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Jiri Bicak

Publications and source records attributed to Jiri Bicak.

At least 19 recordsLinked to original sources
arXiv2023

Light Deflection in Plasma in the Hartle-Thorne Metric and in Other Axisymmetric Spacetimes with a Quadrupole Moment

The light propagation in plasma medium around stationary gravitating objects is studied in the geometrical optics limit. Static metrics with quadrupole moments are considered, however, the main attention is paid to the stationary Hartle-Thorne metric and Kerr metric. Their different effects on the light deflection are compared. The deflection angle is given in a general analytic form, the detailed calculations are performed in the weak field limits and illustrated graphically. The trajectories of the light rays are constructed and compared, emphasizing the role of the quadrupole moment.

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arXiv2023

Migrating Carrollian particles on magnetized black hole horizons

By considering a misaligned (asymptotically uniform) magnetic field in the background of a rotating black hole, we uncover a possibility for a highly non-trivial motion of Carrollian particles on the black hole horizon that is characterized by a time-dependent velocity field and reminds us (because of its latitudinal oscillations) of a 'monarch butterfly migration'.

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arXiv2022

Light propagation in a plasma on an axially symmetric and stationary spacetime: Separability of the Hamilton-Jacobi equation and shadow

The properties of light rays around compact objects surrounded by a plasma are affected by both strong gravitational fields described by a general-relativistic spacetime and by a dispersive and refractive medium, characterized by the density distribution of the plasma. We study these effects employing the relativistic Hamiltonian formalism under the assumption of stationarity and axisymmetry. The necessary and sufficient conditions on the metric and on the plasma frequency are formulated, such that the rays can be analytically determined from a fully separated Hamilton-Jacobi equation. We demonstrate how these results allow to analytically calculate the photon region and the shadow, if they exist. Several specific examples are discussed in detail: the "hairy" Kerr black holes, the Hartle-Thorne spacetime metrics, the Melvin universe, and the Teo rotating traversable wormhole. In all of these cases a plasma medium is present as well.

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arXiv2021

Quantum Detection of Conicity

We investigate the sensitivity of an Unruh-DeWitt detector to the global features of a deficit angle that are otherwise classically inaccessible. Specifically, we consider a detector placed inside an infinite thin hollow cylinder whose spacetime is everywhere flat but outside of which the spacetime has a deficit angle and study its response to a scalar field to which it couples. We find that the response of the detector is sensitive to the deficit angle, despite the fact that it does not interact with the cylinder.

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arXiv2021

Quantum Detection of Inertial Frame Dragging

A relativistic theory of gravity like general relativity produces phenomena differing fundamentally from Newton's theory. An example, analogous to electromagnetic induction, is gravitomagnetism, or the dragging of inertial frames by mass-energy currents. These effects have recently been confirmed by classical observations. Here we show, for the first time, that they can be observed by a quantum detector. We study the response function of Unruh De-Witt detectors placed in a slowly rotating shell. We show that the response function picks up the presence of rotation even though the spacetime inside the shell is flat and the detector is locally inertial. The detector can distinguish between the static situation when the shell is non-rotating and the stationary case when the shell rotates and the dragging of inertial frames, i.e. gravitomagnetic effects, arise. Moreover, it can do so when the detector is switched on for a finite time interval within which a light signal cannot travel to the shell and back to convey the presence of rotation.

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arXiv2020

Quantum Distinction of Inertial Frames: Local vs. Global

We study the response function of Unruh-deWitt detectors placed in a flat spacetime inside a thin matter shell. We show that the response function distinguishes between the local and global (Minkowski) inertial frames and picks up the presence of the shell even when the detector is switched on for a finite time interval within which a light signal cannot travel to the shell and back as required by a classical measurement. We also analyze how the response of the detector depends on its location within the shell.

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arXiv2011

Centrifugal force induced by relativistically rotating spheroids and cylinders

Starting from the gravitational potential of a Newtonian spheroidal shell we discuss electrically charged rotating prolate spheroidal shells in the Maxwell theory. In particular we consider two confocal charged shells which rotate oppositely in such a way that there is no magnetic field outside the outer shell. In the Einstein theory we solve the Ernst equations in the region where the long prolate spheroids are almost cylindrical; in equatorial regions the exact Lewis "rotating cylindrical" solution is so derived by a limiting procedure from a spatially bound system. In the second part we analyze two cylindrical shells rotating in opposite directions in such a way that the static Levi-Civita metric is produced outside and no angular momentum flux escapes to infinity. The rotation of the local inertial frames in flat space inside the inner cylinder is thus exhibited without any approximation or interpretational difficulties within this model. A test particle within the inner cylinder kept at rest with respect to axes that do not rotate as seen from infinity experiences a centrifugal force. Although the spacetime there is Minkowskian out to the inner cylinder nevertheless that space has been induced to rotate, so relative to the local inertial frame the particle is traversing a circular orbit.

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arXiv2010

Rotating charged black holes accelerated by an electric field

The Ernst method of removing nodal singularities from the charged C-metric representing uniformly accelerated black holes with mass $m$, charge $q$ and acceleration $A$ by "adding" an electric field $E$ is generalized. Utilizing the new form of the C-metric found recently, Ernst's simple "equilibrium" condition $mA=qE$ valid for small accelerations is generalized for arbitrary $A$. The nodal singularity is removed also in the case of accelerating and rotating charged black holes, and the corresponding equilibrium condition is determined.

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arXiv2010

Post-Minkowskian closed-form Hamiltonian for gravitating N-body systems

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.

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arXiv2010

Classical limits of boost-rotation symmetric spacetimes

Boost-rotation symmetric spacetimes are exceptional as they are the only exact asymptotically flat solutions to the Einstein equations describing spatially bounded sources ("point-like" particles, black holes) undergoing non-trivial motion ("uniform acceleration") with radiation. We construct the Newtonian limit of these spacetimes: it yields fields of uniformly accelerated sources in classical mechanics. We also study the special-relativistic limit of the charged rotating C-metric and so find accelerating electromagnetic magic field.

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arXiv2009

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the "magic field" of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr-Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the "accelerating magic field" represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born's solution for two uniformly accelerated monopole charges.

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arXiv2009

The Newtonian limit of spacetimes for accelerated particles and black holes

Solutions of vacuum Einstein's field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor-Swaminarayan solutions, self-accelerating "dipole particles", and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes.

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arXiv2008

Inertial frame rotation induced by rotating gravitational waves

We calculate the rotation of the inertial frames within an almost flat cylindrical region surrounded by a pulse of non-axially-symmetric gravitational waves that rotate about the axis of our cylindrical polar coordinates. Our spacetime has only one Killing vector. It is along the z-axis and hypersurface orthogonal. We solve the Einstein equations to first order in the wave amplitude and superpose such linearized solutions to form a wave pulse. We then solve the relevant Einstein equation to second order in the amplitude to find the rotation of inertial frames produced by the pulse. The rotation is without time delay. The influence of gravitational wave angular momentum on the inertial frame demonstrates that Mach's principle can not be expressed in terms of the influence of the stress-energy-momentum tensor alone but must involve also influences of gravitational wave energy and angular momentum.

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arXiv2008

Gravitational waves and dragging effects

Linear and rotational dragging effects of gravitational waves on local inertial frames are studied in purely vacuum spacetimes. First the linear dragging caused by a simple cylindrical pulse is investigated. Surprisingly strong transversal effects of the pulse are exhibited. The angular momentum in cylindrically symmetric spacetimes is then defined and confronted with some results in literature. In the main part, the general procedure is developed for studying weak gravitational waves with translational but not axial symmetry which can carry angular momentum. After a suitable averaging the rotation of local inertial frames due to such rotating waves can be calculated explicitly and illustrated graphically. This is done in detail in the accompanying paper. Finally, the rotational dragging is given for strong cylindrical waves interacting with a rotating cosmic string with a small angular momentum.

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arXiv2008

Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.

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arXiv2008

Cosmological perturbation theory, instantaneous gauges and local inertial frames

Linear perturbations of Friedmann-Robertson-Walker universes with any curvature and cosmological constant are studied in a general gauge without decomposition into harmonics. Desirable gauges are selected as those which embody best Mach's principle: in these gauges local inertial frames can be determined instantaneously via the perturbed Einstein field equations from the distributions of energy and momentum in the universe. The inertial frames are identified by their `accelerations and rotations' with respect to the cosmological frames associated with the `Machian gauges'. In closed spherical universes, integral gauge conditions are imposed to eliminate motions generated by the conformal Killing vectors. The meaning of Traschen's integral constraint vectors is thus elucidated. For all three types of FRW universes the Machian gauges admit much less residual freedom than the synchronous or generalized harmonic gauge. Mach's principle is best exhibited in the Machian gauges in closed spherical universes. Independent of any Machian motivation the general perturbation equations and discussion of gauges are useful for cosmological perturbation theory.

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arXiv2008

Helical Symmetry in Linear Systems

We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman--Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.

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