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José Luis Jaramillo

Publications and source records attributed to José Luis Jaramillo.

At least 37 records · Page 2Linked to original sources
arXiv2016

A perspective on Black Hole Horizons from the Quantum Charged Particle

Black hole apparent horizons possess a natural notion of stability, whose spectral characterization can be related to the problem of the stationary quantum charged particle. Such mathematical relation leads to an "analyticity conjecture" on the dependence of the spectral properties on a complex "fine-structure-constant" parameter, that can reduce the study of the spectrum of the (non-selfadjoint) MOTS-stability operator to that of the (selfadjoint) Hamiltonian of the quantum charged particle. Moreover, this perspective might open an avenue to the spinorial treatment of apparent horizon (MOTS-)stability and to the introduction of semiclassical tools to explore some of the qualitative aspects of this black hole spectral problem.

gr-qc↗
arXiv2016

An Ocean Drum: quasi-geostrophic energetics from a Riemann geometry perspective

We revisit the discussion of the energetics of quasi-geostrophic flows from a geometric perspective based on the introduction of an effective metric, built in terms of the flow stratification and the Coriolis parameter. In particular, an appropriate notion of normal modes is defined through a spectral geometry problem in the ocean basin (a compact manifold with boundary) for the associated Laplace-Beltrami scalar operator. This spectral problem can be used to systematically encode non-local aspects of stratification and topography. As examples of applications we revisit the isotropy assumption in geostrophic turbulence, identify (a patch of) the hyperbolic space $\mathbb{H}^3$ as the leading-order term in the effective geometry for the deep mesoscale ocean and, finally, discuss some diagnostic tools based on a simple statistical mechanics toy-model to be used in numerical simulations and/or observations of quasi-geostrophic flows.

physics.flu-dyn↗
arXiv2014

Black hole horizons and quantum charged particles

We point out a structural similarity between the characterization of black hole apparent horizons as stable marginally outer trapped surfaces (MOTS) and the quantum description of a non-relativistic charged particle moving in given magnetic and electric fields on a closed surface. Specifically, the spectral problem of the MOTS-stability operator corresponds to a stationary quantum particle with a formal fine-structure constant $α$ of negative sign. We discuss how such analogy enriches both problems, illustrating this with the insights into the MOTS-spectral problem gained from the analysis of the spectrum of the quantum charged particle Hamiltonian.

gr-qc↗
arXiv2014

A Young-Laplace law for black hole horizons

Black hole horizon sections, modelled as marginally outer trapped surfaces (MOTS), possess a notion of stability admitting a spectral characterization. Specifically, the "principal eigenvalue" λ_o of the MOTS-stability operator (an elliptic operator on horizon sections) must be non-negative. We discuss the expression of λ_o for axisymmetric stationary black hole horizons and show that, remarkably, it presents the form of the Young-Laplace law for soap bubbles in equilibrium, if λ_o is identified with a formal pressure difference between the inner and outer sides of the "bubble". In this view, that endorses the existing fluid analogies for black hole horizons, MOTS-stability is interpreted as a consequence of a pressure increase in the black hole trapped region.

gr-qc↗
arXiv2014

An excision scheme for black holes in constrained evolution formulations: spherically symmetric case

Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead appropriate boundary conditions at the excised surface. In this work we present recent developments of this technique in the case of constrained formulations of Einstein equations and for spherically symmetric spacetimes. We present a new set of boundary conditions to apply to the elliptic system in the fully-constrained formalism of Bonazzola et al. (2004), at an arbitrary coordinate sphere inside the apparent horizon. Analytical properties of this system of boundary conditions are studied and, under some assumptions, an exponential convergence toward the stationary solution is exhibited for the vacuum spacetime. This is verified in numerical examples, together with the applicability in the case of the accretion of a scalar field onto a Schwarzschild black hole. We also present the successful use of the excision technique in the collapse of a neutron star to a black hole, when excision is switched on during the simulation, after the formation of the apparent horizon. This allows the accretion of matter remaining outside the excision surface and for the stable long-term evolution of the newly formed black hole.

gr-qc↗
arXiv2012

A note on degeneracy, marginal stability and extremality of black hole horizons

Given a stationary axisymmetric black hole horizon admitting a section characterised as a strictly future stable marginally outer trapped surface, we extend the equivalence between the notions of horizon degeneracy and marginal stability to the fulfillment, under the dominant energy condition, of the A=8π|J| geometric relation between the area $A$ and the angular momentum J of a horizon section.

gr-qc↗
arXiv2012

Black-hole horizons as probes of black-hole dynamics I: post-merger recoil in head-on collisions

The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging prob- lem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black- hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [1] with Robinson- Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3 + 1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on collision of nonspinning black holes and demonstrate its validity to track the qualita- tive aspects of recoil dynamics at infinity. We also make contact with the suggestion that the antikick can be described in terms of a "slowness parameter" and how this can be computed from the local properties of the horizon. In a companion paper [2] we will further elaborate on the geometric aspects of this approach and on its relation with other approaches to characterize dynamical properties of black-hole horizons.

gr-qc↗
arXiv2012

Black-hole horizons as probes of black-hole dynamics II: geometrical insights

In a companion paper [1], we have presented a cross-correlation approach to near-horizon physics in which bulk dynamics is probed through the correlation of quantities defined at inner and outer spacetime hypersurfaces acting as test screens. More specifically, dynamical horizons provide appropriate inner screens in a 3+1 setting and, in this context, we have shown that an effective-curvature vector measured at the common horizon produced in a head-on collision merger can be correlated with the flux of linear Bondi-momentum at null infinity. In this paper we provide a more sound geometric basis to this picture. First, we show that a rigidity property of dynamical horizons, namely foliation uniqueness, leads to a preferred class of null tetrads and Weyl scalars on these hypersurfaces. Second, we identify a heuristic horizon news-like function, depending only on the geometry of spatial sections of the horizon. Fluxes constructed from this function offer refined geometric quantities to be correlated with Bondi fluxes at infinity, as well as a contact with the discussion of quasi-local 4-momentum on dynamical horizons. Third, we highlight the importance of tracking the internal horizon dual to the apparent horizon in spatial 3-slices when integrating fluxes along the horizon. Finally, we discuss the link between the dissipation of the non-stationary part of the horizon's geometry with the viscous-fluid analogy for black holes, introducing a geometric prescription for a "slowness parameter" in black-hole recoil dynamics.

gr-qc↗
arXiv2012

Area inequalities for stable marginally trapped surfaces

We discuss a family of inequalities involving the area, angular momentum and charges of stably outermost marginally trapped surfaces in generic non-vacuum dynamical spacetimes, with non-negative cosmological constant and matter sources satisfying the dominant energy condition. These inequalities provide lower bounds for the area of spatial sections of dynamical trapping horizons, namely hypersurfaces offering quasi-local models of black hole horizons. In particular, these inequalities represent particular examples of the extension to a Lorentzian setting of tools employed in the discussion of minimal surfaces in Riemannian contexts.

gr-qc↗
arXiv2012

Black hole Area-Angular momentum inequality in non-vacuum spacetimes

We show that the area-angular momentum inequality A\geq 8π|J| holds for axially symmetric closed outermost stably marginally trapped surfaces. These are horizon sections (in particular, apparent horizons) contained in otherwise generic non-necessarily axisymmetric black hole spacetimes, with non-negative cosmological constant and whose matter content satisfies the dominant energy condition.

gr-qc↗
arXiv2011

Black hole Area-Angular momentum-Charge inequality in dynamical non-vacuum spacetimes

We show that the area-angular momentum-charge inequality (A/(4π))^2 \geq (2J)^2 + (Q_E^2 + Q_M^2)^2 holds for apparent horizons of electrically and magnetically charged rotating black holes in generic dynamical and non-vacuum spacetimes. More specifically, this quasi-local inequality applies to axially symmetric closed outermost stably marginally (outer) trapped surfaces, embedded in non-necessarily axisymmetric black hole spacetimes with non-negative cosmological constant and matter content satisfying the dominant energy condition.

gr-qc↗
arXiv2011

Area-charge inequality for black holes

The inequality between area and charge $A\geq 4πQ^2$ for dynamical black holes is proved. No symmetry assumption is made and charged matter fields are included. Extensions of this inequality are also proved for regions in the spacetime which are not necessarily black hole boundaries.

gr-qc↗
arXiv2011

An introduction to local Black Hole horizons in the 3+1 approach to General Relativity

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an "a priori" ingredient in certain formulations of Einstein equations and as an "a posteriori" tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the "rigidity" properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

gr-qc↗
arXiv2011

Application of initial data sequences to the study of Black Hole dynamical trapping horizons

Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial cuts of a single spacetime hypersurface foliated by (compact) marginally outer trapped surfaces. We present here some work in progress which makes use of uni-parametric sequences of (axisymmetric) binary black hole initial data for exploring the plausibility of this spacetime picture. The modelling of Einstein evolutions by sequences of initial data has proved to be a successful methodological tool in other settings for the understanding of certain qualitative features of evolutions in restricted physical regimes.

gr-qc↗
arXiv2010

Understanding the "anti-kick" in the merger of binary black holes

The generation of a large recoil velocity from the inspiral and merger of binary black holes represents one of the most exciting results of numerical-relativity calculations. While many aspects of this process have been investigated and explained, the "antikick", namely the sudden deceleration after the merger, has not yet found a simple explanation. We show that the antikick can be understood in terms of the radiation from a deformed black hole where the anisotropic curvature distribution on the horizon correlates with the direction and intensity of the recoil. Our analysis is focussed on Robinson-Trautman spacetimes and allows us to measure both the energies and momenta radiated in a gauge-invariant manner. At the same time, this simpler setup provides the qualitative and quantitative features of merging black holes, opening the way to a deeper understanding of the nonlinear dynamics of black-hole spacetimes.

gr-qc↗
arXiv2010

Isolated horizons in numerical relativity: constructing the excised Kerr spacetime in Dirac gauge

Using a constrained formalism for Einstein equations in Dirac gauge, we propose to compute excised quasistationary initial data for black hole spacetimes in full general relativity. Vacuum spacetime settings are numerically constructed by using the isolated horizon formalism; we especially tackle the conformal metric part of our equations, assuming global stationarity. We show that a no-boundary treatment can be used on the horizon for the equation related to the conformal metric. We relate this finding to previous suggestions in the literature, and use our results to assess the widely used conformally flat approximation for computing black hole initial data.

gr-qc↗
arXiv2009

Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example

We present a numerical work aiming at the computation of excised initial data for black hole spacetimes in full general relativity, using Dirac gauge in the context of a constrained formalism for the Einstein equations. Introducing the isolated horizon formalism for black hole excision, we especially solve the non-conformally flat part of the equations, and assess the boundary condition problem for this part. In the stationary single black hole case, we present and justify a no-boundary treatment on the black hole horizon. We compare the data obtained with the well-known analytic Kerr solution in Kerr-Schild coordinates, and assess the widely used conformally flat approximation for simulating axisymmetric black hole spacetimes. Our method shows good concordance on physical and geometrical issues, with the particular application of the isolated horizon multipolar analysis to confirm that the solution obtained is indeed the Kerr spacetime. Finally, we discuss a previous suggestion in the literature for the boundary conditions for the conformal geometry on the horizon.

gr-qc↗