Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/0112062

Pair of null gravitating shells III. Algebra of Dirac's observables

I. Kouletsis·P. Hajicek
View original source ↗Read source document ↗Export metadata ↓

Abstract

The study of the two-shell system started in ``Pair of null gravitating shells I and II'' (gr-qc/0112060--061) is continued. The pull back of the Liouville form to the constraint surface, which contains complete information about the Poisson brackets of Dirac observables, is computed in the singular double-null Eddington-Finkelstein (DNEF) gauge. The resulting formula shows that the variables conjugate to the Schwarzschild masses of the intershell spacetimes are simple combinations of the values of the DNEF coordinates on these spacetimes at the shells. The formula is valid for any number of in- and out-going shells. After applying it to the two-shell system, the symplectic form is calculated for each component of the physical phase space; regular coordinates are found, defining it as a symplectic manifold. The symplectic transformation between the initial and final values of observables for the shell-crossing case is written down.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

I. Kouletsis, P. Hajicek. 2001-12-28. Pair of null gravitating shells III. Algebra of Dirac's observables. https://doi.org/10.1088/0264-9381%2F19%2F10%2F304

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Photon propagation and black hole imaging in Kruglov nonlinear electrodynamics

Nonlinear electrodynamics (NLED) modifies photon propagation through an effective optical geometry, allowing optical phenomena to deviate from those predicted solely by the underlying spacetime metric. In this work, we revisit the Kruglov model, which generalizes Born--Infeld electrodynamics, and investigate the corresponding null geodesics in theeffective geometry through direct numerical integration, without relying on strong-field analytical approximations. We analyze the resulting photon spheres, gravitational lensing, black-hole shadows, and thin accretion-disk images, together with their dependence on the parameter $q$. For sufficiently small positive $q$, the effective angular metric develops a pole that generates stable photon orbits outside the event horizon and locally reverses the azimuthal evolution of photon trajectories, producing a distinctive bending pattern that resembles, although does not originate from, frame dragging. Conversely, negative $q$ introduces a zero of the effective correction factor, which acts as a turning point for photon trajectories and prevents them from entering the region where the background metric becomes complex. It produces measurable changes in light deflection, shadow radius, photon-ring morphology, and relativistic images. In particular, smaller positive values of $q$ produce thinner photon rings and enlarged shadow radii, whereas negative values generally lead to broader photon rings and smaller shadows. Comparison with the current Event Horizon Telescope constraints on Sgr~A* shows that a substantial region of the Kruglov parameter space remains compatible with present observations.

gr-qc↗
arXiv2026

Parity-dependent wave absorption and optical characteristics of a cored magnetic black hole

We study light propagation and coupled gravitational--electromagnetic waves around a black hole supported by a nonlinear magnetic field. The same field action fixes the geometry, the mass--charge relation, and the wave potentials. We calculate two critical impact parameters for light and solve the coupled scattering equations in both parity sectors. In eight solutions of one action, the two optical scales differ by $3.6$--$7.2\%$. The wave absorption also depends on parity. For $\ell=2$, the gap between the larger absorption eigenvalues reaches about $9.0$ percentage points. A wider frequency scan reveals a stronger effect in the second eigenchannel. The difference between the two absorption traces reaches $24.3$ percentage points. The trace equals twice the absorption of an equal incoherent mixture of incoming gravitational and electromagnetic fields. A controlled test of the wave operator shows that the nonlinear electromagnetic factor $κ$ plays an important role in the parity gap. We also examine four $\ell=3$ cases and use charge-matched Reissner--Nordström black holes as a separate control. The optical and wave calculations provide two complementary properties of the same magnetic source.

gr-qc↗
arXiv2026

Perturbative dynamics and relativistic effects of a dyonic Kalb-Ramond black hole

We investigate perturbative dynamics, tidal effects, and relativistic frequency shifts in a dyonic Kalb-Ramond black hole generated by a Lorentz-violating antisymmetric tensor background. The geometry is controlled by the mass $M$, the electric charge $Q$, the magnetic charge $p$, and the Lorentz-violating parameter $\ell$, with the dyonic sector entering through the effective combination $P_{\ell}^{2}=Q^{2}/(1-\ell)^{2}+p^{2}/(1-2\ell)$. First, we analyze the gravitational Doppler effect for radial signal exchange between freely falling and static observers, showing how the dyonic charges weaken the redshift by shifting the frequency ratio toward unity. We then compute the radial and angular tidal forces in a freely falling frame and determine the characteristic radii at which the usual stretching and compression patterns are reversed. The gravitational time delay is also evaluated for null trajectories, showing that the electric and magnetic sectors reduce the delay relative to the reference configuration. In the perturbative sector, we study massless scalar, vector, and spinor test fields together with an effective axial metric model, computing sixth-order WKB spectra and independently checking selected modes using the asymptotic iteration method. At fixed mass and charges, increasing the Lorentz-violating parameter raises the tabulated oscillation frequencies and damping rates in the original time coordinate; their interpretation accounts for time normalization and changes in effective parameters. The independent comparisons support the tested higher-multipole fundamental modes. Time-domain evolutions exhibit damped ringdown followed by power-law tails, whose exponents are estimated through fits incorporating finite time corrections and numerical sensitivity checks.

gr-qc↗