On Gravitational Repulsion

The concepts of negative gravitational mass and gravitational repulsion are alien to general relativity. Still, we show here that small negative fluctuations—small dimples in the primordial density field—that act as if they have an effective negative gravitational mass, play a dominant role in shaping our Universe. These initially tiny perturbations repel matter surrounding them, expand and grow to become voids in the galaxy distribution. These voids—regions with a diameter of 40 h^-1 Mpc which are almost devoid of galaxies—are the largest objects in the Universe.     

Dynamical space and gravitation within a purely geometrical framework: A new approach to gravitation

We state a purely geometrical framework apparently implementing Machian ideas on inertia. Only coupling constants dimensionless in natural units have been introduced in the theory. In anynonvacuum cosmos the field equations describing the gravitational phenomena in cosmological units turn out to be identical to Einstein's equations, with the Einstein gravitational coupling expressed in terms of the parameters defining the cosmological structure. This dependence, however, is not detectable. Indeed, such equations do not need to incorporate the standard Machian requirements (apart from the requirement that they are not conceivable in the total absence of matter) in order to be Machian, since, just on the basis of Mach's principle, one cannot expect to be able to detect Machian effects in Nature by using a system of units based on gravitational phenomena. On the contrary, the equations describing the gravitational field in local atomic units are Machian in the standard sense and, in particular, they incorporate the ideas that the frame has to be fixeddirectly in connection with the observed distribution and motion of matter and that there does not exist any kind of space-time in the total absence of matter. Finally, to reconcile, at least in the weak-field approximation, Einstein's equations (considered as equations describing the gravitational phenomena in local atomic units) with Mach's principle and to be in agreement with cosmological observations, we suggest that our cosmos be identified with a superuniverse model in which the background structure is homogeneous (in space and in time) and isotropic, while our universe is represented by one of the local inhomogeneities of the background. Then we prove that in any region of our universe in which the gravitational field issufficiently weak and smooth the equations, describing the gravitational field in local atomic units, are expected to approximate Einstein's equations all the better, the more the dimensions of our universe are negligible with respect to the dimensions of the background and the background curvature is small. As regards the experimental predictions of the present approach, any prediction for experiments involving only purely gravitational measurements is identical to that of Einstein's theory and the above result also guaranteesa fortiori the agreement with the available experimental data, also asnonpurely gravitational experiments are concerned.This paper appeared as Istituto Matematico L. Tonelli, preprint 78–10 (April 1978) (unpublished).     

Naked singularities in spherically symmetric gravitational collapse: A critique

One of the most important questions in the physics of gravitation phenomena is whether gravitational collapse can lead to the formation of singularities which are not hidden by an event horizon. The Cosmic Censorship Conjecture (CCC) represents the hope that such a drastic event cannot happen in realistic physical situations. However, in the recent past several counter examples to the CCC were demonstrated by several researchers in situations of spherically symmetric gravitational collapse. The disturbing aspect about these counter examples is that they are strong naked singularities—they can crush matter to zero volume and can have a disastrous influence on causal physics. We examine these counter examples for their physical content by working through the dynamical collapse of inhomogeneous dust and argue that these are not physically acceptable counter examples. Our main result is that the singularities when naked are weak and when strong, strongly censored. The strong naked singularities in the counter examples do not arise from dynamical collapse; they result from the intrinsically singular nature of the initial density distributions chosen. The CCC seems to remain robust as far as spherically symmetric collapse is concerned.     

Gravitational Fields and Nonlinear σ-Models

It is shown that different types of gravitational fields can be analyzed as nonlinear -models. We show that the Einstein—Hilbert action for stationary aximmetric fields, Einstein—Rosen gravitational wave, and Gowdy cosmological models can be expressed in terms of a Lagrangian density for the SL(2, R)/SO(2) -model. We discuss the possibility of using these results to quantize gravitational fields.     

Ion beam induced atomic mixing in Fe/Al bilayered samples

Atomic mixing of Fe/Al bilayered samples induced by an energetic xenon beam has been studied by RBS-TEM and sheet resistivity measurements. Mixing is detected at 2.5 × 10¹⁵ Xe/cm² and then proceeds up to 2 × 10¹⁶ Xe/cm². A blocking effect of the mixing for larger doses is observed. Homogeneous concentration is not obtained across the sample. Instead a pronounced graded composition is reached. Several explanations of the mixing process and the subsequent blocking effect are suggested: — sharp gradients in the nuclear energy deposition profile which decrease with dose — grain growth phenomena — precipitation of crystalline xenon acting as efficient annihilation sinks for vacancies.     

Gravitational collapse and naked singularities

Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of ‘effective naked singularities’, which will be quite helpful because general relativity has limitation in its application at the high-energy end. The appearance of naked singularities is not detestable but can open a window for the new physics of strongly curved space-times.     

Atomic and gravitational clock

Atomic and gravitational clocks are governed by the laws of electrodynamics and gravity, respectively. While the strong equivalence principle (SEP) assumes that the two clocks have been synchronous at all times, recent planetary data seem to suggest a possible violation of the SEP. Our past analysis of the implications of an SEP violation on different physical phenomena revealed no disagreement. However, these studies assumed that the two different clocks can be consistently constructed within the framework. The concept of scale invariance, and the physical meaning of different systems of units, are now reviewed and the construction of two clocks that do not remain synchronous—whose rates are related by a nonconstant function _a—is demonstrated. The cosmological character of _a is also discussed.This paper is reprinted with minor editorial modifications fromNature,296, 709 (1982).     

A local relativistic red-shift effect

A relativistic red-shift effect is found that is distinct from the doppler and gravitational red shifts and provides a mechanism for producing large local red shifts without raising kinetic energy problems. This effect produces red shifts in discrete amounts—a situation for which there may be some evidence in quasar observations.     

A class of metric theories of gravitation on Minkowski spacetime

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian , from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.     

Gravitational waves and massive tensor particles in thef-g theory of gravity

Starting from the generally covariant version of the Pauli-Fierz mass term, it is stressed that the tensor fields representing spin-2 particles, eigenstates of strong and gravitational interactions, are linear combinations of one massive and one massless state. This implies that any hadronic reaction, in which massive tensor particles are produced, can be regarded, at least in principle, also as an effective source of gravitons which may become very important in the early stages of the universe; conversely, any process in which gravitational radiation of sufficiently high energy is emitted, should be a source of strongly interacting tensor particles which decay into photons and neutrinos. These two effects could be used for producing and detecting gravitational waves.This essay was awarded an honorable mention (1985) by the Gravity Research Foundation—Ed.     

Gravitational fields with groups of motions on two-dimensional transitivity hypersurfaces in a model with matter and a magnetic field

For gravitational fields with metrics which admit of groups of motions multiply — transitive on 2-dimensional space-like invariant varieties, the exact solutions of the Einstein gravitational equations are given for the case when the sources of the gravitational field are dust-like matter and a magnetic field. A magnetic field is orientated along a direction orthogonal to transitivity hypersurface. The solutions contain arbitrary functions. In the case of transitivity hypersurface of positive curvature and in the absence of a magnetic field, the solution is reduced to the Tolman spherically symmetric solution for dust-like matter. The conditions are studied under which the solutions with a magnetic field become asymptotically isotropic and approach the flat and the open Friedmann models. The case of transitivity hypersurfaces with signature (+ –) is also considered.     

Semiclassical Cosmological Perturbations Generated During Inflation

Interaction with the environment may induce stochastic semiclassical dynamicsin open quantum systems. In the gravitational context, stress-energy fluctuationsof quantum matter fields give rise to a stochastic behavior in the spacetimegeometry. The Einstein—Langevin equation is a suitable tool to take these effectsinto account when addressing the backreaction problem in semiclassical gravity.We analyze within this framework the generation of gravitational fluctuationsduring inflation, which are of great interest for large-scale structure formationin cosmology.     

The Principle of Equivalence,electrodynamics and General Relativity

It is shown that the customary covariant formulation of electrodynamics in General Relativity is incompatible with the Einstein Principle of Equivalence. This is demonstrated for the case of a resistanceless current-carrying wire in a static spherically symmetric gravitational field—where the Einstein Principle of Equivalence implies the existence, in the vicinity of the wire, of a non-zero component of the electric field parallel to the wire, whereas the covariant form of Maxwell's equations does not. An experiment, involving a superconducting current-carrying wire segment placed in the Earth's gravitational field, is suggested. Whether or not a component of electric field parallel to the wire, at a point in the wire's vicinity, would be detected would resolve the issue.     

Influence of gravity on the solidification of eutectics I. theory

In the frame of a simple model, the paper presents a theoretical analysis of the influence of an external force field (gravity) on the solidification of an eutectic complex-forming melt. It is shown in terms of the so-called singular perturbation method that —in contrast to classical theories of freezing — the direct influence of the gravitational field cannot be neglected in such a solidifying melt in which nonlinear processes take place. Under standard (i.e. g₀= 9·81 m s^–2) and zero gravity conditions, the differences in undercoolings and lamellar spacings are determined analytically.     

Global and local principles of relativity

The principles of relativity are assertions about the structure of physical laws, whose validity or nonvalidity can only be empirically confirmed or falsified. The weakest forms of those principles are the so-calledglobal propositions. They furnish statements as to which operations—assumed to be performed simultaneously throughout the whole universe—have no influence upon the physical events. Much stronger principles are those of alocal nature. These assert that the physical properties of a system do not change, when the relation of the system is altered vis-à-vis the universe at large. On formulating these local principles, we presuppose either that it is possible to eliminate any influence of the environment or that the influence can be compensated as in the case of universal forces (e.g., gravitational) which can principally not be removed. Still weaker, however, are those formulations of the relativity principles which postulate relativity only for infinitesimally small space-time domains or regions. This distinction yields clarification of all discussions about existence and meaning of a general relativity principle. Such an analysis was already performed by Einstein and Abraham in 1912.     

Metric-affine variational principles in general relativity II. Relaxation of the Riemannian constraint

We continue our investigation of a variational principle for general relativity in which the metric tensor and the (asymmetric) linear connection are varied independently. As in Part I, the matter Lagrangian is minimally coupled to the connection and the gravitational Lagrangian is taken to be the curvature scalar, but we now relax the Riemannian constraint as far as possible—that is, as far as the projective invariance of the assumed gravitational Lagrangian will allow. The outcome of this procedure is a gravitational theory formulated in a volume-preserving space-time (i.e., with torsion and tracefree nonmetricity). The vanishing of the trace of the nonmetricity is due to the remaining vector constraint. We also discuss the physical significance of the relaxation of the Riemannian constraint, the possible relaxation of the vector constraint, the notion of the hypermomentum current, and its possible relation to elementary particle physics.     

Space-time is four-dimensional

The quantum state of the universe is described by Hartle and Hawking's ground state which is defined by a path integral over all compact metrics. The most probable classical evolution of the universe can be considered to come from some gravitational instanton by a quantum tunneling. These arguments have been generalized to the case of Kaluza-Klein models. It is found that in d= 11 simple supergravity, with a minisuperspace ansatz, all instantons must have a four dimensional sector. It suggests that this is the main reason why space-time is four-dimensional.This essay received the third award from the Gravity Research Foundation for the year 1985—Ed.     

Classical and relativistic forces of inertia

It is shown that — in contrast to the classical physics and special relativity — the self-consistency of general relativity requires that the forces of inertia follow unambiguously from the field equations as inductive gravitational effects of the cosmic matter and that this requirement is perfectly satisfied, without supplementary hypotheses, for the Einstein universe, in full agreement with Mach's principle.     

A Proposal to Measure Antimatter Gravity Using Ultracold Antihydrogen Atoms

The gravitational acceleration of antimatter has never been measured directly. Antihydrogen atoms, being both stable and neutral, are an ideal system for investigating antimatter gravity. Ultralow temperatures in the 10–100 K range are desirable for practical experiments. It is proposed to cool positive antihydrogen ions using laser-cooled ordinary ions. Ultracold neutral antihydrogen atoms might then be obtained by photodetachment. The gravitational acceleration can readily be determined from the time-of-flight between the photodetachment laser pulse and an annihilation detector.