Exterior Gravitational Field Research Articles

On a class of rotating gravitational waves

A class of solutions of the gravitational field equations describing vacuum spacetimes outside rotating cylindrical sources is presented. The spacetime metric for this class is given by equation (35); to render this metric explicit, one must solve the nonlinear differential equation (31). A subclass of these solutions could correspond to the exterior gravitational fields of rotating cylindrical systems that emit gravitational radiation. This class has a special solution - corresponding to the exact solution (32) of equation (31) - in common with the Robinson-Trautman gravitational wave spacetimes, namely, the Siklos solution. The properties of rotating gravitational waves are briefly investigated. In particular, we discuss the energy density of these waves using the gravitational stress-energy tensor.

A Stable Numerical Method for Inverting Shape from Moments

We derive a stable technique, based upon matrix pencils, for the reconstruction of (or approximation by) polygonal shapes from moments. We point out that this problem can be considered the dual of 2-D numerical quadrature over polygonal domains. An analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points. Finally, an application to the problem of gravimetry is explored where the shape of a gravitationally anomalous region is to be recovered from measurements of its exterior gravitational field.

Taub’s plane-symmetric vacuum spacetime reexamined

The gravitational properties of the only static plane-symmetric vacuum solution of Einstein's field equations without a cosmological term (Taub's solution, for brevity) are presented: some already known properties (geodesics, weak field limit, and pertainment to the Schwarzschild family of spacetimes) are reviewed in a physically much more transparent way, as well as new results about its asymptotic structure, possible matchings, and the nature of the source are furnished. The main results point to the fact that the solution must be interpreted as representing the exterior gravitational field due to a negative mass distribution, confirming previous statements to that effect in the literature. Some analogies to Kasner's spatially homogeneous cosmological model are also mentioned.

Canonical quantization of cylindrically symmetric models.

We carry out the canonical quantization of the Levi-Civit\`a family of static and cylindrical solutions. The reduced phase space of this family of metrics is proved to coincide with that corresponding to the Kasner model, including the associated symplectic structures, except that the respective domains of definition of one of the phase space variables are not identical. Using this result, we are able to construct a quantum model that describes spacetimes of both the Levi-Civit\`a and the Kasner type, and in which the three-dimensional spatial topology is not uniquely fixed. Finally, we quantize to completion the subfamily of Levi-Civit\`a solutions which represent the exterior gravitational field of a straight cosmic string. These solutions are conical geometries, i.e., Minkowski spacetime minus a wedge. The quantum theory obtained provides us with predictions about the angular size of this wedge.

On the simplest binary system of stationary black holes

The simplest three-parameter member of the Kramer-Neugebauer family of solutions representing the exterior gravitational field of two identical Kerr black holes is identified. We show that the condition for the existence of two separated horizons in this binary system is less stringent than in the case of a single black hole.

Metric of a rotating, charged, magnetized, deformed mass. II.

A compact analytical form of the solution of the Einstein-Maxwell equations able to describe the exterior gravitational field of a charged rotating massive source possessing arbitrary magnetic dipole and mass-quadrupole moments is presented.

New static axisymmetric solution of the Einstein field equations

A new exact asymptotically flat solution of the Einstein equations able to describe the exterior gravitational field of a static mass possessing a quadrupole moment is presented in explicit form. In contrast with the known solutions of this type earlier obtained by Erez and Rosen(1959) and Gutsunaev and Manko(1985), this solution represents a small deformation of the Schwarzschild solution.

Exterior gravitational field of a charged magnetised axisymmetric mass

We present an exact stationary asymptotically flat solution of the Einstein-Maxwell equations that may describe the exterior gravitational field of an arbitrary-axisymmetric-mass distribution endowed with electric-charge and magnetic-dipole moment. The full metric for the solution obtained is constructed in explicit form.

New exact solution of the Einstein equations for a spinning mass

A new exact asymptotically flat solution of the Einstein equations able to describe the exterior gravitational field of a stationary rotating mass is presented. It contains two independent parameters associated with the total mass and total angular momentum of the source, and reduces in the static limit to the Schwarzschild space-time.

Explicit Calculation of the Solution to Backus′ Problem with a Condition for Uniqueness

In this work a uniqueness result for Backus′ problem for the exterior magnetic or gravitational field of the earth is given. Once this condition is established, an explicit series solution for the magnetic problem is computed and the convergance proved.

Solution of the equations of the relativistic theory of gravitation for equilibrium massive bodies with allowance for their equations of state

The solutions of the equations of the relativistic theory of gravitation that describe the equilibrium state of a spherically symmetric isolated massive body are analyzed. It is shown that if the mass of the body is greater than the critical value equilibrium states do not exist; the minimum sizes of such bodies are always greater than the Schwarzschild sizes. We investigate the equilibrium sizes, the structure of the exterior gravitational field, and the distributions of the interior pressures and densities in the case of characteristic astrophysical objects such as the earth, Jupiter, the sun, neutron stars, and white dwarfs. The results agree satisfactorily with observations.

Kerr–Newman metric endowed with magnetic dipole moment

The full metric representing the nonlinear superposition of the Kerr–Newman solution with a massless magnetic dipole is obtained. This metric is asymptotically flat and describes correctly the exterior gravitational field of a charged, magnetized, spinning mass.

Exact solution of the Einstein-Maxwell equations for the exterior gravitational field of a magnetized rotating mass.

We present for the first time a physically realistic exact asymptotically flat solution of the Einstein-Maxwell equations representing the exterior gravitational field of a stationary rotating mass endowed with a magnetic dipole moment. Our solution reduces in its static pure vacuum limit to the Schwarzschild metric.

Generalizations of the Kerr and Kerr-Newman metrics possessing an arbitrary set of mass-multipole moments

The authors present in a concise analytical form two asymptotically flat metrics describing the superposition of the Kerr solution with an arbitrary static vacuum Weyl field which differ in their angular momentum distributions. They are then used for the construction of two asymptotically flat generalizations of the Kerr-Newman spacetime possessing the full set of mass-multipole moments able to describe the exterior gravitational field of a charged rotating arbitrary axisymmetric mass.

Metric of a rotating, charged, magnetised mass

An exact asymptotically flat solution of the Einstein-Maxwell equations able to describe correctly the exterior gravitational field of a rotating mass endowed with an arbitrary electric charge and arbirary magnetic moment is obtained in a explicit form. Its static pure vacuum limit is the Schwarzschild spacetime.

Stationary solution of the Einstein equations possessing zero total angular momentum

We present an asymptotically flat stationary generalization of the Schwarzschild spacetime describing the exterior gravitational field of a rotating source whose total angular momentum is equal to zero. The full metric is derived in an explicit form, and the weak field approximation for the obtained solution is considered.

The exterior gravitational field of a static and stationary mass with an arbitrary set of multipole moments

New exact asymptotically flat solutions of Einstein's vacuum equations for the description of the exterior gravitational field of a static and stationary mass with an arbitrary mass-multipole structure are presented.

New exact solution for the exterior gravitational field of a charged spinning mass.

An exact asymptotically flat solution of the Einstein-Maxwell equations describing the exterior gravitational field of a charged rotating axisymmetric mass possessing an arbitrary set of multipole moments is presented explicitly.

Comment on "New exact solution for the exterior gravitational field of a spinning mass"

A Comment on the Letter by Manko, Phys. Rev. Lett. 64, 1625 (1990).Received 15 May 1990DOI:https://doi.org/10.1103/PhysRevLett.67.1050©1991 American Physical Society

Some new radiating Kerr-Newman solutions

Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.