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Carlos N. Kozameh

Publications and source records attributed to Carlos N. Kozameh.

At least 19 recordsLinked to original sources
arXiv2026

Ultraviolet-Finite Perturbative Expansion of Quantum Gravity at Null Infinity

We present a perturbative formulation of quantum gravity for asymptotically flat vacuum spacetimes based on the Null Surface Formulation (NSF), in which the expansion is ultraviolet-finite term by term up to the orders computed, without the need for renormalization. The outgoing Bondi shear operators are constructed explicitly up to fourth order, with interaction kernels determined recursively from on-shell gravitational data at null infinity. Ultraviolet finiteness at each order follows from the on-shell structure of the construction and the restriction of all integrations to the compact celestial sphere, eliminating off-shell propagators. The map between the in and out states admits a perturbative construction, and unitarity is verified explicitly up to fourth order. The outgoing operators satisfy the same commutation relations as the incoming ones, indicating that the transformation is canonical and consistent with the unitary implementation. Collinear configurations give rise to infrared singularities, as expected in massless quantum field theories, but do not affect the ultraviolet behavior established here. In coherent states, the expectation value of the shear reproduces the known finite classical graviton scattering at lowest nontrivial order. These results provide a perturbative framework for quantum gravity with improved ultraviolet behavior relative to the covariant approach.

hep-th↗
arXiv2025

Pfaffian Systems, Cartan Connections, and the Null Surface Formulation of General Relativity

This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of spacetime;described by the Einstein field equations;is most elegantly formulated using the Cartan calculus of differential forms. Another important subject in this discussion is the notion of conformal geometry, where the relevant invariants of a metric are characterized by Elie Cartan's normal conformal connection. The previous analysis is then used to develop the null surface formulation (NSF) of general relativity, a radical framework that postulates the structure of light cones rather than the metric itself as the fundamental gravitational variable. Defined by a central Pfaffian system, this formulation allows the entire spacetime geometry to be reconstructed from a single scalar function, $Z$, whose level surfaces are null.

gr-qc↗
arXiv2025

Quantum theory of asymptotically flat spacetimes

A quantum theory of asymptotically flat space-times is presented using the solutions of the Null Surface Formulation (NSF) field equations in a perturbative scheme. Free-field commutation relations are given for the null free data of NSF at future or past null infinity, and the main variables of NSF are then used to define the interior points of the space-time as labels and the metric of the space-time as a derived quantum operator. A non-trivial scattering of gravitons is given.

hep-th↗
arXiv2023

Final velocity and radiated energy in numerical simulations of binary black holes

The evolution of global binary black holes variables such as energy or linear momentum are mainly obtained by applying numerical methods near coalescence, post-Newtonian (PN) expansions, or a combination of both. In this paper, we use a fully relativistic formalism presented several years ago that only uses global variables defined at null infinity together with the gravitational radiation emitted by the source to obtain the time evolution of such variables for binary black holes (BBH) systems. For that, we use the Rochester catalog composed of 776 BBHs simulations. We compute the final velocity, radiated energy, and intrinsic angular momentum predicted by the dynamical equations in this formalism for nonspinning, aligned and antialigned spins, and several different precessing configurations. We compare obtained values with reported values in numerical simulations. As BBHs parameter space is still not completely covered by numerical simulations, we fit phenomenological formulas for practical applications to the radiated energy and final velocities obtained. Also, we compare the fits with reported values. In conclusion, we see that our formulae and correlations for the variables described in this work are consistent with those found in the general literature.

gr-qc↗
arXiv2021

Numerical evolution of the center of mass and angular momentum for binaries black holes

The asymptotic approach derived by Kozameh-Quiroga (K-Q) provides a modern framework to obtain the evolution of global variables of isolated sources of gravitational radiation. We test the K-Q formalism evolving the equations of motion for the center of mass, the intrinsic angular momentum, and several other global variables, for black hole binary coalescence. First we evolve the equations of motion using 777 simulations from the RIT catalogue numerical data of $ψ_4$ [J. Healy and C.O. Lousto, Third RIT binary black hole simulations catalog, Phys. Rev. D 102, 104018 (2020).]. We then analyze the trajectory of the center of mass and compute the final state of other physical variables after the coalescence has taken place. Finally, we show the results obtained from our equations of motion are consistent with those in the Rochester metadata.

gr-qc↗
arXiv2021

Fundamental residual amplitude modulation in electro-optic modulators

The residual amplitude modulation ($\mathrm{RAM}$) is the undesired, non-zero amplitude modulation that usually occurs when a phase modulation based on the electro-optic effect is imprinted on a laser beam. In this work, we show that electro-optic modulators (EOMs) that are used to generate the sidebands on the laser beam also generate a $\mathrm{RAM}$ in the optical setup. This result contradicts standard textbooks, which assume the amplitude remains unchanged in the process and should be considered as a fundamental $\mathrm{RAM}$ ($\mathrm{RAM_{F}}$) for these devices. We present a classical model for the propagation of an infrared laser with frequency $ω_{0}$ in a wedge-shaped crystal and an EOM with an RF modulating signal of frequency $Ω$. Since $Ω\ll ω_{0}$, we solve Maxwell's equations in a time-varying media via a WKB approximation and we write the electromagnetic fields in terms of quasi-plane waves. From the emerging fields of the setup, we compute the associated $\mathrm{RAM_{F}}$ and show that it depends on the phase-modulation depth $m$ and the quotient $\left(\fracΩ{ω_{0}}\right)$. The $\mathrm{RAM_{F}}$ values obtained for the EOMs used in gravitational wave detectors are presented. Finally, the cancellation of $\mathrm{RAM_{F}}$ is analyzed.

physics.ins-det↗
arXiv2016

Center of Mass and spin for isolated sources of gravitational radiation

We define the center of mass and spin of an isolated system in General Relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their Newtonian counterparts, though only variables at the null boundary of an asymptotically flat spacetime are used for their definition. We also derive equations of motion linking their time evolution to the emitted gravitational radiation. The results are then compared to other approaches. In particular one obtains unexpected similarities as well as some differences with results obtained in the Post Newtonian literature . These equations of motion should be useful when describing the radiation emitted by compact sources such as coalescing binaries capable of producing gravitational kicks, supernovas, or scattering of compact objects.

gr-qc↗
arXiv2012

Spin and Center of Mass in Axially Symmetric Einstein-Maxwell Spacetimes

We give a definition and derive the equations of motion for the center of mass and angular momentum of an axially symmetric, isolated system that emits gravitational and electromagnetic radiation. A central feature of this formulation is the use of Newman-Unti cuts at null infinity that are generated by worldlines of the spacetime. We analyze some consequences of the results and comment on the generalization of this work to general asymptotically flat spacetimes.

gr-qc↗
arXiv2005

Electromagnetic Dipole Radiation Fields, Shear-Free Congruences and Complex Center of Charge World Lines

We show that for asymptotically vanishing Maxwell fields in Minkowski space with non-vanishing total charge, one can find a unique geometric structure, a null direction field, at null infinity. From this structure a unique complex analytic world-line in complex Minkowski space that can be found and then identified as the complex center of charge. By ''sitting'' - in an imaginary sense, on this world-line both the (intrinsic) electric and magnetic dipole moments vanish. The (intrinsic) magnetic dipole moment is (in some sense) obtained from the `distance' the complex the world line is from the real space (times the charge). This point of view unifies the asymptotic treatment of the dipole moments For electromagnetic fields with vanishing magnetic dipole moments the world line is real and defines the real (ordinary center of charge). We illustrate these ideas with the Lienard-Wiechert Maxwell field. In the conclusion we discuss its generalization to general relativity where the complex center of charge world-line has its analogue in a complex center of mass allowing a definition of the spin and orbital angular momentum - the analogues of the magnetic and electric dipole moments.

gr-qc↗
arXiv2005

The Large Footprints of H-Space on Asymptotically Flat Space-Times

We show that certain structures defined on the complex four dimensional space known as H-Space have considerable relevance for its closely associated asymptotically flat real physical space-time. More specifically for every complex analytic curve on the H-space there is an asymptotically shear-free null geodesic congruence in the physical space-time. There are specific geometric structures that allow this world-line to be chosen in a unique canonical fashion giving it physical meaning and significance.

gr-qc↗
arXiv2003

On low energy quantum gravity induced effects on the propagation of light

Present models describing the interaction of quantum Maxwell and gravitational fields predict a breakdown of Lorentz invariance and a non standard dispersion relation in the semiclassical approximation. Comparison with observational data however, does not support their predictions. In this work we introduce a different set of ab initio assumptions in the canonical approach, namely that the homogeneous Maxwell equations are valid in the semiclassical approximation, and find that the resulting field equations are Lorentz invariant in the semiclassical limit. We also include a phenomenological analysis of possible effects on the propagation of light, and their dependence on energy, in a cosmological context.

gr-qc↗
arXiv2001

Astrophysical limits on quantum gravity motivated birefringence

We obtain observational upper bounds on a class of quantum gravity related birefringence effects, by analyzing the presence of linear polarization in the optical and ultraviolet spectrum of some distant sources. In the notation of Gambini and Pullin we find $χ< 10^{-3}$.

gr-qc↗
arXiv2000

Null surfaces formulation in 3D

The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One method makes explicit use of the conformal factor while the other only uses conformal information. The resulting set of equations contain the same geometrical meaning as the 4-D formulation without the technical complexities of the higher dimensional analog. A canonical family of null surfaces in this formulation, the light cone cuts of null infinity, are constructed on asymptotically flat space times and some of their kinematical aspects discussed. A particular example, which nevertheless contains most of the generic features is explicitly constructed and analyzed, revealing the behavior predicted in the full theory.

gr-qc↗
arXiv1999

A method to determine the polarization of high energy gamma-rays

A method to determine the polarization direction of a very high energy (50 MeV - 30 GeV), linearly polarized gamma ray is analyzed and discussed. We study the differential cross section for pair production and show that the only relevant piece of information comes from the reconstruction of the pair trajectory. In particular the polarization information is coded in the azimuthal distribution of the created pair. We show that the Azimuthal Ratio (AR), defined as the ratio of produced pairs parallel to the polarization vector to pairs perpendicular to this vector, yields a very practical method to determine incoming polarization. We investigate the behavior of this function for different angular resolutions of the measuring apparatus and different energies of the incoming pairs.

astro-ph↗
arXiv1999

Null Surfaces and the Bach Equations

It is shown that the integrability conditions that arise in the Null Surface Formulation (NSF) of general relativity (GR) impose a field equation on the local null surfaces which is equivalent to the vanishing of the Bach tensor. This field equation is written explicitly to second order in a perturbation expansion. The field equation is further simplified if asymptotic flatness is imposed on the underlying space-time. The resulting equation determines the global null surfaces of asymptotically flat, radiative space-times. It is also shown that the source term of this equation is constructed from the free Bondi data at future null infinity. Possible generalizations of this field equation are analyzed. In particular we include other field equations for surfaces that have already appeared in the literature which coincide with ours at a linear level. We find that the other equations do not yield null surfaces for GR.

gr-qc↗
arXiv1996

On the quantization of the Null-Surface formulation of GR

We define and discuss various quantum operators that describe the geometry of spacetime in quantum general relativity. These are obtained by combining the Null-Surface Formulation of general relativity, recently developed, with asymptotic quantization. One of the operators defined describes a ``fuzzy'' quantum light cone structure. Others, denoted ``spacetime-point operators'', characterize geometrically-defined physical points. We discuss the interpretation of these operators. This seems to suggest a picture of quantum spacetime as made of ``fuzzy'' physical points. We derive the commutation algebra of the quantum spacetime point operators in the linearization around flat space.

gr-qc↗
arXiv1996

Superselection Sectors in Asymptotic Quantization of Gravity

Using the continuity of the scalar $Ψ_2$ (the mass aspect) at null infinity through $i_o$ we show that the space of radiative solutions of general relativity can be thought of a fibered space where the value of $Ψ_2$ at $i_o$ plays the role of the base space. We also show that the restriction of the available symplectic form to each ``fiber'' is degenerate. By finding the orbit manifold of this degenerate direction we obtain the reduced phase space for the radiation data. This reduced phase space posses a global structure, i.e., it does not distinguishes between future or past null infinity. Thus, it can be used as the space of quantum gravitons. Moreover, a Hilbert space can be constructed on each ``fiber'' if an appropriate definition of scalar product is provided. Since there is no natural correspondence between the Hilbert spaces of different foliations they define superselection sectors on the space of asymptotic quantum states.

gr-qc↗