arXiv subjects

Zoltán Perjés

Publications and source records attributed to Zoltán Perjés.

At least 19 recordsLinked to original sources

arXiv2005

Covariant Linear Perturbations in a Concordance Model

We present the complete solution of the first order metric and density perturbation equations in a spatially flat (K=0), Friedmann-Robertson-Walker (FRW) universe filled with pressureless ideal fluid, in the presence of cosmological constant. We use covariant linear perturbation formalism and the comoving gauge condition to obtain the field and conservation equations. The solution contains all modes of the perturbations, i.e. scalar, vector and tensor modes, and we show that our results are in agreement with the Sachs & Wolfe metric perturbation formalism.

gr-qc↗

arXiv2004

$C^\infty$ perturbations of FRW models with a cosmological constant

Spatially homogeneous and isotropic cosmological models, with a perfect fluid matter source and non-vanishing cosmological constant, are studied. The equations governing linear perturbations of the space-time and the variation of energy density are given. The complete solution of the problem is obtained for $C^{\infty}$ perturbations, using a comoving time. The Sachs-Wolfe fluctuations of the temperature of the cosmic background radiation are obtained for the relatively growing density perturbations. It is found that the observable celestial microwave fluctuation pattern underwent a reversal approximately two billion years ago. What is observed today is a negative image of the last scattering surface with an attenuation of the fluctuations, due to the presence of the cosmological constant.

astro-ph↗

arXiv2002

Perturbations of rotating cosmological black holes

Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.

gr-qc↗

arXiv2002

Charged black holes: Wave equations for gravitational and electromagnetic perturbations

A pair of wave equations for the electromagnetic and gravitational perturbations of the charged Kerr black hole are derived. The perturbed Einstein-Maxwell equations in a new gauge are employed in the derivation. The wave equations refer to the perturbed Maxwell spinor $Φ_0$ and to the shear $σ$ of a principal null direction of the Weyl curvature. The whole construction rests on the tripod of three distinct derivatives of the first curvature $κ$ of a principal null direction.

gr-qc↗

arXiv2002

Slowly rotating charged fluid balls and their matching to an exterior domain

The slow-rotation approximation of Hartle is developed to a setting where a charged rotating fluid is present. The linearized Einstein-Maxwell equations are solved on the background of the Reissner-Nordstrom space-time in the exterior electrovacuum region. The theory is put to action for the charged generalization of the Wahlquist solution found by Garcia. The Garcia solution is transformed to coordinates suitable for the matching and expanded in powers of the angular velocity. The two domains are then matched along the zero pressure surface using the Darmois-Israel procedure. We prove a theorem to the effect that the exterior region is asymptotically flat if and only if the parameter C_{2}, characterizing the magnitude of an external magnetic field, vanishes. We obtain the form of the constant C_{2} for the Garcia solution. We conjecture that the Garcia metric cannot be matched to an asymptotically flat exterior electrovacuum region even to first order in the angular velocity. This conjecture is supported by a high precision numerical analysis.

gr-qc↗

arXiv2002

Fundamental equations for the gravitational and electromagnetic perturbations of a charged black hole

A pair of wave equations is presented for the gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled and determines the propagation of the electromagnetic perturbation. The other is for the propagation of the shear of a principal null direction and has a source term given by the solution of the first equation. This result is expected to have important applications in astrophysical models.

gr-qc↗

arXiv2002

Vacuum Kerr-Schild metrics generated by nontwisting congruences

The Kerr-Schild pencil of metrics $\tilde g_{ab}=g_{ab}+V l_al_b$, with $g_{ab}$ and $\tilde g_{ab}$ satisfying the vacuum Einstein equations, is investigated in the case when the null vector $l$ has vanishing twist. This class of Kerr-Schild metrics contains two solutions: the Kasner metric and a metric wich can be obtained from the Kasner metric by a complex coordinate transformation. Both are limiting cases of the Kóta-Perjés metrics. The base space-time is a pp-wave.

gr-qc↗

arXiv2002

Solution of the vacuum Kerr-Schild problem

The complete solution of the vacuum Kerr-Schild equations in general relativity is presented, including the space-times with a curved background metric. The corresponding result for a flat background has been obtained by Kerr.

gr-qc↗

arXiv2002

Kerr-Schild metrics revisited I. The ground state

The Kerr-Schild pencil of metrics $g_{ab}+\La l_al_b$ is investigated in the generic case when it maps an arbitrary vacuum space-time with metric $g_{ab}$ to a vacuum space-time. The theorem is proved that this generic case, with the field $l$ shearing, does not contain the shear-free subclass as a smooth limit. It is shown that one of the Kóta-Perjés metrics is a solution in the shearing class.

gr-qc↗

arXiv2002

Kerr-Schild metrics revisited II. The complete vacuum solution

The complete solution of Einstein's gravitational equations with a vacuum-vacuum Kerr-Schild pencil of metrics $g_{ab}+V l_al_b$ is obtained. Our result generalizes the solution of the Kerr-Schild problem with a flat metric $g_{ab}$ (represented by the Kerr theorem) to the case when $g_{ab}$ is the metric of a curved space-time.

gr-qc↗

arXiv2000

Petrov types of slowly rotating fluid balls

Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are stated on the possible Petrov types of various fluid models. It is shown that Petrov type II solutions must reduce to the de Sitter spacetime in the static limit. Two space-times with a physically satisfactory energy-momentum tensor are investigated in detail. For the rotating incompressible fluid, it is proven that the Petrov type cannot be D. The equation of the rotation function $ω$ can be solved for the Tolman type IV fluid in terms of quadratures. It is also shown that the rotating version of the Tolman IV space-time cannot be Petrov type D.

gr-qc↗

arXiv2000

A slowly rotating perfect fluid body in an ambient vacuum

A global model of a slowly rotating perfect fluid ball in general relativity is presented. To second order in the rotation parameter, the junction surface is an ellipsoidal cylinder. The interior is given by a limiting case of the Wahlquist solution, and the vacuum region is not asymptotically flat. The impossibility of joining an asymptotically flat vacuum region has been shown in a preceding work.

gr-qc↗

arXiv2000

A Class of Einstein-Maxwell Fields Generalizing the Equilibrium Solutions

The Einstein-Maxwell fields of rotating stationary sources are represented by the SU(2,1) spinor potential $Ψ_A$ satisfying \[ \nabla \cdot [Θ^{-1}(Ψ_A\nabla Ψ_B-Ψ_B\nabla Ψ_A)]=-2Θ^{-2}\vec{C}\cdot (Ψ_A\nabla Ψ_B-Ψ_B\nabla Ψ_A) \] where $Θ=Ψ^{\dagger }\cdot Ψ$ is the SU(2,1) norm of $Ψ$% . The Ernst potentials are expressed in terms of the spinor potential by $% {\cal E}=\frac{Ψ_1-Ψ_2}{Ψ_1+Ψ_2}$, $Φ=\frac{Ψ_3}{% Ψ_1+Ψ_2}$ . The group invariant vector $\vec{C}=-2i\func{Im}\{Ψ^{\dagger}\cdot \nabla Ψ\}$ is generated exclusively by the rotation of the source, hence it is appropriate to refer to $\vec{C}$ as the {\em swirl} of the field. Static fields have no swirl. The fields with no swirl are a class generalizing the equilibrium ($| e| =m$) class of Einstein-Maxwell fields. We obtain the integrability conditions and a highly symmetrical set of field equations for this class, as well as exact solutions and an open research problem.

gr-qc↗

arXiv1999

The Wahlquist metric cannot describe an isolated rotating body

It is proven that the Wahlquist perfect fluid space-time cannot be smoothly joined to an exterior asymptotically flat vacuum region. The proof uses a power series expansion in the angular velocity, to a precision of the second order. In this approximation, the Wahlquist metric is a special case of the rotating Whittaker space-time. The exterior vacuum domain is treated in a like manner. We compute the conditions of matching at the possible boundary surface in both the interior and the vacuum domain. The conditions for matching the induced metrics and the extrinsic curvatures are mutually contradictory.

gr-qc↗

arXiv1998

A rotating incompressible perfect fluid space-time

A rigidly rotating incompressible perfect fluid solution of Einstein's gravitational equations is discussed. The Petrov type is D, and the metric admits a four-parameter isometry group. The Gaussian curvature of the constant-pressure surfaces is positive and they have two ring-shaped cusps.

gr-qc↗

arXiv1998

Spin effects in radiating compact binaries

We review and summarize our results concerning the influence of the spins of a compact binary system on the motion of the binary and on its gravitational reaction. We describe briefly our method which lead us to compute the secular changes in the post-Newtonian motion and the averaged radiative losses. Our description is valid to 1.5 post-Newtonian order. All spin-orbit and some spin-spin effects are considered which contribute at this accuracy. This approach enabled us to give both the evolutions of the constants of the nonradiative motion and of the relevant angular variables under radiation reaction.

gr-qc↗

arXiv1998

Rotating incompressible perfect fluid source of the NUT metric

A global solution of the Einstein equations is given, consisting of a perfect fluid interior and a vacuum exterior. The rigidly rotating and incompressible perfect fluid is matched along the hypersurface of vanishing pressure with the stationary part of the Taub-NUT metric. The fluid core generates a negative-mass NUT space-time. The matching procedure leaves one parameter in the global solution.

gr-qc↗

arXiv1998

Rotating perfect fluid sources of the NUT metric

Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the vacuum exterior which consists only of a stationary region of the Taub-NUT space-time. The solution of the matching conditions leaves generally three parameters in the global solution. Examples of perfect fluid sources are discussed.

gr-qc↗