain bounds on the radial and tangential stresses. As a possible astrophysical test of our results, we obtain the general bound on the gravitational redshift for compact objects in extended gravity theories. General implications of minimum mass bounds for the gravitational stability of fundamental particles and for the existence of holographic duality between bulk and boundary degrees of freedom are also considered.

gr-qc↗

arXiv2016

The Compton-Schwarzschild correspondence from extended de Broglie relations

The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial gravity. In a mass-radius diagram, the two lines intersect near the Planck point $(l_P,m_P)$, where quantum gravity effects become significant. Since canonical (non-gravitational) quantum mechanics is based on the concept of wave-particle duality, encapsulated in the de Broglie relations, these relations should break down near $(l_P,m_P)$. It is unclear what physical interpretation can be given to quantum particles with energy $E \gg m_Pc^2 $, since they correspond to wavelengths $λ\ll l_P$ or time periods $T \ll t_P$ in the standard theory. We therefore propose a correction to the standard de Broglie relations, which gives rise to a modified Schr{\" o}dinger equation and a modified expression for the Compton wavelength, which may be extended into the region $E \gg m_Pc^2$. For the proposed modification, we recover the expression for the Schwarzschild radius for $E \gg m_Pc^2$ and the usual Compton formula for $E \ll m_Pc^2$. The sign of the inequality obtained from the uncertainty principle reverses at $m \approx m_P$, so that the Compton wavelength and event horizon size may be interpreted as minimum and maximum radii, respectively. We interpret the additional terms in the modified de Broglie relations as representing the self-gravitation of the wave packet.

gr-qc↗

arXiv2015

Bose-Einstein condensate strings

We consider the possible existence of gravitationally bound general relativistic strings consisting of Bose-Einstein condensate (BEC) matter which is described, in the Newtonian limit, by the zero temperature time-dependent nonlinear Schrödinger equation (the Gross-Pitaevskii equation), with repulsive interparticle interactions. In the Madelung representation of the wave function, the quantum dynamics of the condensate can be formulated in terms of the classical continuity equation and the hydrodynamic Euler equations. In the case of a condensate with quartic nonlinearity, the condensates can be described as a gas with two pressure terms, the interaction pressure, which is proportional to the square of the matter density, and the quantum pressure, which is without any classical analogue though, when the number of particles in the system is high enough, the latter may be neglected. Assuming cylindrical symmetry, we analyze the physical properties of the BEC strings in both the interaction pressure and quantum pressure dominated limits, by numerically integrating the gravitational field equations. In this way we obtain a large class of stable stringlike astrophysical objects, whose basic parameters (mass density and radius) depend sensitively on the mass and scattering length of the condensate particle, as well as on the quantum pressure of the Bose-Einstein gas.

gr-qc↗

arXiv2015

Cosmic strings in $f\left(R,L_m\right)$ gravity

We consider Kasner-type static, cylindrically symmetric interior string solutions in the $f\left(R,L_m\right)$ theory of modified gravity. The physical properties of the string are described by an anisotropic energy-momentum tensor satisfying the condition $T_t^t=T_z^z$; that is, the energy density of the string along the $z$-axis is equal to minus the string tension. As a first step in our study we obtain the gravitational field equations in the $f\left(R,L_m\right)$ theory for a general static, cylindrically symmetric metric, and then for a Kasner-type metric, in which the metric tensor components have a power law dependence on the radial coordinate $r$. String solutions in two particular modified gravity models are investigated in detail. The first is the so-called "exponential" modified gravity, in which the gravitational action is proportional to the exponential of the sum of the Ricci scalar and matter Lagrangian, and the second is the "self-consistent model", obtained by explicitly determining the gravitational action from the field equations under the assumption of a power law dependent matter Lagrangian. In each case, the thermodynamic parameters of the string, as well as the precise form of the matter Lagrangian, are explicitly obtained.

gr-qc↗

arXiv2015

Dynamics of cosmic strings with higher-dimensional windings

We consider F-strings with arbitrary configurations in the Minkowski directions of a higher-dimensional spacetime, which also wrap and spin around $S^1$ subcycles of constant radius in an arbitrary internal manifold, and determine the relation between the higher-dimensional and the effective four-dimensional quantities that govern the string dynamics. We show that, for any such configuration, the motion of the windings in the compact space may render the string effectively tensionless from a four-dimensional perspective, so that it remains static with respect to the large dimensions. Such a critical configuration occurs when (locally) exactly half the square of the string length lies in the large dimensions and half lies in the compact space. The critical solution is then seen to arise as a special case, in which the wavelength of the windings is equal to their circumference. As examples, long straight strings and circular loops are considered in detail, and the solutions to the equations of motion that satisfy the tensionless condition are presented. These solutions are then generalized to planar loops and arbitrary three-dimensional configurations. Under the process of dimensional reduction, in which higher-dimensional motion is equivalent to an effective worldsheet current (giving rise to a conserved charge), this phenomenon may be seen as the analogue of the tensionless condition which arises for superconducting and chiral-current carrying cosmic strings.

hep-ph↗