Matching stationary spacetimes

Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary time-like hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2-dimensional matching surface on the space manifold. We prove existence and uniqueness results to the matching problem for stationary perfect fluid spacetimes with spherical, planar, hyperbolic and cylindrical symmetry. Finally, we find an explicit interior for the cylindrical analogue of the NUT spacetime.     

Maximal hypersurfaces in stationary asymptotically flat spacetimes

Existence of maximal hypersurfaces and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike near infinity.. The first class consists of strongly causal asymptotically flat spacetimes which contain no black hole or white hole (but may contain ergoregions where the Killing orbits fail to be timelike). The second class of spacetimes possess a black hole and a white hole, with the black and white hole horizons intersecting in a compact 2-surfaceS.Supported in part by KBN grant #2 1047 9101Supported in part by NSF grant PHY-8918388.     

Extremally accelerated observers in stationary axisymmetric spacetimes

Stationary observers with the extremal value of the total thrust, considered in stationary axisymmetric spacetimes, have interesting privileges: they Fermi-transport their 4-acceleration, and those with zero vertical acceleration measure that the particles on local radially non-accelerated circular orbits co- and counter-rotate with the same modulus of velocity.     

Orthogonal decomposition of axi-symmetric stationary spacetimes

Zeitschrift für Physik A Hadrons and nuclei - We show that for a wide class of field equations the orbits of the isometry group defining axial symmetry and stationarity admit orthogonal...     

Complete integrability of geodesic motion in general higher-dimensional rotating black-hole spacetimes

We explicitly exhibit n-1=[D/2]-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n=[(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.     

Scalar field quantization in stationary,non-static spacetimes

A quantization procedure is given for the scalar field on stationary, axisymmetric background spacetimes with orthogonal 2-surfaces. The procedure is based on observers orthogonal to surfaces of constant Killing time, and thus agrees with the usual procedure for static spacetimes. For stationary but nonstatic spacetimes the procedure differs from the usual one but nonetheless leads to a natural quantization scheme. Applying the procedure to flat space in rotating coordinates gives the standard, inertial Minkowski vacuum. For the Kerr spacetime, the procedure yields a particle definition which is well-defined everywhere outside the horizon. The above observers are just nonrotating ZAMO's, and the vacuum state smoothly interpolates between the “in” and “out” Boulware vacua.     

Physical frames along circular orbits in stationary axisymmetric spacetimes

Three natural classes of orthonormal frames, namely Frenet-Serret, Fermi–Walker and parallel transported frames, exist along any timelike world line in spacetime. Their relationships are investigated for timelike circular orbits in stationary axisymmetric spacetimes, and illustrated for black hole spacetimes. Dedicated to Bahram Mashhoon for his 60th birthday.     

Geodesic connectedness of stationary spacetimes with optimal growth

In the last fifteen years variational methods have been widely applied in the study of geodesic connectedness of stationary spacetimes. In this paper we introduce fine estimates which allow us to apply such methods to this problem in an optimal way, improving by far previous results on the subject. Our estimates also seem useful for extending the existing results in other related subjects, for example, connectedness by timelike geodesics and existence of normal trajectories.     

Einstein equations and inertial forces in axially symmetric stationary spacetimes

We investigate the relations between the inertial forces and the Einstein equations in axially symmetric stationary spacetimes. For the vacuum stationary axially symmetric spacetimes, we use the Geroch formalism to express the Einstein equations in terms of inertial forces. For the spacetimes with the perfect fluid sources, we use the formalism developed by Hansen and Winicour for establishing the relations. As expected intuitively, the gradients of inertial forces represent the field equations.     

Nonexistence of conformally flat slices in Kerr and other stationary spacetimes

It is proved that stationary solutions to the vacuum Einstein field equations with a nonvanishing angular momentum have no Cauchy slice that is maximal, conformally flat, and nonboosted. The proof is based on results coming from a certain type of asymptotic expansion near null and spatial infinity--which also show that the development of Bowen-York-type data cannot have a development admitting a smooth null infinity--and from the fact that stationary solutions do admit a smooth null infinity.     

A class of empty spacetimes admitting a rational first integral of the geodesic equation

The empty space field equations are solved for one of the canonical forms obtained previously by Vaz and Collinson for the metrics of space-times admitting a surface generating Killing pair, one member of which is hypersurface orthogonal.     

Complete analytic solution of the geodesic equation in Schwarzschild-(anti-)de Sitter spacetimes

The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti-)de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The solutions are completely classified by the structure of the zeros of the characteristic polynomial which depends on the energy, angular momentum, and the cosmological constant.     

On quadratic first integrals of the geodesic equations for type {22} spacetimes

It is shown that every type {22} vacuum solution of Einstein's equations admits a quadratic first integral of the null geodesic equations (conformal Killing tensor of valence 2), which is independent of the metric and of any Killing vectors arising from symmetries. In particular, the charged Kerr solution (with or without cosmological constant) is shown to admit a Killing tensor of valence 2. The Killing tensor, together with the metric and the two Killing vectors, provides a method of explicitly integrating the geodesics of the (charged) Kerr solution, thus shedding some light on a result due to Carter.     

Mass,action, and entropy of Taub-Bolt-de Sitter spacetimes

We apply a recent proposal for defining conserved mass in asymptotically de Sitter spacetimes to the class of Taub-Bolt-de Sitter spacetimes. We compute the action, entropy, and conserved mass of these spacetimes, and find that in certain instances the mass and entropy can exceed that of pure de Sitter spacetime, in violation of recent suggestive conjectures to the contrary.     

Some canonical forms for the metric of spacetimes admitting a rational first integral of the geodesic equation

Canonical forms are obtained for the metrics of space-times admitting a surface generating Killing pair, one member of which is hypersurface orthogonal.     

Acausality in Gowdy spacetimes

We present a parametrization of T ³ and S ¹ × S ² Gowdy cosmological models which allows us to study both types of topologies simultaneously. We show that there exists a coordinate system in which the general solution of the linear polarized special case (with both topologies) has exactly the same functional dependence. This unified parametrization is used to investigate the existence of Cauchy horizons at the cosmological singularities, leading to a violation of the strong cosmic censorship conjecture. Our results indicate that the only acausal spacetimes are described by the Kantowski-Sachs and the Kerr-Gowdy metrics.