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Hal M. Haggard

Publications and source records attributed to Hal M. Haggard.

At least 19 recordsLinked to original sources
arXiv2025

Spinfoam tunneling of quantum geometries in angle variables

Tunneling processes offer a promising path for finding signatures of quantum gravity. While tunneling of geometry has long been recognized in the literature, few detailed analyses in covariant Loop Quantum Gravity have been carried out. We investigate spinfoam transitions in the holonomy representation, which naturally encodes the extrinsic curvature of boundary states. To reduce technical complications to a minimum, we study these amplitudes within the simple framework of the Ponzano-Regge spinfoam model for three-dimensional Euclidean quantum gravity. We identify the geometries dominating the spinfoam path integral in the classically forbidden regime when formulated in terms of dihedral angles as boundary data. We characterize these non-classical geometries and show that their contributions to the spinfoam amplitude are exponentially suppressed in the semiclassical limit via analytic continuation of the discrete gravity action. We argue that they satisfy all the desired properties of tunneling processes. We also shed light on quantum black-to-white-hole transitions, in particular clarifying the origin of the exponential suppression of various quantum amplitudes, while at the same time laying the basis for a future complete calculation of the amplitude in covariant Loop Quantum Gravity.

gr-qc↗
arXiv2024

Tunneling of quantum geometries in spinfoams

Quantum gravitational tunneling effects are expected to give rise to a number of interesting observable phenomena, including, in particular, the evolution of black holes at the end of their existence or the emergence of the early universe from a quantum phase. Covariant Loop Quantum Gravity provides a framework to study these phenomena, yet a precise identification of tunneling processes is still not known. Motivated by this question, we consider a related, simpler case, that of Ponzano-Regge amplitudes: we find a surprising and detailed analogy of a class of simple transition amplitudes with tunneling processes in non-relativistic quantum mechanics.

gr-qc↗
arXiv2023

Emergence of Riemannian Quantum Geometry

In this chapter we take up the quantum Riemannian geometry of a spatial slice of spacetime. While researchers are still facing the challenge of observing quantum gravity, there is a geometrical core to loop quantum gravity that does much to define the approach. This core is the quantum character of its geometrical observables: space and spacetime are built up out of Planck-scale quantum grains. The interrelations between these grains are described by spin networks, graphs whose edges capture the bounding areas of the interconnected nodes, which encode the extent of each grain. We explain how quantum Riemannian geometry emerges from two different approaches: in the first half of the chapter we take the perspective of continuum geometry and explain how quantum geometry emerges from a few principles, such as the general rules of canonical quantization of field theories, a classical formulation of general relativity in which it appears embedded in the phase space of Yang-Mills theory, and general covariance. In the second half of the chapter we show that quantum geometry also emerges from the direct quantization of the finite number of degrees of freedom of the gravitational field encoded in discrete geometries. These two approaches are complimentary and are offered to assist readers with different backgrounds enter the compelling arena of quantum Riemannian geometry.

gr-qc↗
arXiv2022

Combining Photometry and Astrometry to Improve Orbit Retrieval of Directly Imaged Exoplanets

Future missions like Roman, HabEx, and LUVOIR will directly image exoplanets in reflected light. While current near infrared direct imaging searches are only sensitive to young, self-luminous planets whose brightness is independent of their orbital phase, reflected light imaging will reveal changes in planet brightness over the course of an orbit due to phase variations. One of the first objectives will be determining the planet's orbit via astrometry, the projected position of the planet with respect to its host star in the sky plane. We show that phase variations can significantly improve the accuracy and precision of orbital retrieval with two or three direct images. This would speed up the classification of exoplanets and improve the efficiency of subsequent spectroscopic characterization. We develop a forward model to generate synthetic observations of the two dimensional position of the planet with respect to its host star on the sky plane, and the planet/star flux ratio. Synthetic data are fitted with Keplerian orbits and Henyey-Greenstein phase variations to retrieve orbital and phase parameters. For astrometric uncertainties of 0.01 AU in projected separation and flux ratio uncertainties of 10^-12, using photometry in orbit retrieval improves the accuracy of semi-major axis by 47% for two epochs and 61% for three epochs if the phase curves have a known shape, but unknown amplitude. In the more realistic scenario where the shape and amplitude of the phase curve are a priori unknown, photometry still improves accuracy by 16% for two epochs and 50% for three.

astro-ph.EP↗
arXiv2021

Discrete gravity dynamics from effective spin foams

The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently introduced effective spin foam models, which are particularly numerically efficient. Previous work has raised the concern of a flatness problem in spin foam dynamics, identifying the potential for the dynamics to lead to flat geometries in the small $\hbar$ semiclassical limit. The numerical results presented here expose a rich semiclassical regime, but one that must be understood as an interplay between the various parameters of the spin foam model. In particular, the scale of the triangulation, fixed by the areas of its boundary triangles, the discreteness of the area spectrum, input from Loop Quantum Gravity, and the curvature scales around the bulk triangles, all enter the characterization of the semiclassical regime identified here. In addition to these results on the dynamics, we show that the subtle nature of the semiclassical regime is a generic feature of the path integral quantization of systems with second class constraints.

gr-qc↗
arXiv2021

Effective Spin Foam Models for Four-Dimensional Quantum Gravity

A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity and holography, situate areas as their fundamental variables. However, this choice of kinematics can easily lead to gravitational dynamics peaked on flat spacetimes. We show that this is due to how regions are glued in the gravitational path integral via a discrete spin foam model. We introduce a family of `effective' spin foam models that incorporate a quantum area spectrum, impose gluing constraints as strongly as possible, and leverage the discrete general relativity action to specify amplitudes. These effective spin foam models avoid flatness in a restricted regime of the parameter space. The simpler effective spin foam models will be useful for numerical studies and in the investigation of coarse graining and renormalization.

gr-qc↗
arXiv2020

Small Spins of Primordial Black Holes from Random Geometries: Bekenstein-Hawking Entropy and Gravitational Wave Observations

Black hole entropy is a robust prediction of quantum gravity with no established phenomenological consequences to date. We use the Bekenstein-Hawking entropy formula and general-relativistic statistical mechanics to determine the probability distribution of random geometries uniformly sampled in phase space. We show that this statistics (in the limit $\hbar\to 0$) is relevant to large curvature perturbations, resulting in a population of primordial black holes with zero natal spin. In principle, the identification of such a population at LIGO, Virgo, and future gravitational wave observatories could provide the first observational evidence for the statistical nature of black hole entropy.

gr-qc↗
arXiv2018

Holographic description of boundary gravitons in (3+1) dimensions

Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's holographic formulation. Holography holds promise for simplifying computations in quantum gravity. While holographic descriptions of three-dimensional spacetimes and of spacetimes with a negative cosmological constant are well-developed, a complete boundary description of zero curvature, four-dimensional spacetime is not currently available. Building on previous work in three-dimensions, we provide a new route to four-dimensional holography and its boundary gravitons. Using Regge calculus linearized around a flat Euclidean background with the topology of a solid hyper-torus, we obtain the effective action for a dual boundary theory which describes the dynamics of the boundary gravitons. Remarkably, in the continuum limit and at large radii this boundary theory is local and closely analogous to the corresponding result in three-dimensions. The boundary effective action has a degenerate kinetic term that leads to singularities in the one-loop partition function that are independent of the discretization. These results establish a rich boundary dynamics for four-dimensional flat holography.

hep-th↗
arXiv2018

Spin fluctuations and black hole singularities: the onset of quantum gravity is spacelike

Due to quantum fluctuations, a black hole of mass $M$ represents an average over an ensemble of black hole geometries with angular momentum. This observation is apparently at odds with the fact that the curvature singularity inside a rotating black hole is timelike, while the one inside a non-rotating black hole is spacelike. Is the average of timelike singularities really spacelike? We use the Bekenstein-Hawking entropy formula to introduce a microcanonical ensemble for spin fluctuations and show that the onset of quantum gravity is always spacelike. We discuss the impact of this result on singularity resolution in quantum gravity and hint at the possibility of an observational test.

gr-qc↗
arXiv2018

White Holes as Remnants: A Surprising Scenario for the End of a Black Hole

Quantum tunneling of a black hole into a white hole provides a model for the full life cycle of a black hole. The white hole acts as a long-lived remnant, solving the black-hole information paradox. The remnant solution of the paradox has long been viewed with suspicion, mostly because remnants seemed to be such exotic objects. We point out that (i) established physics includes objects with precisely the required properties for remnants: white holes with small masses but large finite interiors; (ii) non-perturbative quantum-gravity indicates that a black hole tunnels precisely into such a white hole, at the end of its evaporation. We address the objections to the existence of white-hole remnants, discuss their stability, and show how the notions of entropy relevant in this context allow them to evade several no-go arguments. A black hole's formation, evaporation, tunneling to a white hole, and final slow decay, form a unitary process that does not violate any known physics.

gr-qc↗
arXiv2018

Inferring Planetary Obliquity Using Rotational & Orbital Photometry

The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over most of a planet's orbit can be inverted to infer obliquity. However, few studies of more general planets with arbitrary albedo markings have been made and, in particular, a simple theoretical understanding of why it is possible to extract obliquity from light curves is missing. Reflected light seen by a distant observer is the product of a planet's albedo map, its host star's illumination, and the visibility of different regions. It is useful to treat the product of illumination and visibility as the kernel of a convolution. Time-resolved photometry constrains both the albedo map and the kernel, the latter of which sweeps over the planet due to rotational and orbital motion. The kernel's movement distinguishes prograde from retrograde rotation for planets with non-zero obliquity on inclined orbits. We demonstrate that the kernel's longitudinal width and mean latitude are distinct functions of obliquity and axial orientation. Notably, we find that a planet's spin axis affects the kernel -- and hence time-resolved photometry -- even if this planet is East-West uniform or spinning rapidly, or if it is North-South uniform. We find that perfect knowledge of the kernel at 2-4 orbital phases is usually sufficient to uniquely determine a planet's spin axis. Surprisingly, we predict that East-West albedo contrast is more useful for constraining obliquity than North-South contrast.

astro-ph.EP↗
arXiv2018

The Degrees of Freedom of Area Regge Calculus: Dynamics, Non-metricity, and Broken Diffeomorphisms

Discretization of general relativity is a promising route towards quantum gravity. Discrete geometries have a finite number of degrees of freedom and can mimic aspects of quantum geometry. However, selection of the correct discrete freedoms and description of their dynamics has remained a challenging problem. We explore classical area Regge calculus, an alternative to standard Regge calculus where instead of lengths, the areas of a simplicial discretization are fundamental. There are a number of surprises: though the equations of motion impose flatness we show that diffeomorphism symmetry is broken for a large class of area Regge geometries. This is due to degrees of freedom not available in the length calculus. In particular, an area discretization only imposes that the areas of glued simplicial faces agrees; their shapes need not be the same. We enumerate and characterize these non-metric, or `twisted', degrees of freedom and provide tools for understanding their dynamics. The non-metric degrees of freedom also lead to fewer invariances of the area Regge action---in comparison to the length action---under local changes of the triangulation (Pachner moves). This means that invariance properties can be used to classify the dynamics of spin foam models. Our results lay a promising foundation for understanding the dynamics of the non-metric degrees of freedom in loop quantum gravity and spin foams.

gr-qc↗
arXiv2018

exocartographer: A Bayesian Framework for Mapping Exoplanets in Reflected Light

Future space telescopes will directly image extrasolar planets at visible wavelengths. Time-resolved reflected light from an exoplanet encodes information about atmospheric and surface inhomogeneities. Previous research has shown that the light curve of an exoplanet can be inverted to obtain a low-resolution map of the planet, as well as constraints on its spin orientation. Estimating the uncertainty on 2D albedo maps has so far remained elusive. Here we present exocartographer, a flexible open-source Bayesian framework for solving the exo-cartography inverse problem. The map is parameterized with equal-area HEALPix pixels. For a fiducial map resolution of 192 pixels, a four-parameter Gaussian process describing the spatial scale of albedo variations, and two unknown planetary spin parameters, exocartographer explores a 198-dimensional parameter space. To test the code, we produce a light curve for a cloudless Earth in a face-on orbit with a 90$^\circ$ obliquity. We produce synthetic white light observations of the planet: 5 epochs of observations throughout the planet's orbit, each consisting of 24 hourly observations with a photometric uncertainty of $1\%$ (120 data). We retrieve an albedo map and$-$for the first time$-$its uncertainties, along with spin constraints. The albedo map is recognizably of Earth, with typical uncertainty of $30\%$. The retrieved characteristic length scale is 88$\pm 7 ^\circ$, or 9800 km. The obliquity is recovered with a $1-σ$ uncertainty of $0.8^\circ$. Despite the uncertainty in the retrieved albedo map, we robustly identify a high albedo region (the Sahara desert) and a large low-albedo region (the Pacific Ocean).

astro-ph.EP↗
arXiv2018

Analytic Reflected Lightcurves for Exoplanets

The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this paper, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points ($δ$-maps), and spherical harmonics ($Y_l^m$-maps). In particular, we use Wigner $D$-matrices to express an harmonic lightcurve for an arbitrary viewing geometry as a non-linear combination of harmonic lightcurves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected lightcurves, as well as fast calculation of lightcurves for mapping exoplanets based on time-resolved photometry. To these ends we make available Exoplanet Analytic Reflected Lightcurves (EARL), a simple open-source code that allows rapid computation of reflected lightcurves.

astro-ph.EP↗
arXiv2017

SL(2,C) Chern-Simons Theory, Flat Connections, and Four-dimensional Quantum Geometry

A correspondence between three-dimensional flat connections and constant curvature four-dimensional simplices is used to give a novel quantization of geometry via complex SL(2,C) Chern-Simons theory. The resulting quantum geometrical states are hence represented by the 3d blocks of analytically continued Chern-Simons theory. In the semiclassical limit of this quantization the three-dimensional Chern-Simons action, remarkably, becomes the discrete Einstein-Hilbert action of a 4-simplex, featuring the appropriate boundary terms as well as the essential cosmological term proportional to the simplex's curved 4-volume. Both signs of the curvature and associated cosmological constant are present in the class of flat connections that give rise to this correspondence. We provide a Wilson graph operator that picks out this class of connections. We discuss how to promote these results to a model of Lorentzian covariant quantum gravity encompassing both signs of the cosmological constant. This paper presents the details for the results reported in reference [1] (arXiv:1509.00458).

hep-th↗
arXiv2016

Odd Harmonics in Exoplanet Photometry: Weather or Artifact?

Photometry of short-period planetary systems allows astronomers to monitor exoplanets, their host stars, and their mutual interactions. In addition to the transits of a planet in front of its star and the eclipses of the planet by its star, researchers have reported flux variations at the orbital frequency and its harmonics: planetary reflection and/or emission and Doppler beaming of starlight produce one peak per orbit, while ellipsoidal variations of a tidally distorted star and/or planet produce two maxima per orbit. Researchers have also reported significant photometric variability at three times the orbital frequency, sometimes much greater than the predictions of tidal theory. The reflected phase variations of a homogeneous planet contains power at even orbital harmonics-important for studies of ellipsoidal variations-but cannot contain odd orbital harmonics. We show that odd harmonics can, however, be produced by an edge-on planet with a time-variable map, or an inclined planet with a North-South (N-S) asymmetric map. Either of these scenarios entail weather: short-period planets are expected to have zero obliquity and hence N-S symmetric stellar forcing. North-South asymmetry in a giant planet would therefore suggest stochastic localized features, such as weather. However, we find that previous claims of large-amplitude odd modes in Kepler photometry are artifacts of removing planetary transits rather than modeling them. The only reliable claims of odd harmonics remain HAT-P-7b and Kepler-13Ab, for which the third mode amplitude is 6-8% of the planetary flux. Although time-variable albedo maps could in principle explain these odd harmonics, upper-limits on the infrared variability of hot Jupiters make this hypothesis unlikely. We urge theorists to study the effects of close-in planets on stellar atmospheres, as this remains the only plausible hypothesis.

astro-ph.EP↗
arXiv2016

Quantum Gravity Effects around Sagittarius A*

Recent VLBI observations have resolved Sagittarius A* at horizon scales. The Event Horizon Telescope is expected to provide increasingly good images of the region around the Schwarzschild radius $r_S$ of Sgr A* soon. A number of authors have recently pointed out the possibility that non-perturbative quantum gravitational phenomena could affect the space surrounding a black hole. Here we point out that the existence of a region around $\frac76 r_S$ where these effects should be maximal.

gr-qc↗