Positive Energy Density Research Articles

Dilaton gravity, charged dust, and (quasi-) black holes

We consider Einstein-Maxwell-dilaton gravity with charged dust and interaction of the form $P(\chi) F_{\mu\nu} F^{\mu\nu}$, where $P(\chi)$ is an arbitrary function of the dilaton field $\chi$ that can be normal or phantom. For any regular $P(\chi)$, static configurations are possible with arbitrary functions $g_{00} = \exp(2\gamma(x^i))$ ($i=1,2,3$) and $\chi = \chi(\gamma)$, without any assumption of spatial symmetry. The classical Majumdar-Papapetrou system is restored by putting $\chi =$ const. Among possible solutions are black-hole (BH) and quasi-black-hole (QBH) ones. Some general results on BH and QBH properties are deduced and confirmed by examples. It is found, in particular, that asymptotically flat BHs and QBHs can exist with positive energy densities of matter and both scalar and electromagnetic fields.

Freely falling observer and black hole radiation

We find radiation in an infalling frame and present an explicit analytic evidence of the failure of no drama condition by showing that an infalling observer finds an infinite negative energy density at the event horizon. The negative and positive energy density regions are divided by the newly defined zero-energy curve (ZEC). The evaporating black hole is surrounded by the negative energy which can also be observed in the infalling frame.

Cosmology in a certain vector-tensor theory of gravitation

We study relevant cosmological topics in the framework of a certain vector-tensor theory of gravitation (hereafter VT). This theory is first compared with the so-called extended electromagnetism (EE). These theories have a notable resemblance and both explain the existence of a cosmological constant. It is shown that, in EE, a positive dark energy density requires a Lagrangian leading to quantum ghosts, whereas VT is free from these ghosts. On account of this fact, the remainder of the paper is devoted to study cosmology in the framework of VT. Initial conditions, at high redshift, are used to solve the evolution equations of all the VT scalar modes. In particular, a certain scalar mode characteristic of VT -which does not appear in general relativity (GR)- is chosen in such a way that it evolves separately. In other words, the scalar modes of the standard model based on GR do not affect the evolution of the VT characteristic mode; however, this scalar mode influences the evolution of the standard GR ones. Some well known suitable codes (CMBFAST and COSMOMC) have been modified to include our VT initial conditions and evolution equations, which are fully general. One of the resulting codes -based on standard statistical methods- has been used to fit VT predictions and observational evidences about both Ia supernovae and cosmic microwave background anisotropy. Seven free parameters are used in this fit. Six of them are often used in GR cosmology and the seventh one is characteristic of VT. From the statistical analysis it follows that VT seems to be advantageous against GR in order to explain cosmological observational evidences.

Metamaterial Model of Tachyonic Dark Energy

Dark energy with negative pressure and positive energy density is believed to be responsible for the accelerated expansion of the universe. Quite a few theoretical models of dark energy are based on tachyonic fields interacting with itself and normal (bradyonic) matter. Here we propose an experimental model of tachyonic dark energy based on hyperbolic metamaterials. Wave equation describing propagation of extraordinary light inside hyperbolic metamaterials exhibits 2+1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect bends this spacetime resulting in effective gravitational force between extraordinary photons. We demonstrate that this model has a self-interacting tachyonic sector having negative effective pressure and positive effective energy density. Moreover, a composite multilayer SiC-Si hyperbolic metamaterial exhibits closely separated tachyonic and bradyonic sectors in the long wavelength infrared range. This system may be used as a laboratory model of inflation and late time acceleration of the universe.

Minkowskian Solution of General Relativity with Cosmological Constant and the Accelerating Universe

A Minkowskian solution of the equation of General Relativity (as written by Einstein in 1915) is trivial because it simply means that both members of the equation are equal to zero. However, if alternatively, one considers the complete equation with a non-zero constant Λ (Einstein 1917), a Minkowskian solution is no longer trivial because it amounts to impose a constraint on the right hand side of the equation (i.e. a non-null stress-energy tensor). If furthermore one identifies (as usual) this tensor to the one of a perfect fluid, one finds that this fluid has a positive energy density and a negative pressure that depend on the three constants of the equation (i.e. gravitational constant G, cosmological constant Λ and velocity of light c). When doing that (§1), one has to consider the “Minkowskian Vacuum” as a physical object of GR (an enigmatic non-baryonic Minkowskian fluid). Can one build a model of this object on the basis of a dynamical equilibrium between the effective gravitational attraction due to the positive energy density versus the negative pressure repulsion? We propose to study such a model, where the (enigmatic) fluid is assumed to exist only in a limited sphere whose surface acts like a “test body” sensitive to the gravitational field created by the fluid. No static equilibrium exists, but a pseudoNewtonian “dynamical equilibrium” (§2) can be reached if the pseudoEuclidean fluid is in state of expansion. Up to there, we have simply constructed a model of an “abstract Universe” (i.e. the limited sphere: There is no fluid outside this sphere!) that gives to a (purely mathematical) constant Λ a concrete physical meaning. We discover finally that our expanding fluid has not only dynamical (gravitational) properties (§3) but also optical properties that are connected with Doppler Redshift (§4). Remembering that recent observations in Cosmology indicate that the “real Universe” seems to be “Flat” and in “Accelerated Expansion”; remembering also (after all) that the archetypal Flat Universe is simply a Minkowskian Universe, we logically wonder if the unexpected Minkowskian global solution, could not be also a significant cosmological model (conclusion).

The Cosmological Constant Puzzle: Vacuum Energies from QCD to Dark Energy

The accelerating expansion of the Universe points to a small positive vacuum energy density and negative vacuum pressure. A strong candidate is the cosmological constant in Einstein’s equations of General Relativity. The vacuum dark energy density extracted from astrophysics is 10 56 times smaller than the value expected from the Higgs potential in Standard Model particle physics. The dark energy scale is however close to the range of possible values expected for the light neutrino mass. We investigate this physics in a simple toy model where the chirality of the neutrino is treated by analogy as an Ising-like “spin” degree of freedom.

About the Role of the Higgs Boson in the Evolution of the Early Universe

After the discovery of the Higgs particle the most relevant structures of the SM have been verified and for the first time we know all parameters of the SM within remarkable accuracy. Together with recent calculations of the SM renormalization group coefficients up to three loops we can safely extrapolate running couplings high up in energy. Assuming that the SM is a low energy effective theory of a cutoff theory residing at the Planck scale, we are able to calculate the effective bare parameters of the underlying cutoff system. It turns out that the effective bare mass term changes sign not far below the Planck scale, which means that in the early universe the SM was in the symmetric phase. The sign-flip, which is a result of a conspiracy between the SM couplings and their screening/antiscreening behavior, triggers the Higgs mechanism. Above the Higgs phase transition the bare mass term in the Higgs potential must have had a large positive value, enhanced by the quadratic divergence of the bare Higgs mass. Likewise the quartically enhanced positive vacuum energy density is present in the symmetric phase. The Higgs system thus provides the large dark energy density in the early universe, which triggers slow-roll inflation, i.e. the SM Higgs is the inflaton scalar field. Reheating is dominated by the decay of the heavy Higgses into (in the symmetric phase) massless top/anti-top quark pairs. The new scenario possibly could explain the baryon-asymmetry essentially in terms of SM physics

Dark matter as a ghost free conformal extension of Einstein theory

We discuss ghost free models of the recently suggested mimetic dark matter theory. This theory is shown to be a conformal extension of Einstein general relativity. Dark matter originates from gauging out its local Weyl invariance as an extra degree of freedom which describes a potential flow of the pressureless perfect fluid. For a positive energy density of this fluid the theory is free of ghost instabilities, which gives strong preference to stable configurations with a positive scalar curvature and trace of the matter stress tensor. Instabilities caused by caustics of the geodesic flow, inherent in this model, serve as a motivation for an alternative conformal extension of Einstein theory, based on the generalized Proca vector field. A potential part of this field modifies the inflationary stage in cosmology, whereas its rotational part at the post inflationary epoch might simulate rotating flows of dark matter.

Energy density and velocity of electromagnetic waves in lossy chiral medium

The average energy density of the macroscopic quasimonochromatic electromagnetic field \U0001d4b0ts(t,r) in a linear passive chiral lossy medium described by the constitutive E–H relations is determined using a microscopic model. According to the model, \U0001d4b0ts(t,r) is equal to the sum of the average energy densities of the electromagnetic field in free space \U0001d4b0t0(t,r) and electromagnetic oscillations in structural elements \U0001d4b0s(t,r) induced by the electromagnetic wave. Making use of the Poynting theorem, the energy density and power density of losses are derived as functions of the Poynting vector, polarization of the electromagnetic waves, phase shift between the field vectors and refractive index of a chiral medium. The exact energy velocity of the quasimonochromatic electromagnetic waves satisfying relativistic causality is determined using \U0001d4b0ts(t,r). The approximate energy velocities of the quasimonochromatic electromagnetic wave are determined using energy density components approximating \U0001d4b0ts(t,r) (e.g., the sum of the positive energy densities of the macroscopic electric and magnetic fields as well as the energy density of magnetoelectric cross-coupling). Comparison of the exact and approximate energy velocities with the group velocity in the case of a chiral lossy medium with a single-resonant frequency clarifies the concept of the electromagnetic energy and demonstrates the fundamental significance of the exact energy velocity.

Phase transitions during cyclic inflation and non-Gaussianity

Typically, cold inflation with positive vacuum energy density dilutes all matter except the quantum fluctuations, which are stretched outside the Hubble patch during inflation. However, the cyclic-inflation scenario, in which the Universe undergoes many asymmetric cycles leading to an overall exponential growth, operates in the presence of thermal matter. Thus, while some of the nice properties of cold inflation are preserved, in cyclic inflationary models, thermal excitations are continually produced, and there exists a unique opportunity of imprinting interesting thermal history in cosmic microwave background radiation. In particular, we will see that a phase transition can lead to observably large higher-order non-Gaussianities as the critical temperature is approached and that these are increasingly divergent with the order of the correlations.

The nonlinear future stability of the FLRW family of solutions to the irrotational Euler–Einstein system with a positive cosmological constant

In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1 + 3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p = c^2 \rho, 0 < c^2 < 1/3 , the background metric + fluid solutions are globally future-stable under small irrotational perturbations of their initial data. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,\infty) X T^3 , are future causally geodesically complete. Our analysis is based on a combination of energy estimates and pointwise decay estimates for quasilinear wave equations featuring dissipative inhomogeneous terms. Our main new contribution is showing that when 0 < c^2 < 1/3 , exponential spacetime expansion is strong enough to suppress the formation of fluid shocks. This contrasts against a well-known result of Christodoulou, who showed that in Minkowski spacetime, the corresponding constant-state irrotational fluid solutions are unstable.

No-go theorem for static scalar field dark matter halos with no Noether charges

Classical scalar fields have been considered as a possible effective description of dark matter. We show that, for any metric theory of gravity, no static, spherically symmetric, regular, spatially localized, attractive, stable spacetime configuration can be sourced by the coherent excitation of a scalar field with positive definite energy density and no Noether charges. In the weak field regime, the result also applies for configurations with a repulsive gravitational potential. This extends Derrick's theorem to the case of a general (noncanonical) scalar field, including the self-gravitational effects. Some possible ways out are briefly discussed.

Hawking radiation from small black holes at strong coupling and large N

In a previous work an approximate static metric was found of a test black string that stretches from the boundary to the horizon of the planar Schwarzschild–AdS5 geometry. This is the gravity dual of the Unruh state for , SU(N) super Yang–Mills theory on a four-dimensional Schwarzschild background, at large N and large ’tHooft coupling. We compute the holographic stress tensor of the gravitational solution and it turns out to possess many essential features of the Unruh state for weakly coupled Hawking radiation, such as the appearance of a negative energy density near the black hole horizon and a positive energy density at infinity. It also confirms recent results that at leading order in N, the expectation value of the stress tensor in the Unruh state is finite on both the future and past horizons, and that at this order there are no flux terms as is expected in the black droplet phase.

Ten scenarios from early radiation to late time acceleration with a minimally coupled dark energy

We consider General Relativity with matter, radiation and a minimally coupled dark energy defined by an equation of state w. Using dynamical system method, we find the equilibrium points of such a theory assuming an expanding Universe and a positive dark energy density. Two of these points correspond to classical radiation and matter dominated epochs for the Universe. For the other points, dark energy mimics matter, radiation or accelerates Universe expansion. We then look for possible sequences of epochs describing a Universe starting with some radiation dominated epoch(s) (mimicked or not by dark energy), then matter dominated epoch(s) (mimicked or not by dark energy) and ending with an accelerated expansion. We find ten sequences able to follow this Universe history without singular behaviour of w at some saddle points. Most of them are new in dark energy literature. To get more than these ten sequences, w has to be singular at some specific saddle equilibrium points. This is an unusual mathematical property of the equation of state in dark energy literature, whose physical consequences tend to be discarded by observations. This thus distinguishes the ten above sequences from an infinity of ways to describe Universe expansion.

Can dark energy emerge from quantum effects in a compact extra dimension?

The origin of the observed acceleration of the expansion of the universe is a major problem of modern cosmology and theoretical physics. Simple estimations of the contribution of vacuum to the density energy of the universe in quantum field theory are known to lead to catastrophic large values compared to observations. Such a contribution is therefore generally not regarded as a viable source for the acceleration of the expansion. In this letter we propose that the vacuum contribution actually provides a small positive value to the density energy of the universe. The underlying mechanism is a manifestation of the quantum nature of the gravitational field, through a Casimir-like effect from an additional compact dimension of space. A key ingredient is to assume that only modes with wavelength shorter than the Hubble length contribute to the vacuum. Such a contribution gives a positive energy density, has a Lorentz invariant equation of state in the usual 4D spacetime and hence can be interpreted as a cosmological constant. Its value agrees with observations for a radius of a 5th extra dimension given by $35\,\mu$m. This implies a modification of the gravitational inverse square law around this scale, close but below existing limits from experiments testing gravity at short range.

Alfvén wave mixing and non-JWKB waves in stellar winds

Alfvén wave mixing equations used in locally incompressible turbulence transport equations in the solar wind contain as a special case, non-Jeffreys–Wentzel–Kramers–Brouillon (non-JWKB) wave equations used in models of Alfvén wave driven winds. We discuss the canonical wave energy equation; the physical wave energy equation, and the JWKB limit of the wave interaction equations. Lagrangian and Hamiltonian variational principles for the waves are developed. Noether’s theorem is used to derive the canonical wave energy equation which is associated with the linearity symmetry of the equations. A further conservation law associated with time translation invariance of the action, applicable for steady background wind flows is also derived. In the latter case, the conserved density is the Hamiltonian density for the waves, which is distinct from the canonical wave energy density. The canonical wave energy conservation law is a special case of a wider class of conservation laws associated with Green’s theorem for the wave mixing system and the adjoint wave mixing system, which are related to Noether’s second theorem. In the sub-Alfvénic flow, inside the Alfvén point of the wind, the backward and forward waves have positive canonical energy densities, but in the super-Alfvénic flow outside the Alfvén critical point, the backward Alfvén waves are negative canonical energy waves, and the forward Alfvén waves are positive canonical energy waves. Reflection and transmission coefficients for the backward and forward waves in both the sub-Alfvénic and super-Alfvénic regions of the flow are discussed.

Energy Parameter Control System of Strength Machine for Material Tests under Cyclic Bending and Torsion

The paper presents strength machine control system for characterization of fatigue properties of materials based on a new, recently defined, energy fatigue damage parameter. It is used in new procedure for precise determination of the fatigue characteristics of materials with the controlled strain energy density parameter. The new parameter distinguishes positive and negative values strain energy density histories during variable loading. In case of modern, cyclically unstable materials the new closed-loop control system of strength machine allows to univocally establish the relevant stress-strain based fatigue characteristic under bending and torsion. This control system has been implemented with the use of National Instruments LabVIEW software. The mechatronic stand based on fatigue machine for material testing under bending moment and torsion moment has been described and preliminarily material tests have been done.

Localizing the angular momentum of linear gravity

In a previous article [Phys. Rev. D 82 104040 (2010)], we derived an energy-momentum tensor for linear gravity that exhibited positive energy density and causal energy flux. Here we extend this framework by localizing the angular momentum of the linearized gravitational field, deriving a gravitational spin tensor which possesses similarly desirable properties. By examining the local exchange of angular momentum (between matter and gravity) we find that gravitational intrinsic spin is localized, separately from orbital angular momentum, in terms of a gravitational spin tensor. This spin tensor is then uniquely determined by requiring that it obey two simple physically motivated algebraic conditions. Firstly, the spin of an arbitrary (harmonic-gauge) gravitational plane wave is required to flow in the direction of propagation of the wave. Secondly, the spin tensor of any transverse-traceless gravitational field is required to be traceless. (The second condition ensures that local field redefinitions suffice to cast our gravitational energy-momentum tensor and spin tensor as sources of gravity in a quadratic approximation to general relativity.) Additionally, the following properties arise in the spin tensor spontaneously: all transverse-traceless fields have purely spatial spin, and any field generated by a static distribution of matter will carry no spin at all. Following the structure of our previous paper, we then examine the (spatial) angular momentum exchanged between the gravitational field and an infinitesimal detector, and develop a microaveraging procedure that renders the process gauge-invariant. The exchange of nonspatial angular momentum (i.e., moment of energy) is also analyzed, leading us to conclude that a gravitational wave can displace the center of mass of the detector; this conclusion is also confirmed by a first principles treatment of the system. Finally, we discuss...

Rindler-type geometry inside a black hole

An anisotropic fluid with positive energy density and negative pressures is proposed in the black hole interior. The gravitational field is constant everywhere inside and is given by the horizon surface gravity. Even though the geometry is of Rindler type it is curved because of the spherical symmetry used and is singular at the origin. The Israel junction conditions are studied on the stretched horizon instead of using a matching process on the null surface r=2M. The entropy of any inner sphere is mass independent, maximally packed and unaffected by the outer layers.

Probability distributions for quantum stress tensors in four dimensions

We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional spacetime. Specifically, there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. We are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bounds, the asymptotic forms for large positive argument, and possible fits to the intermediate region. The first 65 moments are used for these purposes. All of our results are subject to the caveat that these distributions are not uniquely determined by the moments. However, we also give bounds on the cumulative distribution function that are valid for any distribution fitting these moments.We apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.