A singularity-free particle model in general relativity

In general relativity a general static solution describing spherically symmetric distributions of scalar and electrically charged dust is obtained and applied to the construction of a singularity-free extended particle model.     

An integrable model in general relativity

Melnikov-method-based theoretical results are demonstrated concerning the relative effectiveness of any two weak excitations in suppressing homoclinic/heteroclinic chaos of a relevant class of dissipative, low-dimensional and non-autonomous systems for the main resonance between the chaos-inducing and chaos-suppressing excitations. General analytical expressions are derived from the analysis of generic Melnikov functions providing the boundaries of the regions as well as the enclosed area in the amplitude/initial phase plane of the chaos-suppressing excitation where homoclinic/heteroclinic chaos is inhibited. The relevance of the theoretical results on chaotic attractor elimination is confirmed by means of Lyapunov exponent calculations for a two-well Duffing oscillator. Received 21 May 2002 / Received in final form 13 September 2002 Published online 29 November 2002     

Bianchi Type-IX viscous fluid cosmological model in general relativity

Bianchi Type-IX viscous fluid cosmological model is investigated. To get a deterministic model, we have assumed the conditiona = b ^m(m is a constant) between metric potentials andη ∞θ whereη is the coefficient of shear viscosity andθ the scalar of expansion in the model. The coefficient of bulk viscosity (ς) is taken as constant. The physical and geometrical aspects of the model are also discussed.     

Bianchi type IX string cosmological model in general relativity

We have investigated Bianchi type IX string cosmological models in general relativity. To get a determinate solution, we have assumed a condition ρ=λ i.e. rest energy density for a cloud of strings is equal to the string tension density. The various physical and geometrical aspects of the models are also discussed.     

The evolving,flowless drainhole: A nongravitating-particle model in general relativity theory

Nonstationary, spherically symmetric solutions of the coupled field equationsR =2,, and =0, in which the coupling polarity is opposite to the orthodox, are derived. The basic solution, termed the evolving, flowless drainhole manifold, has these properties: (1) geodesic completeness; (2) a topological hole that shrinks to a point at a singular event and immediately begins to expand back to infinite size; (3) multiple branching of geodesics that arrive at the singular event; (4) asymptotic flatness at spatial infinity, luminal infinity, and temporal infinity; (5) isometric symmetry under time reversal and under space reflection through the drainhole; (6) conformal symmetry under space-time dilatations that leave the singular event fixed, and also under space-time inversions that interchange the singular event and a point at infinity. An earlier, static drainhole solution of the same equations was able to represent an ordinary star's external field or to serve as a model of a simple gravitating or nongravitating particle, replacing in these capacities the Kruskal-Fronsdal-Schwarzschild black-hole manifolds. The evolving, flowless drainhole can be thought of as modeling the death and rebirth of a scalar particle that is infinitely large in the infinite past and the infinite future. This particle does not gravitate, for the ether flow whose spatial variations in the static drainhole solution are identified with gravitation is removed from consideration in the evolving, flowless drainhole solution by being turned off at the outset. What is left is space alone, evolving dynamically in accordance with the field equations.Presented at the Seventh International Conference on Gravitation and Relativity (GR7), Tel Aviv, Israel, 23–28 June 1974.     

A charged particle in bimetric general relativity

The gravitational field of a charged particle is investigated on the basis of the bimetric general relativity theory. It is found that the field differs from the Reissner-Nordström field only very close to the sphereR=m+(m ² –Q ²)^1/2. This sphere is impenetrable, and its interior is unphysical.     

A new coordinate condition in general relativity

In this paper, a new coordinate condition in general relativity is proposed. This coordinate condition is just Euler's equations of the harmonic map theory. It is shown that in case of rectangular coordinates our coordinate condition reduces to Fock's harmonic coordinate condition. Using this new coordinate condition the different spherical symmetric solutions of the Einstein equations are discussed. The axisymmetric case is also investigated.     

Kinks in general relativity

The problem of classifying topologically distinct general relativistic metrics is discussed. For a wide class of parallelizable space-time manifolds it is shown that a certain integer-valued topological invariant n always exists, and that quantization when n is odd will lead to spinor wave functionals.     

Time in general relativity

In order to distinguish between physical and coordinate effects in an arbitrary gravitational field, the space coordinate system and the clock rates must be specified operationallya priori. Once this is done, it is no longer possible to set up an initial surface arbitrarily, since this operation must be consistent with certain physical experiments, whose results depend upon the particular physical situation. A method is given for setting up the initial surface, and the time evolution of the system is discussed.NASA Predoctoral Fellow.     

A new test of general relativity

The emission of gravitational radiation by the recently discovered binary pulsar system will cause its orbital periodP to decrease at a rate which can now be predicted to beP ^–1 dP/dt= –(3 ± 2) × 10^–9yr^–1 if the only orbital perturbations are of general-relativistic origin. It is shown that other sources of period change are probably less important. The accuracy of this prediction as well as the possibility of its verification will improve greatly over the next few years. This is the first observation that can test general relativity beyond the post-Newtonian approximation.Work supported in part by National Science Foundation under grant No. MPS 74-15524.This essay received the fifth award from the Gravity Research Foundation for 1975 (Editor).     

A Finslerian extension of general relativity

A Finslerian extension of general relativity is examined with particular emphasis on the Finslerian generalization of the equation of motion in a gravitational field. The construction of a gravitational Lagrangian density by substituting the osculating Riemannian metric tensor in the Einstein density is studied. Attention is drawn to an interesting possibility for developing the theory of test bodies against the Finslerian background.     

Singularities in general relativity

The problem of singularities is examined from the stand-point of a local observer. A singularity is defined as a state with an infinite proper rest mass density. The approach consists of three steps: (i) The complete system of equations describing a non-symmetric motion of a perfect fluid under assumption of adiabatic thermodynamic processes and of no release of nuclear energy is reduced to six Einstein field equations and their four first integrals for six remaining unknown componentsgik. (ii) A differential relation for the behavior of the rest mass density is deduced. It shows that any inhomogeneity and anisotropy in the distribution and motion of a non-rotating ideal fluid accelerates collapse to a singularity which will be reached in a finite proper time. Collapse is also inevitable in a rotating fluid in the case of extremely high pressure when the relativistic limit of the equation of state must be applied. In the case of a lower or zero pressure the relation does not give an unambiguous answer if the matter is rotating. (iii) The influence of rotation on the motion of an incoherent matter is investigated. Some qualitative arguments are given for a possible existence of a narrow class of singularity-free solutions of Einstein equations. Assuming rotational symmetry the Einstein partial differential equations together with their first integrals are reduced to a system of simultaneous ordinary differential equations suitable for numerical integration. Without integrating this system the existence of the class of singularity-free solutions is confirmed and exactly delimited. These solutions, representing a new general relativistic effect, are, however, of no importance for the application in cosmology or astrophysics. It is proved that in all the other cases interesting from the point of view of application the occurrence of a point singularity in incoherent matter with a rotational symmetry is inevitable even if the rotation is present.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General Relativity     

An anisotropic magnetized viscous fluid cosmological model in general relativity

We investigate the behavior of a magnetic field in a viscous fluid cosmological model where the free gravitational field is of Petrov type D and the coefficient of shear viscosity is proportional to the rate of expansion in the model. Also discussed are the behavior of the model when the magnetic field tends to zero and some other physical properties.     

Tachyons in general relativity

The tachyonic version of the Schwarzschild (bradyonic) gravitational field within the framework of extended relativity is considered. The metric of a tachyonic black hole is obtained through superluminal transformations from a bradyonic metric. The extended space-time manifold of this geometry which includes both black and white tachyonic holes is analysed, and the differences between the tachyonic and bradyonic versions are noted. It is shown that the meanings of black holes, tachyons and bradyons depend on the character of the reference frame and are not absolute.     

A rotating dust cloud in general relativity II

I give a stationary solution of Einstein's equations representing a rotating cloud of dust. The solution is asymptotically flat, and has no curvature singularities. However, embedded in the cloud is a rotating surface layer of negative mass which precisely cancels the mass of the dust cloud. The solution throws light on the van Stockum class of rotating dust solutions, of which it is a member.     

A quadratic spinor Lagrangian for general relativity

We present a newfinite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof, is fully 4-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof.This essay received the fourth award from the Gravity Research Foundation, 1994—Ed.     

Exact model for a gaseous regular bouncing sphere in general relativity

An exact model for a relativistic gaseous sphere (i.e., one whose density vanishes at the outer boundary of the nonstatic sphere together with the pressurep) is given. The model has a bounce: The collapsing sphere comes momentarily to rest when the boundary is still outside the Schwarzschild radius of the matter sphere, then there is a macroscopic bounce, and the matter of the expanding sphere spreads all over the universe. This bouncing solution of Einstein's field equations is physically valid at any moment, i.e., the pressure and the density are positive inside the fluid sphere, and their respective gradients are negative. The mass function is positive, and the circumference is an increasing function of radial coordinate. This solution may represent at easily surveyable model for a supernova explosion where the explosion is so violent that no remnant whatsoever is left.     

Nongeodesic motion in general relativity

The equations of motion of a spinning body in the gravitational field of a much larger mass are found using both the Corinaldesi-Papapetrou spin supplementary condition (SSC) and the Pirani SSC. These equations of motion are compared with our previous result derived from Gupta's quantum theory of Gravitation. It is found that the spin-dependent terms differ in each of the above three results due to a different location of the center of mass of the spinning body. As expected, these terms are not affected by the choice of either Schwarzschild or isotropic coordinates. Finally, for the presently planned Stanford gyroscope experiment, we find the maximum secular displacement of the orbit of the gyro with respect to the orbit of its non-rotating housing to be of the order of (10⁻⁷ cm/year)t, a result much smaller than Schiff's result which is proportional to time squared.