arXiv subjects

David Mattingly

Publications and source records attributed to David Mattingly.

At least 19 recordsLinked to original sources

arXiv2026

Einstein-aether Elliptic Charges and the First Law of Asymptotically AdS Black Holes

We investigate the thermodynamic role of asymptotic aether alignment for universal horizons in Einstein-aether theory. In the static, spherically symmetric, asymptotically AdS sector with $c_{14}=0$, the known first law for universal horizons contains an additional term whenever the aether is misaligned with the timelike Killing vector at infinity. While this term has recently been interpreted in Ho\v{r}ava--Lifshitz gravity as the contribution of an elliptic charge associated with khronon reparameterizations, no corresponding explanation was available in Einstein-aether theory. We show that, in the same sector, Einstein-aether theory possesses a previously unidentified symmetry of the reduced action, generated by infinitesimal transformations of the form $\delta u^a=f a^a$, where $a^a$ is the aether acceleration and $f$ obeys an elliptic constraint. We derive the associated current and charge, and show that the aligned limit is naturally interpreted as the ensemble in which this aether-charge contribution vanishes. This provides the Einstein-aether counterpart of the elliptic-charge mechanism in Ho\v{r}ava--Lifshitz gravity and clarifies the thermodynamic significance of asymptotic aether alignment.

gr-qc↗

arXiv2026

Metric affine gravity with dynamical chronology protection

Modified theories of gravity often introduce geometric structure beyond general relativity to address unresolved problems in the gravitational sector without invoking ad hoc matter fields. Mimetic gravity, for example, generates an effective cosmological dark sector by isolating the conformal mode of the metric, while Horava-Lifshitz gravity attains power-counting renormalizability by endowing spacetime with a preferred dynamical foliation. Although chronology protection was not the original motivation for either theory, both can realize it classically through stable causality. This suggests that chronology protection itself may be elevated from a derived property to a guiding principle for constructing modified gravitational theories, especially if its implementation at the quantum-gravitational level leaves infrared imprints in the effective action. Motivated by this possibility, we introduce a toy metric-affine gravity model whose chronology-protecting sector is purely geometric. The model breaks projective invariance and selects a timelike, closed non-metricity one-form. In the globally exact sector, this one-form defines a time function, realizing stable causality through affine geometry. On the matter-free, spatially flat FLRW branch, the gravitational sector contains the two tensor modes of GR and a single scalar mode. We investigate the classical cosmological effects and scalar-mode dynamics of this purely geometric chronology-protecting extension of general relativity.

gr-qc↗

arXiv2025

Physical limits on information metrics and quantum gravity as gravitized quantum theory

There is a long history in both general relativity and quantum mechanics of removing fixed background structures, thereby making observed objects and measurement processes dynamical. We continue this evolution by combining central insights from both theories to argue that physical limits on information collection resulting from quantum gravity coupled with general covariance preclude the fixed information geometry still assumed in both information theory and quantum mechanics. As a consequence there must be a gravitized, generally covariant extension of both theories. We also propose a novel experimental test involving intrinsic triple and higher order quantum interferences that would provide evidence for dynamical information metrics and a dynamical Born rule.

gr-qc↗

arXiv2025

Information Metrics and Possible Limitations of Local Information Objectivity in Quantum Gravity

Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's theorem: the Fisher information metric is the unique metric invariant under the assumptions of independent, identically distributed sampling and sufficient statistics. However, quantum gravity typically violates these assumptions, permitting contextual deviations from the Fisher metric that reflect the dynamical experimental and environmental configurations. This yields a possible extension of spacetime general covariance to information geometry. Since compatibility with the metric on probability spaces heavily restricts the form of the Born rule for quantum mechanics, deviations from the Fisher metric also can induce modifications of the Born rule, leading it to vary between observers. We explain some possible variations, advocate for experimental tests, and suggest a new quantum gravity approach based on generally covariant information geometry.

gr-qc↗

arXiv2024

Mixed Gauge-Global Symmetries, Elliptic Modes, and Black Hole Thermodynamics in Ho\v{r}ava-Lifshitz Gravity

In Ho\v{r}ava-Lifshitz gravity, a putative consistent theory of quantum gravity for which there is evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is ``mixed'': it is a local symmetry in one coordinate yet global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. The mixed symmetry and associated charge has not yet been accounted for in calculations of universal horizon thermodynamics in Ho\v{r}ava-Lifshitz gravity. This has led to problems, in particular the failure of the first law in a class of asymptotically AdS solutions where the normal to the leaves of the foliation is not aligned with the time translation Killing vector at infinity. We show how the dynamics of the charge corresponding to this symmetry coupled with the other features above resolves this issue. We then briefly comment how this mixed symmetry, the corresponding charge, and the elliptic equations of motion also conspire to evade recent holographic arguments for only local gauge fields in consistent theories of quantum gravity due to the lack of splittability of the elliptic equation and associated mode.

hep-th↗

arXiv2023

Energy Cost of Localization of Relational Quantum Information

Entanglement of spatially separated quantum states is usually defined with respect to a reference frame provided by some external observer. Thus, if one wishes to localize the quantum information within a spatially separated entangled state, one must enact an entanglement extraction protocol also defined with respect to that external frame. Entanglement extraction for Gaussian ground states in such an external frame construction has been shown to require a minimum energy and is hence an interesting process for gravitational physics, where examinations of localization vs. energy cost have a long history. General covariance however, precludes dependence on external frames. In order to enact an extraction protocol in a generally covariant theory, dependence on the external reference frame must first be removed and the states made relational. We examine the implementation of an extraction protocol for Gaussian states, who's center-of-mass and relational degrees of freedom are entangled, in a relational toy model where translation invariance stands in for full diffeomorphism invariance. Constructing fully relational states and the corresponding extraction/localization can, in principle, be done in two ways. External frame position information can be removed through $G$-twirling over translations or one can spontaneously break the translation symmetry via the gradient of an auxiliary field, or $Z$-model. We determine the energetics of quantum information localization after the states have been made fully relational via both the $G$-twirl and $Z$-model. We also show one can smoothly transition between the two approaches via positive operator valued measurements (POVM).

quant-ph↗

arXiv2023

Triple Interference, Non-linear Talbot Effect and Gravitization of the Quantum

Recently we have discussed a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea of gravitizing the quantum. In this paper we elaborate on a specific test of this new approach to quantum gravity using triple interference in a varying gravitational field. Our discussion is driven by a profound analogy with recent triple-path interference experiments performed in the context of non-linear optics. We emphasize that the triple interference experiment in a varying gravitational field would deeply influence the present understanding of the kinematics of quantum gravity and quantum gravity phenomenology. We also discuss the non-linear Talbot effect as another striking phenomenological probe of gravitization of the geometry of quantum theory.

gr-qc↗

arXiv2022

Gravitizing the Quantum

We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea of gravitizing the quantum. In particular, in this formulation of quantum gravity the quantum geometry is still consistent with the principles of unitarity and also captures fundamental aspects of (quantum) gravity, such as topology change. Furthermore, we address specific ways of testing this new approach to quantum gravity by utilizing multi-path interference and optical lattice atomic clocks.

gr-qc↗

arXiv2022

Infrared Properties of Quantum Gravity: UV/IR Mixing, Gravitizing the Quantum -- Theory and Observation

We discuss the possible appearance of several rather exotic phenomena in quantum gravity, including UV/IR mixing, novel modifications of infrared phenomenology that extend effective field theory approaches, and the relaxation of the usual notions of locality. We discuss the relevance of such concepts in quantum gravity for quantum information science, cosmology and general quantum gravity phenomenology.

hep-th↗

arXiv2021

Energy-entropy relation for asymptotically Lifshitz spacetimes with universal horizons

We numerically solve for 2+1 asymptotically Lifshitz universal horizon solutions in Horava-Lifshitz gravity for dynamical exponents $z=2$ through $z=8$. We find that for all $z$ there is a thermodynamical first law and Smarr formula. Furthermore, we find that the energy-entropy relation expected for a thermal state in a two dimensional Lifshitz field theory, $E=\frac{2}{z+2}TS$, is also satisfied for universal horizons, including the correct $z$ scaling.

gr-qc↗

arXiv2018

Algebra of Universal Horizon Preserving Diffeomorphisms

In relativistic gravity, requiring a spacetime hypersurface be a Killing horizon breaks the general covariance of general relativity. The residual algebra of horizon preserving diffeomorphisms can be extended to a Virasoro algebra near the horizon, the central charge of which yields the Bekenstein-Hawking entropy via the Cardy formula. This near horizon symmetry approach provides an argument for why black hole entropy computations in various quantum gravity models all agree. An exception may be Ho\v{r}ava-Lifshitz gravity, where causal horizons are not Killing horizons but rather universal horizons. As a first step towards determining if the entropy of universal horizons can be calculated by a near horizon symmetry approach we compute the classical algebra of universal horizon preserving diffeomorphisms. We find that the algebra is similar to the algebra in the Killing horizon case, but with a modification that agrees with other approaches to universal horizon thermodynamics.

gr-qc↗

arXiv2018

Dynamical obstruction to perpetual motion from Lorentz-violating black holes

Black holes in Lorentz-violating theories have been claimed to violate the second law of thermodynamics by perpetual motion energy extraction. We revisit this question for a Penrose splitting process in a spherically symmetric setting with two species of particles that move on radial geodesics that extend to infinity. We show that energy extraction by this process cannot happen in any theory in which gravity is attractive, in the sense of a geometric inequality that we describe. This inequality is satisfied by all known Einstein-\ae{}ther and Ho\v{r}ava black hole solutions.

gr-qc↗

arXiv2017

Constructing entanglement wedges for Lifshitz spacetimes with Lifshitz gravity

Holographic relationships between entanglement entropy on the boundary of a spacetime and the area of minimal surfaces in the bulk provide an important entry in the bulk/boundary dictionary. While constructing the necessary causal and entanglement wedges is well understood in asymptotically AdS spacetimes, less is known about the equivalent constructions in spacetimes with different asymptotics. In particular, recent attempts to construct entanglement and causal wedges for asymptotically Lifshitz solutions in relativistic gravitational theories have proven problematic. We note a simple observation, that a Lifshitz bulk theory, specifically a covariant formulation of Ho\v{r}ava-Lifshitz gravity coupled to matter, has causal propagation defined by Lifshitz modes. We use these modes to construct causal and entanglement wedges and compute the geometric entanglement entropy, which in such a construction matches the field theory prescription.

gr-qc↗

arXiv2016

Asymptotically Lifshitz spacetimes with universal horizons in $(1 + 2)$ dimensions

Horava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two derivative Horava gravity Lagrangian that are necessary for static, asymptotically Lifshitz spacetimes with flat transverse dimensions to contain a universal horizon, which plays a similar thermodynamic role as the Killing horizon in general relativity. Specializing to z=2 in 1+2 dimensions, we then numerically construct such regular solutions over the whole spacetime. We calculate the mass for these solutions and show that, unlike the asymptotically anti-de Sitter case, the first law applied to the universal horizon is straightforwardly compatible with a thermodynamic interpretation.

hep-th↗

arXiv2014

Searching for Traces of Planck-Scale Physics with High Energy Neutrinos

High energy cosmic neutrino observations provide a sensitive test of Lorentz invariance violation, which may be a consequence of quantum gravity theories. We consider a class of non-renormalizable, Lorentz invariance violating operators that arise in an effective field theory description of Lorentz invariance violation in the neutrino sector inspired by Planck-scale physics and quantum gravity models. We assume a conservative generic scenario for the redshift distribution of extragalactic neutrino sources and employ Monte Carlo techniques to describe superluminal neutrino propagation, treating kinematically allowed energy losses of superluminal neutrinos caused by both vacuum pair emission and neutrino splitting. We consider EFTs with both non-renormalizable CPT-odd and non-renormalizable CPT-even operator dominance. We then compare the spectra derived using our Monte Carlo calculations in both cases with the spectrum observed by IceCube in order to determine the implications of our results regarding Planck-scale physics. We find that if the drop off in the neutrino flux above ~2 PeV is caused by Planck scale physics, rather than by a limiting energy in the source emission, a potentially significant pileup effect would be produced just below the drop off energy in the case of CPT-even operator dominance. However, such a clear drop off effect would not be observed if the CPT-odd, CPT-violating term dominates.

hep-ph↗

arXiv2014

Universal horizons in maximally symmetric spaces

Universal horizons in Ho\v{r}ava-Lifshitz gravity and Einstein-{\ae}ther theory are the equivalent of causal horizons in general relativity and appear to have many of the same properties, including a first law of horizon thermodynamics and thermal radiation. Since universal horizons are infrared solutions of a putative power counting renormalizable quantum gravitational theory, fully understanding their thermodynamics will shed light on the interplay between black hole thermodynamics and quantum gravity. In this paper, we provide a complete classification, including asymptotic charges, of all four dimensional static and spherically symmetric universal horizon solutions with maximally symmetric asymptotics -- the equivalents of the Schwarzschild, Schwarzschild de Sitter or Schwarzschild anti-de Sitter spacetimes. Additionally we derive the associated first laws for the universal horizon solutions. Finally we prove that independent of asymptotic boundary conditions, any spherically symmetric solution in Ho\v{r}ava-Lifshitz gravity with a universal horizon is also a solution of Einstein-{\ae}ther theory, thereby broadening and complementing the known equivalence region of the solution spaces.

hep-th↗

arXiv2013

Towards thermodynamics of universal horizons in Einstein-æther theory

Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-æther theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons", which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the timelike vector and show via the tunneling approach that the universal horizon radiates as a blackbody at a fixed temperature, even if the scalar field equations also violate local Lorentz invariance. This suggests that the class of holographic theories may be much broader than currently assumed.

hep-th↗

arXiv2012

Mechanics of universal horizons

Modified gravity models such as Hořava-Lifshitz gravity or Einstein-æther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-æther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-æther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.

hep-th↗