Response functions of free mass gravitational wave antennas

Rainer Weiss and collaborators have from first principles derived the response of a free mass interferometer (or 2-arm gravitational wave antenna) to plane polarized gravitational waves [1]. We here obtain equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) by a simple differencing of the 3-pulse Doppler response functions of two 1-arm antennas [2]. A 4-pulse response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions (3n+1 pulse!) for antennas having multiple passes, or having more arms.The research described in this paper was carried out at the Jet Propulsion Laboratory, under contract with the National Aeronautics and Space Administration.     

Special relativistic gravitational theory

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional short-range gravity are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.Plovdiv University Paissii Hilendarskii.Moscow Institute of Railway Transport Engineers.     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

On the assumptions made in treating the gravitational wave problem by the high-frequency approximation

The assumptions that enter into the formulation of the gravitational wave problem in the limit of high frequency are discussed. It is shown that depending on the relation between the amplitude parameter and the frequency parameter the concept of back-reaction can have different physical interpretations. We also show that as a direct consequence of these assumptions high-frequency gravitational waves do not disperse in a vacuum. Finally, we make some conjectures about a coordinate-free characterization of high frequency for some cases and also about the use of the invariants of the Weyl tensor for the problem of finding a background space-time given a vacuum space-time containing high-frequency gravitational radiation.     

Exact gravitational field of the infinitely long rotating hollow cylinder

The vacuum line element inside an infinitely long rotating hollow cylinder is the usual flat space line element. It is fitted in a most general way to the general cylindrical vacuum field outside at the singular hypersurfaceR ₀=const, representing the infinitely thin hollow cylinder. With the use of the jump conditions atR ₀=const the surface densities , of which the energy-momentum-stress tensor of the shell consists, are calculated. The physical properties of the cylinder, as derived from the eigenvalues and -vectors of , and the generated gravitational field are discussed in full detail.     

Stability and structure of Newtonian gravitars

The solution r² for a scalar field (gravitational constant), which is asymptotically exact for supercompact configurations and which Saakyan and Mnatsakanyan obtained from the numerical solution of the hydrostatics equations in the Newtonian approximation of the Jordan-Brans-Dicke theory, is used to study the gravitational stability of such configurations. We have found the stability condition 2/3 for polytropic configurations ( is the polytropic exponent) instead of 4/3, which is known for configurations of low compactness. Analytic solutions of the equations of internal structure are found for configurations which are intermediate with respect to stability (=2/3) and for some other important series of configurations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 98–102, July, 1982.In conclusion, the present author expresses his indebtedness and gratitude to V. N. Ponomarev, for assistance in executing the work.     

Curvature collineations

A classification of plane-fronted pure gravitational waves in terms of curvature collineations is given.Presented at the International Conference on Gravitation and Relativity, Copengagen, July 1971.     

Geodesics for the NUT metric and gravitational monopoles

In order to provide insight about the physical interpretation of the NUT parameter, we solve the geodesic equations for the NUT metric. We show that the properties of NUT geodesics are similar to the properties of trajectories for charged particles orbiting about a magnetic monopole. In summary, we show that (1) the orbits lie on the surface of a cone, (2) the conserved total angular momentum is the sum of the orbital angular momentum plus the angular momentum due to the monopole field, (3) the monopole field angular momentum is independent of the separation between the source of the gravitational field and the test particle, and (4) the geodesics are almost spherically symmetric. The strong similarities between the NUT geodesics and the electromagnetic monopole suggest that the NUT metric is an exact solution for a gravitational magnetic monopole. However, the subtle difference of being only almost spherically symmetric implies that the analogy is not perfect. The almost spherically symmetric nature of the NUT geodesics suggest that the energy of the Dirac string makes a contribution to the solution. We also construct exact solutions for special orbits, discuss a twin paradox, and speculate about the Dirac quantization condition for a gravitational magnetic monopole.     

Third-order geometrical null symmetries of gravitational fields

The first-, the second-, and the third-order null Killing vectors in a gravitational field are explored separately. When an algebraically special Petrov-type free gravitational field isaligned with a source-free (nonnull/null) electromagnetic field, their common propagation vectorl ^a is shown to be a third-order null Killing vector field ( _{l l l} g _ab = 0, _{l l} g _ab 0). When the two fields arenot aligned, the necessary and sufficient conditions for the existence of a third-order null symmetry are obtained in Newman-Penrose formalism.     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Gravitational Waves in Matter

The theory of gravitational waves in matter is given. This covers the questions of constitutive relation, number of independent polarizations, index of refraction, reflection and refraction at an interface, etc. The theory parallels the familiar optics of electromagnetic waves in material media, but there are some striking differences. The use of the Campbell-Morgan formalism in which the gauge-invariant tidal force dyads E and B rather than the gauge-dependent metric perturbations are the unknowns is essential. The main justification of the theory at the moment is as a theoretical exercise worth doing. The assumption: size L of the medium gravitational wave length (infinite medium) rules out application to the already well-understood detection problem, but there may be an application to gravitational wave propagation through molecular gas clouds of galactic or inter-galactic size.     

High frequency gravitational radiation in Kerr-Schild space-times

Vaidya has obtained general solutions of the Einstein equationsR _ab= _{a b} by means of the Kerr-Schild metricsg _ab= _ab +H _{a b} . The vector field _a generates a shear free null geodetic congruence both in Minkowski space and in the Kerr-Schild space-time. If in addition it is hypersurface orthogonal, the Kerr-Schild metric may be interpreted as the background metric in a space-time perturbed by a high frequency gravitational wave. It is shown that Vaidya's solutions satisfying this additional condition are of only two types: (1) Kinnersley's accelerating point mass solution and (2) a similar solution where a space-like curve plays the role of the time-like curve describing the world line of the accelerating mass. The solution named by Vaidya as the radiating Kerr metric does not satisfy the hypersurface orthogonal condition.Supported in part by National Science Foundation Grant MPS 741029.     

Classical theory of the interaction between a spinor field and the gravitational field: First-order field equations

The classical theory of the interaction of a neutral spin-1/2 Dirac field and the gravitational field is studied. For the purely gravitational part of the Lagrangian, written in terms of a vierbein and the local connection coefficient _ab , (regarded as independent field variables), the usual first-order form is adopted. For the Dirac part, however, a different choice is made, in which the covariant derivative of is built with the aid of the vierbein instead of with _ab . This still yields a first-order formalism, but one in which _ab is related to the vierbein in the same way as it would be in the absence of. This ensures that the global connection remains symmetric in andv in the presence of. The way in which the vierbein field equation leads to a familiar Einstein equation with a symmetric and conserved stress tensor on its right side is also analyzed.     

Nonlinear gravitational Lagrangians

Alternative gravitational theories based on Lagrangian densities that depend in a nonlinear way on the Ricci tensor of a metric are considered. It is shown that, provided certain weak regularity conditions are met, any such theory is equivalent, from the Hamiltonian point of view, to the standard Einstein theory for a new metric (which, roughly speaking, coincides with the momentum canonically conjugated to the original metric), interacting with external matterfields whose nature depends on the original Lagrangian density.     

Strong gravitational fields and geometry in the large

The problem of strong gravitational fields (1) can be neither formulated invariantly nor solved in a local manner; it belongs to geometry in the large and requires the discussion of a complete atlas of maps. At 1 a complicated topology of space-time is possible. Requirements for a solution with a complete atlas of maps and a physical example, a rigorous discussion of which has led to new results, are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 15–19, January, 1984.     

Time Multidimension in Gravity

The influence of possible additional (hidden) components of time on a body's motion in the field of a gravitational wave is considered. Contrary to the one-time theory, oscillations of the body height and width sizes in a plane perpendicular to the direction of the wave propagation occur independently from one another. This peculiarity can be used for the experimental check of emission of gravitational waves with distinct time trajectories in cosmic cataclysms. An interesting analogy between electromagnetic and gravitation quantities is discussed in the context of time multidimension.     

Gravitational (dynamic) time dilation according to absolute space-time theory

Proceeding from our absolute space-time conceptions, we obtain the formula for the gravitational frequency shift in an extremely simple way. Using our burst model for photons, we show that the different rates of clocks placed in spatial regions with different gravitational potentials appear as a direct result of the gravitational frequency shift and the axiomatic assumption that at any space point the time unit is to be defined by light clocks with equal arms, i.e., that at any space point the light velocity (in moving frames the there-and-back velocity) has the same numerical valuec. Considering the principle of equivalence, we come to the logical conclusion that the kinematic (Einstein-Lorentz) time dilation is an absolute phenomenon.     

On gravitational conductors,waveguides, and circuits

We show that a material with sufficiently large elastic shear modulus or shear viscosity will act like a gravitational conductor or metal. It will reflect gravitational waves, and it can be used to make gravitational waveguides and circuits. Unlike electromagnetism, a gravitational wave can be guided by a single conductor in transverse mode. Gravitational conductors can obey the dominant energy condition, and they can be larger than their Schwarzschild radius, but they must violate a new condition that is probably satisfied by all existing forms of matter. Direct-current gravitational circuits, although limits of guided gravitational waves, have a simple Newtonian interpretation.This essay is a slightly expanded version of one that received an honorable mention (1978) from the Gravity Research Foundation-Ed.Work supported in part by NSF grant No. PHY78-09616.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.