The Gravitational-Electromagnetic Analogy: A Possible Solution to the Vacuum-Energy and Dark-Energy Problems
Richard J. Cook
备注：
In this second version, a small change in the argument eliminates a number of questionable results and predictions. The resulting argument is consistent with all observational results
There is a set of first-order differential equations for the curvature tensor in general relativity (the curvature equations or CEs for short) that are strikingly similar to the Maxwell equations of electrodynamics. This paper considers whether Mother Nature may have used the same basic pattern for her laws of gravitation and electrodynamics, in which case the CEs might be viewed as the field equations of gravitation in place of Einstein's equation. This is not a new theory of gravitation (because the curvature equations are derivable from Einstein's equation), but rather is a mild reinterpretation of general relativity that solves the vacuum-energy problem and the dark-energy problem of cosmology. The results of this paper allow one to understand how the effective energy density of the observed cosmological constant can be so vastly smaller than estimates of the vacuum energy of quantum fields and why the vacuum energy of quantum fields does not contribute as a source of curvature.
The similarities between linearized gravity and electromagnetism are known since the early days of General Relativity. Using an exact approach based on tidal tensors, we show that such analogy holds only on very special conditions and depends crucially on the reference frame. This places restrictions on the validity of the "gravito-electromagnetic" equations commonly found in the literature.
We propose a new approach to a physical analogy between General Relativity and Electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations. The following realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third we …
The interaction between gravitational and electromagnetic waves in the presence of a static magnetic field is studied. The field strength of the static field is allowed to surpass the Schwinger critical field, such that the quantum electrodynamical (QED) effects of vacuum polarization and magnetization are significant. Equations governing the interaction are derived and analyzed. It turns out that the energy conversion from gravitational to electromagnetic waves can be significantly altered due to the QED effects. The consequences of our results are discussed.
We present a method that yields three decoupled covariant equations for three complex scalars, which completely govern electromagnetic perturbations of non-vacuum, locally rotationally symmetric class II spacetimes. One of these equations is equivalent to the previously established generalized Regge-Wheeler equation for electromagnetic fields. The remaining two equations are a direct generalization of the Bardeen-Press equations. The approach undertaken makes use of the well established 3+1 (and 2+1+1) formalism, and therefore, it is an ideal setting for specifying interpretable energy-momentu…
When an electrically charged source is capable of both emitting the electromagnetic waves and creating charged particles from the vacuum, its radiation gets so much amplified that only the backreaction of the vacuum makes it finite. The released energy and charge are calculated in the high-frequency approximation. The technique of expectation values is advanced and employed.
By resolving the Riemann curvature relative to a unit timelike vector into electric and magnetic parts, we consider duality relations analogous to the electromagnetic theory. It turns out that the duality symmetry of the Einstein action implies the Einstein vacuum equation without the cosmological term. The vacuum equation is invariant under interchange of active and passive electric parts giving rise to the same vacuum solutions but the gravitational constant changes sign. Further by modifying the equation it is possible to construct interesting dual solutions to vacuum as well as to flat spa…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to measure certain aspects of geometry. We show that there is actually much more which cannot be so measured; relatively little of a spacetime's geometry is in fact imprinted in any particular electromagnetic field. This is demonstrated by finding a much larger class of metric transformations---involving five free functions---which preserve Maxwell solutions b…
We present an electromagnetic analog of gravitational wave memory. That is, we consider what change has occurred to a detector of electromagnetic radiation after the wave has passed. Rather than a distortion in the detector, as occurs in the gravitational wave case, we find a residual velocity (a "kick") to the charges in the detector. In analogy with the two types of gravitational wave memory ("ordinary" and "nonlinear") we find two types of electromagnetic kick.
We consider a multilevel hydrogen atom in interaction with the quantum electromagnetic field and separately calculate the contributions of the vacuum fluctuation and radiation reaction to the rate of change of the mean atomic energy of the atom for uniform acceleration. It is found that the acceleration disturbs the vacuum fluctuations in such a way that the delicate balance between the contributions of vacuum fluctuation and radiation reaction that exists for inertial atoms is broken, so that the transitions to higher-lying states from ground state are possible even in vacuum. In contrast to …
We study how two fully-featured hydrogenlike atoms harvest entanglement from the electromagnetic field vacuum, even when the atoms are spacelike separated. We compare the electromagnetic case ---qualitatively and quantitatively--- with previous results that used scalar fields and featureless, idealized atomic models. Our study reveals the new traits that emerge when we relax these idealizations, such as anisotropies in entanglement harvesting and the effect of exchange of angular momentum. We show that, under certain circumstances, relaxing previous idealizations makes vacuum entanglement harv…
In previous work it has been shown that the electromagnetic quantum vacuum, or electromagnetic zero-point field, makes a contribution to the inertial reaction force on an accelerated object. We show that the result for inertial mass can be extended to passive gravitational mass. As a consequence the weak equivalence principle, which equates inertial to passive gravitational mass, appears to be explainable. This in turn leads to a straightforward derivation of the classical Newtonian gravitational force. We call the inertia and gravitation connection with the vacuum fields the quantum vacuum in…
The effect of electromagnetic radiation birefringence in the field of a relativistically rotating pulsar or magnetar within the framework of vacuum nonlinear electrodynamic
We consider arbitrary stationary and axisymmetric black holes in general relativity in $(d +1)$ dimensions (with $d \geq 3$) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of axisymmetric electromagnetic perturbations is positive definite. This establishes that all vacuum black holes are stable to axisymmetric electromagnetic perturbations. Our results also hold for asymptotically deSitter black holes that satisfy the vacuum Einstein equation with a positive cosmological constant. Our results also apply to extremal black holes pr…
We calculate renormalised vacuum expectation values of electromagnetic stress-energy tensor in the static spherically-symmetrical wormhole topology. We find that for metric tensor sufficiently slow varied with distance violation of the averaged weak energy condition takes place irrespectively of the detailed form of metric. This is a necessary condition for the electromagnetic vacuum to be able to support the wormhole geometry.
We consider classical particles coupled to the quantized electromagnetic field in the background of a spatially flat Robertson-Walker universe. We find that these particles typically undergo Brownian motion and acquire a non-zero mean squared velocity which depends upon the scale factor of the universe. This Brownian motion can be interpreted as due to non-cancellation of anti-correlated vacuum fluctuations in the time dependent background space-time. We consider several types of coupling to the electromagnetic field, including particles with net electric charge, a magnetic dipole moment, and …
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative solutions of Maxwell's vacuum field equations. The gravitational case involves a novel form of the radiative Robinson--Trautman solutions of Einstein's vacuum field equations.
Archimedes is a feasibility study of a future experiment to ascertain the interaction of vacuum fluctuations with gravity. The experiment should measure the force that the earth's gravitational field exerts on a Casimir cavity by using a small force detector. Here we analyse the main parameters of the experiment and we present its conceptual scheme, which overcomes in principle the most critical problems.
In [5] we investigated the response of vacuum energy to a gravitational field by considering a Casimir apparatus in a weak gravitational field. Our approach was based on a conjecture involving the interpretation of spacetime as a refractive medium and its effect on vacuum energy composed of virtual massless scalar particles. There it was shown how the case of virtual photons as the constituents of vacuum could be inferred from that of the massless scalar field. Here we explicitly show how the same conjecture applies to the electromagnetic vacuum composed of virtual photons. Specifically we sho…
Magnetic and vorticity fields evolution equations are known to obey the same equation when effects of dissipation and sources terms are negligible. We investigate the analogy between the two fields for non-vanishing dissipation and sources. In addition to the Reynolds (Re)and Prandtl (Pr_M) numbers, we define a new number (S_M) that is given by the ratio of the diffusive term to the Biermann battery term and which allows for a different classification of magnetised fluid behaviour. Numerical simulations of the two fields are then carried out given a parameter space made of Reynolds, Prandtl an…
We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within …
We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and Barrett \cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on non-vacuum {\it locally rotationally symmetric} (LRS) class II space-times. Ultimately, we show how to derive six real decoupled equations governing the total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new, and result from expanding the complex EM 2-vector which we defined in \cite{Burston2007} in terms of EM 2-vector harmonic amplitudes. We are then able to show that there are four precise combinations of the amplitudes…
In open quantum systems, we study the quantum Fisher information of acceleration for a uniformly accelerated two-level atom coupled to fluctuating electromagnetic fields in the Minkowski vacuum. With the time evolution, for the initial atom state parameter $θ\neqπ$, the quantum Fisher information can exist a maximum value and a local minimum value before reaching a stable value. In addition, in a short time, the quantum Fisher information varies with the initial state parameter, and the quantum Fisher information can take a maximum value at $θ=0$. The quantum Fisher information may exist two p…
It has been shown [1,2] that the electromagnetic quantum vacuum makes a contribution to the inertial mass, $m_i$, in the sense that at least part of the inertial force of opposition to acceleration, or inertia reaction force, springs from the electromagnetic quantum vacuum. As experienced in a Rindler constant acceleration frame the electromagnetic quantum vacuum mainfests an energy-momentum flux which we call the Rindler flux (RF). The RF, and its relative, Unruh-Davies radiation, both stem from event-horizon effects in accelerating reference frames. The force of radiation pressure produced b…
A new version of the Teukolksy Master Equation, describing any massless field of different spin $s=1/2,1,3/2,2$ in the Kerr black hole, is presented here in the form of a wave equation containing additional curvature terms. These results suggest a relation between curvature perturbation theory in general relativity and the exact wave equations satisfied by the Weyl and the Maxwell tensors, known in the literature as the de Rham-Lichnerowicz Laplacian equations. We discuss these Laplacians both in the Newman-Penrose formalism and in the Geroch-Held-Penrose variant for an arbitrary vacuum spacet…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and related with them physical aspects. Based on the vacuum field theory no-geometry approach, developed in \cite{BPT,BPT1}, the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. A problem closely related to the radiation reaction force is analyzed aiming to explain the Wheeler and Feynman reaction radiation mechanism, well known as the absorption radiation theory, and strongly dependent on the Mach type interaction of a char…
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to emulate electromagnetic gauge transformations under substitutions belonging to the gauge symmetry group of perturbative gravitation. These definitions have the advantage that on a flat background, with the aid of a covariantly constant timelike vector field, a subset of the linearised gravitational field equations can be written in a form that is fully anal…
We investigate, in the framework of open quantum systems, the entanglement dynamics of two circularly accelerated two-level atoms with the same centripetal acceleration interacting with a bath of fluctuating electromagnetic fields in the Minkowski vacuum. We assume that the two atoms rotate synchronically with their separation perpendicular to the rotating plane, and study the entanglement degradation, creation, revival, and enhancement by solving the Markovian master equation. In contrast to the scalar-field case, the entanglement dynamics is crucially dependent on the atomic polarizations in…
We study the spontaneous excitation of a radially polarized static multilevel atom outside a spherically symmetric black hole in multi-polar interaction with quantum electromagnetic fluctuations in the Boulware, Unruh and Hartle-Hawking vacuum states. We find that spontaneous excitation does not occur in the Boulware vacuum, and, in contrast to the scalar field case, spontaneous emission rate is not well-behaved at the event horizon as result of the blow-up of the proper acceleration of the static atom. However, spontaneous excitation can take place both in the Unruh and the Hartle-Hawking vac…
Pulsars are thought to be highly magnetized rotating neutron stars accelerating charged particles along magnetic field lines in their magnetosphere and visible as pulsed emission from the radio wavelength up to high energy X-rays and gamma-rays. Being highly compact objects with compactness close to $Ξ= R_s/R\approx0.5$, where $\Rs=2\,G\,M/c^2$ is the Schwarzschild radius and $\{M,R\}$ the mass and radius of the neutron star, general-relativistic effects become important close to their surface. This is especially true for the polar caps where radio emission is supposed to emanate from, leading…
We show that a nontrivial topologies of the spatial section of Minkowski space-time allow for motion of a charged particle under quantum vacuum fluctuations of the electromagnetic field. This is a potentially observable effect of these vacuum fluctuations. We derive mean squared velocity dispersion when the charged particle lies in Minkowski space-time with compact spatial sections in one, two and/or three directions. We concretely examine the details of these stochastic motions when the spatial section is endowed with different globally homogeneous and inhomogeneous topologies. We also show t…
We investigate the renormalized vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field inside and outside of a conducting cylindrical shell in the cosmic string spacetime. By using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases.
The Einstein field equations in linear post-Newtonian approximation can be written in analogy with electromagnetism, in the so-called gravito-electromagnetic formalism. We use this analogy to study the gravitational field of a massive ring: in particular, we consider a continuous mass distribution on Keplerian orbit around a central body, and we work out the gravitational field generated by this mass distribution in the intermediate zone between the central body and the ring, focusing on the gravito-magnetic component that originates from the rotation of the ring. In doing so, we generalize an…
We investigate the entanglement dynamics of two uniformly accelerated atoms with the same acceleration perpendicular to their separation. The two-atom system is treated as an open system coupled with fluctuating electromagnetic fields in the Minkowski vacuum, and in the Born-Markov approximation the master equation that describes the completely positive time evolution of the two-atom system is derived. In particular, we investigate the phenomena of entanglement degradation, generation, revival and enhancement. As opposed to the scalar-field case, the entanglement dynamics is crucially dependen…
