arXiv subjects

J. L. Jaramillo

Publications and source records attributed to J. L. Jaramillo.

At least 19 recordsLinked to original sources

arXiv2012

Towards a cross-correlation approach to strong-field dynamics in Black Hole spacetimes

The qualitative and quantitative understanding of near-horizon gravitational dynamics in the strong-field regime represents a challenge both at a fundamental level and in astrophysical applications. Recent advances in numerical relativity and in the geometric characterization of black hole horizons open new conceptual and technical avenues into the problem. We discuss here a research methodology in which spacetime dynamics is probed through the cross-correlation of geometric quantities constructed on the black hole horizon and on null infinity. These two hypersurfaces respond to evolving gravitational fields in the bulk, providing canonical "test screens" in a "scattering"-like perspective onto spacetime dynamics. More specifically, we adopt a 3+1 Initial Value Problem approach to the construction of generic spacetimes and discuss the role and properties of dynamical trapping horizons as canonical inner "screens" in this context. We apply these ideas and techniques to the study of the recoil dynamics in post-merger binary black holes, an important issue in supermassive galactic black hole mergers.

gr-qc↗

arXiv2010

Pseudospectral Collocation Methods for the Computation of the Self-Force on a Charged Particle: Generic Orbits around a Schwarzschild Black Hole

[abridged] The inspiral of a stellar compact object into a massive black hole is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of these slowly inspiraling systems. To that end, the use of very precise theoretical waveform templates in the data analysis is required. To build them we need to have a deep understanding of the gravitational backreaction mechanism responsible for the inspiral. The self-force approach describes the inspiral as the action of a local force that can be obtained from the regularization of the perturbations created by the stellar compact object on the massive black hole geometry. In this paper we extend a new time-domain technique for the computation of the self-force from the circular case to the case of eccentric orbits around a non-rotating black hole. The main idea behind our scheme is to use a multidomain framework in which the small compact object, described as a particle, is located at the interface between two subdomains. Then, the equations at each subdomain are homogeneous wave-type equations, without distributional sources. In this particle-without-particle formulation, the solution of the equations is smooth enough to provide good convergence properties for the numerical computations. This formulation is implemented by using a pseudospectral collocation method for the spatial discretization, combined with a Runge Kutta algorithm for the time evolution. We present results from several simulations of eccentric orbits in the case of a scalar charged particle around a Schwarzschild black hole. In particular, we show the convergence of the method and its ability to resolve the field and its derivatives across the particle location. Finally, we provide numerical values of the self-force for different orbital parameters.

gr-qc↗

arXiv2010

Mass and Angular Momentum in General Relativity

We present an introduction to mass and angular momentum in General Relativity. After briefly reviewing energy-momentum for matter fields, first in the flat Minkowski case (Special Relativity) and then in curved spacetimes with or without symmetries, we focus on the discussion of energy-momentum for the gravitational field. We illustrate the difficulties rooted in the Equivalence Principle for defining a local energy-momentum density for the gravitational field. This leads to the understanding of gravitational energy-momentum and angular momentum as non-local observables that make sense, at best, for extended domains of spacetime. After introducing Komar quantities associated with spacetime symmetries, it is shown how total energy-momentum can be unambiguously defined for isolated systems, providing fundamental tests for the internal consistency of General Relativity as well as setting the conceptual basis for the understanding of energy loss by gravitational radiation. Finally, several attempts to formulate quasi-local notions of mass and angular momentum associated with extended but finite spacetime domains are presented, together with some illustrations of the relations between total and quasi-local quantities in the particular context of black hole spacetimes. This article is not intended to be a rigorous and exhaustive review of the subject, but rather an invitation to the topic for non-experts. In this sense we follow essentially the expositions in Szabados 2004, Gourgoulhon 2007, Poisson 2004 and Wald 84, and refer the reader interested in further developments to the existing literature, in particular to the excellent and comprehensive review by Szabados (2004).

gr-qc↗

arXiv2008

Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations

Bonazzola, Gourgoulhon, Grandclément, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic system. We have carried out a preliminary analysis of the mathematical structure of that system, in particular focusing on the equations governing the evolution for the deviation of a conformal metric from a flat fiducial one. The choice of a Dirac's gauge for the spatial coordinates guarantees the mathematical characterization of that system as a (strongly) hyperbolic system of conservation laws. In the presence of boundaries, this characterization also depends on the boundary conditions for the shift vector in the elliptic subsystem. This interplay between the hyperbolic and elliptic parts of the complete evolution system is used to assess the prescription of inner boundary conditions for the hyperbolic part when using an excision approach to black hole spacetime evolutions.

gr-qc↗

arXiv2008

From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.

gr-qc↗

arXiv2007

A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.

gr-qc↗

arXiv2007

Trapping Horizons as inner boundary conditions for black hole spacetimes

We present a set of inner boundary conditions for the numerical construction of dynamical black hole space-times, when employing a 3+1 constrained evolution scheme and an excision technique. These inner boundary conditions are heuristically motivated by the dynamical trapping horizon framework and are enforced in an elliptic subsystem of the full Einstein equation. In the stationary limit they reduce to existing isolated horizon boundary conditions. A characteristic analysis completes the discussion of inner boundary conditions for the radiative modes.

gr-qc↗

arXiv2006

Numerical implementation of isolated horizon boundary conditions

We study the numerical implementation of a set of boundary conditions derived from the isolated horizon formalism, and which characterize a black hole whose horizon is in quasi-equilibrium. More precisely, we enforce these geometrical prescriptions as inner boundary conditions on an excised sphere, in the numerical resolution of the Conformal Thin Sandwich equations. As main results, we firstly establish the consistency of including in the set of boundary conditions a "constant surface gravity" prescription, interpretable as a lapse boundary condition, and secondly we assess how the prescriptions presented recently by Dain et al. for guaranteeing the well-posedness of the Conformal Transverse Traceless equations with quasi-equilibrium horizon conditions extend to the Conformal Thin Sandwich elliptic system. As a consequence of the latter analysis, we discuss the freedom of prescribing the expansion associated with the ingoing null normal at the horizon.

gr-qc↗

arXiv2005

A 3+1 perspective on null hypersurfaces and isolated horizons

The isolated horizon formalism recently introduced by Ashtekar et al. aims at providing a quasi-local concept of a black hole in equilibrium in an otherwise possibly dynamical spacetime. In this formalism, a hierarchy of geometrical structures is constructed on a null hypersurface. On the other side, the 3+1 formulation of general relativity provides a powerful setting for studying the spacetime dynamics, in particular gravitational radiation from black hole systems. Here we revisit the kinematics and dynamics of null hypersurfaces by making use of some 3+1 slicing of spacetime. In particular, the additional structures induced on null hypersurfaces by the 3+1 slicing permit a natural extension to the full spacetime of geometrical quantities defined on the null hypersurface. This 4-dimensional point of view facilitates the link between the null and spatial geometries. We proceed by reformulating the isolated horizon structure in this framework. We also reformulate previous works, such as Damour's black hole mechanics, and make the link with a previous 3+1 approach of black hole horizon, namely the membrane paradigm. We explicit all geometrical objects in terms of 3+1 quantities, putting a special emphasis on the conformal 3+1 formulation. This is in particular relevant for the initial data problem of black hole spacetimes for numerical relativity. Illustrative examples are provided by considering various slicings of Schwarzschild and Kerr spacetimes.

gr-qc↗

arXiv2004

Inner boundary conditions for black hole Initial Data derived from Isolated Horizons

We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable standard parameters of the Conformal Thin Sandwich formulation. These conditions altogether are sufficient for the construction of a horizon that is instantaneously in equilibrium in the sense of the Isolated Horizons formalism. We then investigate the application of these conditions to the Initial Data Problem of binary black holes and discuss the relation of our analysis with other proposals that exist in the literature.

gr-qc↗

arXiv2003

Group-cohomology refinement to classify $G$-symplectic manifolds

``Pseudo-cohomology'', as a refinement of Lie group cohomology, is soundly studied aiming at classifying of the symplectic manifolds associated with Lie groups. In this study, the framework of symplectic cohomology provides fundamental new insight, which enriches the analysis previously developed in the setting of Cartan-Eilenberg $H^2(G,U(1))$ cohomology.

math-ph↗

arXiv2002

Revisited gauge principle: towards a unification of space-time and internal gauge interactions

The minimal coupling principle is revisited under the quantum perspectives of the space-time symmetry. This revision is better realized on a Group Approach to Quantization (GAQ) where group cohomology and extensions of groups play a preponderant role. We firstly consider the case of the electromagnetic potential; the Galilei and/or Poincare group is (non-centrally) extended by the "local" U(1) group. This group can also be seen as a central extension, parametrized by both the mass and the electric charge, of an infinite-dimensional group, on which GAQ leads to the dynamics of a particle moving in the presence of an electromagnetic field. Then we try the gravitational interaction of a particle by turning into "local" the space-time translations. However, promoting to "local" the space-time subgroup of the true symmetry of the quantum free relativistic particle, i.e. the centrally extended by U(1) Poincare group, results in a new electromagnetic-like force of pure gravitational origin. This is a consequence of the space-time translations not being an invariant subgroup of the extended Poincare group and constitutes a preliminary attempt to a non-trivial mixing of space-time and internal gauge interactions.

math-ph↗

arXiv2002

New insights in particle dynamics from group cohomology

The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a group which is obtained from a centrally extended kinematical group (Poincare or Galilei) by making local some subgroup. The corresponding dynamics is generated by a vector field inside the kernel of a presymplectic form which is derived from the canonical left-invariant one-form on the extended group. A non-relativistic limit is derived from the geodesic motion via an Inonu-Wigner contraction. A deeper analysis of the cohomological structure reveals the possibility of a new force associated with a non-trivial mixing of gravity and electromagnetism leading to in principle testable predictions.

hep-th↗

arXiv2002

Extended diffeomorphism algebras in (quantum) gravitational physics

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is characterized by the fundamental role assigned to a basic underlying symmetry. The developed mathematical formalism makes contact with the relevant gravitational notions by means of the addition of some extra structure. The specific manners in which this is accomplished, together with their corresponding physical interpretation, lead to different gravitational models. Distinct strategies are in fact briefly outlined, showing the versatility of the present conceptual framework.

gr-qc↗

arXiv2002

Space-time dynamics from algebra representations

We present a model for introducing dynamics into a space-time geometry. This space-time structure is constructed from a C*-algebra defined in terms of the generators of an irreducible unitary representation of a finite-dimensional Lie algebra G. This algebra is included as a subalgebra in a bigger algebra F, the generators of which mix the representations of G in a way that relates different space-times and creates the dynamics. This construction can be considered eventually as a model for 2-D quantum gravity.

gr-qc↗

arXiv2002

An effective quantum mechanism for mass generation in diffeomorphism-invariant theories

We propose a scenario for particle-mass generation, assuming the existence of a physical regime where, firstly, physical particles can be considered as point-like objects moving in a background space-time and, secondly, their mere presence spoils the invariance under the local diffeomorphism group, resulting in an anomalous realization of the latter. Under these hypotheses, we describe mass generation starting from the massless free theory. The mechanism is not sensitive to the detailed description of the underlying theory at higher energies, leaning only on general structural features of it, specifically diffeomorphism invariance.

hep-th↗

arXiv2000

A first analysis regarding matter-dynamical diffeomorphism coupling

A first attempt at adding matter degrees of freedom to the two-dimensional ``vacuum'' gravity model presented in gr-qc/9907071 is analyzed in this paper. Just as in the previous pure gravity case, quantum diffeomorphism operators (constructed from a Virasoro algebra) possess a dynamical content; their gauge nature is recovered only after the classical limit. Emphasis is placed on the new physical modes modelled on a SU(1,1)-Kac-Moody algebra. The non-trivial coupling to ``gravity'' is a consequence of the natural semi-direct structure of the entire extended algebra. A representation associated with the discrete series of the rigid SU(1,1) is revisited in the light of previously neglected crucial global features which imply the appearance of an SU(1,1)-Kac-Moody fusion rule, determining the rather entangled quantum structure of the physical system. In the classical limit, an action which explicitly couples gravity and matter modes governs the dynamics.

gr-qc↗

arXiv2000

Dynamical content of quantum diffeomorphisms in two-dimensional quantum gravity

A model for 2D-quantum gravity from the Virasoro symmetry is studied. The notion of space-time naturally arises as a homogeneous space associated with the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the Lie-algebra central extension for the critical values of the conformal anomaly. The rest of the generators in the group, L_n (n>1, n<-1), mix space-times with different constant curvature. Only in the classical limit all space-times can be identified, defining a unique Minkowski space-time, and the operators L_n (n<1, n<-1) gauged away. This process entails a restriction to SL(2,R) subrepresentations, which creates a non-trivial two-dimensional symplectic classical phase space. The present model thus suggests that the role of general covariance in quantum gravity is different from that played in the classical limit.

gr-qc↗