Observables from modified dispersion relations on curved spacetimes:circular orbits, redshift and lateshift
Christian Pfeifer
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Contribution to the Proceedings, 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (MG15)
The Hamiltonian formulation of modified dispersion relations (MDRs) allows for their implementation on generic curved spacetimes. In turn it is possible to derive phenomenological effects. I will present how to construct the kappa-Poincare dispersion relation on curved spacetimes, its spherically symmetric realizations, among them the kappa deformation of Schwarzschild spacetime, and its implementation on Friedmann-Lemaitre-Robertson-Walker spacetimes with arbitrary scale factor. In addition we will construct the general first order modifications of the general relativistic dispersion relation. Afterwards we will use the perturbative MDRs to calculate specific observables such as the redshift, lateshift and photon circular orbits.
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of circularly polarized beams of radiation. As a result, polarized light rays are still null but not geodesic curves. To achieve these results we construct null frames associated with a set of (non-geodesic) null rays and use these frames for description of the high-frequency wave propagation. We call this approach spin optics approximation. It is completely co…
We study the geometrical-optics expansion for circularly-polarized electromagnetic waves propagating on a curved spacetime in general relativity. We show that higher-order corrections to the Faraday and stress-energy tensors may be found via a system of transport equations, in principle. At sub-leading order, the stress-energy tensor possesses terms proportional to the wavelength whose sign depends on the handedness of the circular polarization. Due to such terms, the direction of energy flow is not aligned with the gradient of the eikonal phase, in general, and the wave may carry a transverse…
We extend complete complementarity relations to curved spacetimes by considering a succession of infinitesimal local Lorentz transformations, which implies that complementarity remains valid as the quanton travels through its world line and the complementarity aspects in different points of spacetime are connected. This result allows the study of these different complementary aspects of a quantum system as it travels through spacetime. In particular, we study the behavior of these different complementary properties of massive spin-$1/2$ particles in the Schwarzschild spacetime. For geodetic ci…
The scalar radiation emitted by a source in geodesic circular orbit around a regular Bardeen black hole is analyzed. We use the quantum field theory in curved spacetime framework to obtain the emitted power of radiation by computing the one-particle emission amplitude of scalar particles in the curved background. We compare our results to a similar setting in the spacetime of a Reissner-Nordström black hole.
We use our previously developed identification of dispersion relations with Hamilton functions on phase space to locally implement the $κ$-Poincaré dispersion relation in the momentum spaces at each point of a generic curved spacetime. We use this general construction to build the most general Hamiltonian compatible with spherical symmetry and the Plank-scale-deformed one such that in the local frame it reproduces the $κ$-Poincaré dispersion relation. Specializing to Planck-scale-deformed Schwarzschild geometry, we find that the photon sphere around a black hole becomes a thick shell since pho…
In this work, we derive two formulas encoding the polarization direction and luminosity of synchrotron radiations from the moving electrons in curved spacetime under the geometric optics approximation. As an application, we further study the polarized images of synchrotron radiations from electron sources in Schwarzschild black hole spacetime with a vertical and uniform magnetic field. In particular, by focusing on the circular orbits of electrons on the equatorial plane, we show the polarized images of the synchrotron radiations from these orbits for different observational angles and discuss…
It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, F --> F cos θ + *F sin θ. These transformations are indeed a symmetry of the theory in Noether sense. The associated constant of motion is the difference in the intensity between self- and anti-self dual components of the electromagnetic field or, equivalently, the difference between the right and left circularly polarized components. This conservation law holds even if the electromagnetic field interacts with an arbitrary classical gravitational background. After re-examining these…
The physical and mathematical properties of the non-linearly coupled black-hole-orbiting-ring system are studied analytically to second order in the dimensionless angular velocity $M_{\text{ir}}ω_{\text{H}}$ of the black-hole horizon (here $M_{\text{ir}}$ is the irreducible mass of the slowly rotating central black hole). In particular, we determine analytically, to first order in the dimensionless ring-to-black-hole mass ratio $m/M_{\text{ir}}$, the shift $ΔΩ_{\text{mb}}/Ω_{\text{mb}}$ in the orbital frequency of the {\it marginally bound} circular geodesic that characterizes the composed cur…
The (1, 0)+(0, 1) representation of the group SL(2, C) provides a six-component spinor equivalent to the electromagnetic field tensor. By means of the (1, 0)+(0, 1) description, one can treat the photon field in curved spacetime via spin connection and the tetrad formalism, which is of great advantage to study the gravitational spin-orbit coupling of photons. Once the gravitational spin-orbit coupling is taken into account, the traditional radius of the circular photon orbit in the Schwarzschild geometry should be replaced with two different radiuses corresponding to the photons with the helic…
Circular massless cosmic strings which move with the speed of light in the de Sitter universe are described. Construction of the background geometry is based on parabolic isometries of the de Sitter spacetime. Microscopic circular cosmic strings may appear at the Planck epoch and then grow up to the Hubble size. We analyze: images of the strings, influence of strings on trajectories of matter, formation of overdensities, and shifts of energies of photons. These effects allow one to discriminate massless strings from their massive cousins. The present work extends our results on straight massle…
We analyze the gravitational radiation emitted from a particle in circular motion around a Schwarzschild black hole using the framework of quantum field theory in curved spacetime at tree level. The gravitational perturbations are written in a gauge-invariant formalism for spherically symmetric spacetimes. We discuss the results, comparing them to the radiation emitted by a particle when it is assumed to be orbiting a massive object due to a Newtonian force in flat spacetime.
The worldline of a spinning test body moving in curved spacetime can be provided by the Mathisson-Papapetrou-Dixon (MPD) equations when its centroid, i.e. its center of mass, is fixed by a Spin Supplementary Condition (SSC). In the present study, we continue the exploration of shifts between different centroids started in a recently published work [ Phys. Rev. D 104, 024042 (2021)], henceforth Paper I, for the Schwarzschild spacetime, by examining the frequencies of circular equatorial orbits under a change of the SSC in the Kerr spacetime. In particular, we examine the convergence in the term…
Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole
