Achieving geodetic motion for LISA test masses: ground testing results

The low-frequency resolution of space-based gravitational wave observatories such as LISA (Laser Interferometry Space Antenna) hinges on the orbital purity of a free-falling reference test mass inside a satellite shield. We present here a torsion pendulum study of the forces that will disturb an orbiting test mass inside a LISA capacitive position sensor. The pendulum, with a measured torque noise floor below 10 fN m/square root of Hz from 0.6 to 10 mHz, has allowed placement of an upper limit on sensor force noise contributions, measurement of the sensor electrostatic stiffness at the 5% level, and detection and compensation of stray dc electrostatic biases at the millivolt level.     

Point charge in a static,spherically symmetric Brans-Dicke field

We determine in closed form the electrostatic potential of a point test charge held at rest in a static, spherically symmetric Brans-Dicke field. This result is a generalization of the previously obtained expression for the potential of a test charge at rest near a Schwarzschild black hole. Moreover, our solution is valid for the coupled gravitational and massless scalar fields.     

Nonlinear analysis of the equilibrium shape of a charged conducting drop in an electrostatic suspension

An analytical asymptotic expression is derived that describes the equilibrium shape of a charged drop of an ideal incompressible conducting liquid suspended in superposed collinear uniform electrostatic and gravitational fields. The expression is obtained in an approximation quadratic in the small amplitude of deviation of the equilibrium drop from a sphere, with the electrostatic field dimensionless strength taken as a measure of the deviation amplitude. With allowance for the gravitational and electrostatic fields and interaction between the drop self-charge and external electrostatic field, the equilibrium shape of the drop is found to be very close to a spheroid when the charge and the electrostatic field strength are far from their critical values. The analysis is carried out with a refined procedure of calculation of the equilibrium shape of drops placed in external force fields.     

Gravity and the quantum vacuum inertia hypothesis

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 inertia hypothesis . To date only the electromagnetic field has been considered. It remains to extend the hypothesis to the effects of the vacuum fields of the other interactions. We propose an idealized experiment involving a cavity resonator which, in principle, would test the hypothesis for the simple case in which only electromagnetic interactions are involved. This test also suggests a basis for the free parameter η(ν) which we have previously defined to parametrize the interaction between charge and the electromagnetic zero‐point field contributing to the inertial mass of a particle or object.     

Nonlinear vibrations of a charged drop in an electrostatic suspension

The problem of nonlinear vibrations of a charged drop of an ideal incompressible conducting fluid in an electrostatic suspension is analytically solved in an approximation quadratic in two small parameters: vibration amplitude and equilibrium deformation of the shape of the drop in an electrostatic field. To solve the problem analytically, the desired quantities are expanded in semiinteger powers of the small parameters. It is shown that the charge of the drop and the gravitational field influence the shape of the drop, nonlinear corrections to the vibration frequencies, and critical conditions for instability of the drop against the surface charge. At near-critical values of the charge, the shape of the nonlinearly vibrating drop falls far short of being a sphere or a spheroid, which should be taken into account in treating experimental data.     

Antimatter gravity studies with interferometry

There has never been a direct measurement of the gravitational force on antimatter. This paper describes a possible measurement of this force by measuring the phase shift of neutral antimatter in a transmission-grating interferometer caused by the Earth’s gravitational field. This experiment avoids the severe problem of shielding stray electromagnetic fields necessary for making a gravity measurement with charged particles, and also avoids the need to trap neutral particles. The neutral antimatter for this experiment could be either antihydrogen, positronium, or antineutrons. This revised version was published online in August 2006 with corrections to the Cover Date.     

Field theoretic treatment of gravitational interaction in electrodynamics

A theory of gravitational interaction in classical electrodynamics is developed on the basis of an earlier-proposed minimal relativistic model of gravitation. From the variation principle, a system of gaugeinvariant equations of the interacting electromagnetic and gravitational fields is deduced and their common energy-momentum tensor is constructed. A rigorous solution to the problem of regularizing the field mass of a point charge is given with consideration for the coupling energy of the gravitational interaction. The propagation of electromagnetic waves in the gravitational field is discussed. It is shown that, under the condition of the existing resonant ratio 2: 3 for the periods of Mercury’s orbital revolution and daily rotation, tidal forces cause a regular shift in the planet’s perihelion in an observable forward direction.     

Nonlinear analytical calculation of the equilibrium shape of a charged drop uniformly accelerated in an electrostatic field

An analytical asymptotic expression for the equilibrium shape of a charged drop of an ideal incompressible conducting liquid uniformly accelerated in collinear electrostatic and gravitational fields is derived in an approximation quadratic with respect to the deviation of the equilibrium shape of the drop from a sphere. It is found that the equilibrium shape of the drop is close to a prolate spheroid when its self-charge and the external electric field strength are far from their values critical in terms of instability against the self-charge and induced charge. This spheroid experiences an insignificant pear-shaped distortion even when the charge of the drop and the electrostatic field strength are high.     

Can Dilaton Fields in Astrophysical Objects be Detected?

We analyze a new class of static exact solutions of Einstein-Maxwell-Dilaton gravity with arbitrary scalar coupling constant , representing a gravitational body endowed with electromagnetic dipole moment. This class possesses mass, dipole and scalar charge parameters. A discussion of the geodesic motion shows that the scalar field interaction is so weak that it cannot be measured in gravitational fields like the sun, but it could perhaps be detected in gravitational fields like pulsars. The scalar force can be attractive or repulsive. This gives rise to the hypothesis that the magnetic field of some astrophysical objects could be fundamental.     

Unified equation of motion of a test charge in electromagnetic and gravitational fields

This work starts by generalizing in a gravitational field the fundamental quantum mechanical commutation relations between the coordinates of a charged test particle and its momentum. Assuming that the components of the momentum of this test charge obey a noncommutative algebra in the presence of an electromagnetic field, it is proved that the commutator can be identified with the electromagnetic field tensor. Using these results, the equation of motion of this charged object in the presence of both the electromagnetic and gravitational fields is derived from their field equations. In this work, the laws of motion of a particle in the electromagnetic and gravitational fields has been unified with the field equations. Although the field equations themselves are not directly unified, this work strongly suggests that the scheme may act as a possible framework for the unification of at least gravitational and electromagnetic interactions.     

Aspects of electrostatics in a weak gravitational field

Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and more transparent procedures and are interpreted in an intuitive manner. Specifically: (a) We discuss possible definitions of the electric field in curved spacetime (and noninertial frames), argue in favour of a specific definition for the electric field and discuss its properties. (b) We show that the electrostatic potential of a charge at rest in the Rindler frame (which is known and is usually expressed as a complicated function of the coordinates) is expressible as A ₀ = q/λ where λ is the affine parameter distance along the null geodesic from the charge to the field point. (c) This relates well with the result that the electric field lines of a charge coincide with the null geodesics; that is, both light and the electric field lines ‘bend’ in the same manner in a weak gravitational field. We provide a simple proof for this result as well as for the fact that the null geodesics (and field lines) are circles in space. (d) We obtain the sum of the electrostatic forces exerted by one charge on another in the Rindler frame and discuss its interpretation. In particular, we compare the results in the Rindler frame and in the inertial frame and discuss their consistency. (e) We show how a purely electrostatic term in the Rindler frame appears as a radiation term in the inertial frame. (In part, this arises because charges at rest in a weak gravitational field possess additional weight due to their electrostatic energy. This weight is proportional to the acceleration and falls inversely with distance—which are the usual characteristics of a radiation field.) (f) We also interpret the origin of the radiation reaction term by extending our approach to include a slowly varying acceleration. Many of these results might have possible extensions for the case of electrostatics in an arbitrary static geometry.     

Temporal extent of surface potentials between closely spaced metals

Variations in the electrostatic surface potential between the proof mass and electrode housing in the space-based gravitational wave mission Laser Interferometer Space Antenna (LISA) is one of the largest contributors of noise at frequencies below a few mHz. Torsion balances provide an ideal test bed for investigating these effects in conditions emulative of LISA. Our apparatus consists of a Au coated Cu plate brought near a Au coated Si plate pendulum suspended from a thin W wire. We have measured a white noise level of 30 microV/sqrt Hz above approximately 0.1 mHz, rising at lower frequencies, for the surface potential variations between these two closely spaced metals.     

Gravitational interaction of a vector field with account of the nonmetricity of space-time

The gravitational interaction of a vector field is investigated in a space with the nonmetricity described by the Weyl vector. The analogue of the Coulomb law for the electrostatic field of a point charge is found in such a space. It is shown that taking account of the nonmetricity of space-time leads to the appearance of a nonlinearity in a massive vector field, resulting in the sine-Gordon and shine-Gordon equations. The screening of the vector-field mass as a consequence of its interaction with the nonmetricity is clarified. The solution for the Reissner-Nordström problem in a Weyl space is obtained, which asymptotically coincides with the solution of the same problem in general relativity, but nowhere does it possess singularities apart from at the origin. The obtained results show that it is reasonable to take account of the nonmetricity when describing the gravitational interaction of a vector field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 50–54, August, 1984.     

Event-driven simulations of insulating grains in an external electric field

In this work we employ event-driven particle dynamics simulations for a system of spherical insulating grains interacting with an external electric field. This system resembles the electrostatic particle separation present on some industrial processes. Here, the particles collide inelastically with each other and with the container walls, for a constant normal and tangential restitution coefficients. During the collisions, the grains can acquire electric charge due to triboelectric contact charging, since two different species of insulating particles are mixed. Particle-particle electric interactions are not considered. Grains are also subjected to the gravitational field and rotation, and are confined in a cubic box with thermal walls in order to prevent the static equilibrium state. We calculate the mass and charge density profile, and the particle charge distribution for different values of the electric field and temperature of the walls. The particle charge distribution and the effect of particle sizes on the separation process were also investigated.     

Testing the Universality of Free Fall for Charged Particles in Space

At first a short analysis of the notion of the Universality of Free Fall (UFF) for charged matter is given. Even if neutral bound systems of charged particles are in full accordance with the UFF, there is still a possibility that an isolated charge couples anomalously to gravitational fields. The experiment of Witteborn and Fairbank aimed at testing the UFF for electrons is shortly reviewed emphasizing the various additional disturbing gravity induced electromagnetic fields. Since these additional gravity induced fields are not very well under control, a space borne version of this experiment will reduce these disturbances considerably. The corresponding estimates for these kinds of tests in space are presented. As a result, gravity–induced stray field can be reduced considerably. Furthermore, also patch–effects can be reduced efficiently due to novel coating techniques. Therefore, due to microgravity conditions and new techniques the UFF for charged particles may be tested with much higher accuracy than in previous experiments.     

Exact partial solutions for the surface dynamics of a dielectric liquid with a charged surface in the gravitational field

We study the evolution of instability in the boundary of a perfect dielectric liquid with a free surface charge in an external electric field. Conformal variables are used to find exact partial solutions to the equations of motion for the case when the charge completely shields the field above the liquid, the electrostatic and gravitational forces being taken into account. The solutions describe the development of instability of the initially planar boundary until sharp dimples are formed on it.     

Theory of Gravitational-Inertial Field of Universe. II. On Critical Systems in Universe

Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which 1. all Galaxies in the Universe “disperse” from each other according to Hubble's law, 2. the “dispersion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, 3. for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximalinertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational “annihilation”. At the maximal value of inertial and gravitational potentials (= c²) the material mass is being completely “evaporated” transforming into radiation mass. The latter is being concentrated in the “horizon” of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.     

Freely Falling 2-Surfaces and the Effective Gravitational Mass

We derive an expression for the effectivegravitational mass for any closed spacelike 2-surface.This effective gravitational energy is defined directlythrough the geometrical quantity of the freely falling 2-surface and thus is well adapted to intuitiveexpectation that the gravitational mass should bedetermined by the motion of a test body moving freely inthe gravitational field. We find that this effective gravitational mass has a reasonable positivevalue for a small sphere in the non-vacuum space-timesand can be negative for the vacuum case. Further, thiseffective gravitational energy is compared with the quasi-local energy based on the (2 + 2)formalism of General Relativity. Although some gaugefreedoms exist, analytic expressions of the quasi-localenergy for vacuum cases are the same as the effective gravitational mass. Especially, we see that thecontribution from the cosmological constant is the samein general cases.     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

Magnetoexciton light absorption in inhomogeneous quasi-two-dimensional systems

The problem of exciton light absorption in quasi-two-dimensional inhomogeneous systems in a strong transverse magnetic field H is analyzed. We assume that a random Gaussian field (“white noise”) acting separately on an electron and a hole is due to (1) fluctuations in the quantum well thickness or (2) fluctuations in the concentrations of the solid solution components. The problem of a magnetoexciton in a random Gaussian white noise field has been reduced to the problem of the motion in an H-dependent effective field of a single particle with the effective magnetic mass of the exciton, which is a function of the magnetic field and parameters of the quantum wells, in a field characterized by “colored noise,” whose correlation function is different from that of the white noise field. In this approximation, the problem of a magnetoexciton in isolated and coupled quantum dots is considered. In the coherent-potential approximation, the exciton absorption in random fields of the first and second type in single and coupled quantum wells has been calculated. The absorption decreases as H increases in the range of strong magnetic fields, which is in agreement with experimental data. Zh. éksp. Teor. Fiz. 114, 1451–1465 (October 1998)