General Relativistic Spacetimes Research Articles

Expansions of non-symmetric gravitational theories about a GR background

A large number of Lagrangian-based non-Riemannian geometrical theories of gravitation are consistently generated by the method of algebraic extension. Of this number, only two possess a physically viable excitation spectrum (particle content) when expanded about Minkowski spacetime. They are NGT (non-symmetric gravitational theory) and AHG (algebraically extended Hilbert gravity). The author undertakes the linear expansion of these two theories about an arbitrary vacuum general relativistic background spacetime. AHG fails to remain ghost free upon a non-flat background while NGT preserves its symmetries and particle content. NGT is the only AE Hermitean theory remaining in contention as an alternative theory to general relativity.

Connection Between Non-Rotating Local Reference Frames by Means of the World Function

AbstractBy means of the world function an approximate transformation showing the Riemann tensor between the Fermi coordinates associated to two non-rotating local reference frames is derived in a General Relativistic space-time. One of the observer’s world lines is resticted to be a time-like geodesic of the space-time, and the other is a time-like curve of a general character. The space-time where the transformation is evaluated is supposed to be of small curvature, and the calculations are carried out in a first order of approximation with respect to the Riemann tensor.

Killing vectors in conformally flat perfect fluid spacetimes

The existence of Killing vectors in conformally flat perfect fluid spacetimes in general relativity is considered. In particular Killing vectors which are neither orthogonal nor parallel to the fluid velocity vector are considered and stationary fields in which the fluid velocity vector is not parallel to the timelike Killing vector field are shown to exist. This class of solutions is shown to include several stationary (but non-static) axisymmetric fields, thus providing counter-examples to a theorem of Collinson (1976). In the case when the fluid is non-expanding, the number of spacelike Killing vectors is shown to depend on the rank of four functions of time which appear in the metric. Some examples of stationary but non-static fields are presented in closed form.

Static, Isotropic Spacetime in New General Relativity

New general relativity predicts a static, isotropic spacetime q\1ite different from the Schwarz­ schild spacetime of general relativity, unless one of the two unknown parameters, c, is exactly zero. In this paper we study its structure as a Riemannian spacetime, paying special attentions to motions of test particles theliein. Recently Kawai and Tomal} have discussed singularities of the static, isotropic spacetime in new general relativity, a gravitational theory based on absolute (or tele-) parallelism. 2 ),*) Here we study structures of the spacetime as probed by spin-1/2 particles and photons. The static, isotropic spacetime of new general relativity is described by the parallel vector fields b={bkl'(x)} with

Static, Isotropic Spacetime in New General Relativity

New general relativity predicts a static, isotropic spacetime quite different from the Schwarzschild spacetime of general relativity, unless one of the two unknown parameters, ε, is exactly zero. In this paper we study its structure as a Riemannian spacetime, paying special attentions to motions of test particles therein.

Lorentzian geometry of globally framed manifolds

A new class of globally framed manifolds (carrying a Lorentz metric) is introduced to establish a relation between the spacetime geometry and framed structures. We show that strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular framed structure. As examples, we present a class of spacetimes of general relativity, having an electromagnetic field, endowed with a framed structure and a causal spacetime with a nonregular contact structure. This paper opens a few new problems, of geometric/physical significance, for further study.

Space time manifolds and contact structures

A new class of contact manifolds (carring a global non‐vanishing timelike vector field) is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4‐dimensional spacetime of general relativity as a contact CR‐submanifold.

Relativistic time scales in the solar system

This paper deals with a self-consistent relativistic theory of time scales in the Solar system based on the construction of the hierarchy of dynamically non-rotating harmonic reference systems for a four-dimensional space-time of general relativity. In our approach barycentric (TB) and terrestrial (TT) times are regarded as the coordinate times of barycentric (BRS) and geocentric (GRS) reference systems, respectively, with an appropriate choice of the units of measurement. This enables us to avoid some of the inconsistencies and ambiguities of the definitions of these scales as these are currently applied. International atomic time (TAI) is shown to be the physical realization of TT on the surface of the Earth. This realization is achieved by a specific procedure to average the readings of atomic clocks distributed over the terrestrial surface, all of them synchronized with respect to TT. Extending TAI beyond the Earth's surface may be performed along a three-dimensional hypersurface TT = const. The unit of measurement of TAI coincides with TB and TT units and is equal to the SI second on the surface of the geoid in rotation. Due to the specific choice of the units of measurement the TB scale differs from the TT (TAI) scale only by relativistic nonlinear and periodic terms resulting from the planetary and lunar theories of motion. The proper time τ0 of any terrestrial observer coincides with the coordinate time τ of the corresponding topocentric reference system (TRS) evaluated at its origin. τ0 is reacted to TT (TAI) by the relativistic transformation involving the GRS velocity of the observer, its height above the geoid and the quadrupole tidal gravitational potential of the external masses. The impact of introducing TB and TT on the units of measurement of length and the basic astronomical constants is discussed.

Conformally flat static space-time in the general scalar-tensor theory of gravitation

Explicit vacuum field equations in the general scalar-tensor theory of gravitation proposed by Nordtvedt are obtained with the aid of the most general conformally flat spherically-symmetric static space-time. It is shown that the most general conformally flat spherically-symmetric static solution of Nordtvedt-Barker vacuum field equations is simply the empty flat space-time of general relativity.

Curvature of generic space-times in general relativity

Transversality theory is used to study the curvature of generic space-times in general relativity and some applications to unique determination of the metric by the curvature are given.

Zeeman-Göbel Topologies

In 1967 E. C. Zeeman argued that the Euclidean (i. e. manifold) topology of Minkowski space-time should be replaced by a strictly finer topology that was to have a closer connection with the indefinite metric. This proposal was extended in 1976 by Rudiger Göbel and Hawking, King and McCarthy to the space-times of General Relativity. It is the purpose of this paper to argue that these suggestions for replacement misrepresent the significance of the manifold topology and overstate the necessity for a finer topology. The motivation behind such arguments is a realist view of space-time topology as against (what can be construed to be) the instrumentalist position underlying some of the suggestions for replacement

QUANTUM EFFECTS NEAR SPACETIME SINGULARITIES

We incorporate quantum effects into the gravitational dynamics in the vicinity of singularity in the case of three important general relativistic spacetimes, namely the spherically symmetric dust-ball collapse, standard Friedmann models and a general cosmological scenario given by Belinskii et al. The quantum state of the universe is represented by a general wave function where the conformal degree of freedom is quantised. It is seen in each case that the spread around the classical state diverges in the limit of approach to the classically singular epoch. Thus, non-classical, non-singular states can occur with finite probability. Our results show that including quantum effects radically changes the usual singularity scenario.

Spin fluids in stationary axis-symmetric space-times

The relations establishing the equivalence of an ordinary perfect fluid stress-energy tensor and a spin fluid stress-energy tensor are derived for stationary axis-symmetric space-times in general relativity. Spin fluid sources for the Gödel cosmology and the van Stockum metric are given.

Spacetimes with a preferred null direction and a two-dimensional group of isometries: the null dust case

The authors consider spacetimes of general relativity admitting a preferred null direction lmu and a two-dimensional Abelian group of isometries G2. A null tetrad formulation of the Killing equations is given, as well as a classification of G2 according to the orientation of lmu with respect to the group transitivity surfaces. Two theorems concerning the action of the isometry group on lmu are presented: the first one deals with spacetimes admitting at least one Killing vector, while the second one deals with spacetimes admitting a G2. The Einstein field equations with a shear-free and diverging null dust source are integrated under the assumptions: (i) the spacetime admits an Abelian G2 whose transitivity surfaces are non-orthogonal to and do not contain the null dust propagation vector; (ii) there exists a Killing vector kmu whose magnitude is almost everywhere bounded at the endpoints of the null dust rays. These spacetimes are of Petrov type II, non-asymptotically flat, and the G2 is non-orthogonally transitive. By switching off the null dust the authors have explicitly obtained the underlying vacuum metrics which generalise some of the diverging Petrov type D vacuum metrics found by Kinnersley (1969).

An initial value gravitational quadrupole radiation theorem

A rigorous version of the quadrupole radiation formula is derived using the characteristic initial value formulation of a general relativistic fluid space-time. Starting from initial data for a Newtonian fluid, an algorithm is presented that determines characteristic initial data for a one-parameter family of general relativistic fluid space-times. At the initial time, a one-parameter family of space-times with this initial data osculates the evolution of the Newtonian fluid and has leading order news function equal to the third time derivative of the transverse Newtonian quadrupole moment.

A new approach to the Regge calculus: I. Formalism

This paper develops a new approach to Regge calculus, a numerical technique used for the calculation of general relativistic spacetimes. The method is developed in an original '3+1' form in such a way that it can be applied to inhomogeneous spacetimes. In a second paper the method will be tested by application to spherically symmetric vacuum spacetimes.

Violations of Causality in the Space-Time of General Relativity

Violations of Causality in the Space-Time of General Relativity

Robertson-Walker Lyttleton-Bondi universe with cosmological constant

The exterior field of the Robertson-Walker metric in the Lyttleton-Bondi universe with cosmological constant is considered. It is shown that in the presence of cosmological constant, the exterior solution of this Universe is simply the empty space-time of general relativity.

Self-gravitating fluid in a conformally-flat space-time

The Einstein field equations for an irrotational perfect fluid with pressurep, equal to energy density are studied when the space-time is conformally flat. The coordinate transformation to co-moving coordinates is discussed. The energy and Hawking-Penrose inequalities are studied. Static and non-static solutions of the field equations are obtained. It is interesting to note that in the static case the only spherically-symmetric conformally flat solution for self-gravitating fluid is simply the empty flat space-time of general relativity.

Physical approach to cosmological homogeneity.

This paper shows that in general relativity space-time will admit three linearly independent spacelike Killing vectors if the cosmic matter is a perfect fluid with a functional relationship between pressure and density and the spacelike eigenvectors of the shear tensor are parallel transported along the world lines of the fluid. In the Newtonian case it is proved that for an irrotational motion of a fluid with pressure and density functionally related spatial uniformity of the matter distribution leads to the homogeneity of the velocity field.