arXiv subjects

P. Marios Petropoulos

Publications and source records attributed to P. Marios Petropoulos.

At least 19 recordsLinked to original sources

arXiv2026

Carroll-Cotton Tensors and Gravitational Radiation at Null Infinity

We provide a first-principles definition of Cotton tensors on conformal Carroll geometries by gauging the conformal Carroll algebra. On the mathematical side, this analysis yields a conformally covariant object designed to quantify deviations from conformal flatness in Carrollian geometries. On the physical side, it offers a powerful geometric tool to describe gravitational radiative degrees of freedom at the conformal boundary of four-dimensional asymptotically flat spacetimes. Unlike the Bondi news, whose fully-covariant definition requires amendment by supplementary data that we identify with the Geroch tensor, the Carroll--Cotton tensors offer the natural geometric objects to quantify deviations from stationarity due to the emission of gravitational waves.

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arXiv2026

Kinetic Theory of Carroll Hydrodynamics

We develop the foundations of Carrollian statistical mechanics by considering a system of interacting instantonic space-filling branes on a flat background, thereby providing the closest Carrollian analogue to the Galilean gas of interacting particles that underpins Boltzmann's collision theory. By adapting Boltzmann's statistical approach within this framework, we provide a first-principles microscopic derivation of the so-called Carrollian fluid equations, which were previously obtained as the vanishing-speed-of-light limit of relativistic conservation laws. We then use this analysis as a basis for formulating the first elements of Carrollian thermodynamics.

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arXiv2026

Carrollian-holographic Derivation of Gravitational Flux-Balance Laws

We demonstrate that the BMS evolution equations for the mass and angular momentum aspects in asymptotically flat Einstein gravity follow from local Carroll, Weyl, and diffeomorphism invariance at the null conformal boundary, upon providing a minimalistic holographic dictionary as the sole input from the bulk. This result is a significant step in the quest for a flat-space holographic correspondence and offers a geometric implementation of the radiative degrees of freedom that source the boundary theory in the presence of bulk gravitational waves.

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arXiv2024

One-dimensional Carrollian fluids I: Carroll-Galilei duality

Galilean and Carrollian algebras acting on two-dimensional Newton-Cartan and Carrollian manifolds are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. We describe the dynamics of these systems as they emerge from the relevant limits of Lorentzian hydrodynamics, and explore the advertised duality relationship. This interchanges longitudinal and transverse directions with respect to the flow velocity, and permutes equilibrium and out-of-equilibrium observables, unveiling specific features of Carrollian physics. We investigate the action of local hydrodynamic-frame transformations in the Galilean and Carrollian configurations, i.e. dual Galilean and Carrollian local boosts, and comment on their potential breaking. Emphasis is laid on the additional geometric elements that are necessary to attain complete systems of hydrodynamic equations in Newton-Cartan and Carroll spacetimes. Our analysis is conducted in general Cartan frames as well as in more explicit coordinates, specifically suited to Galilean or Carrollian use.

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arXiv2024

One-Dimensional Carrollian Fluids III: Global Existence and Weak Continuity in $L^\infty$

The Carrollian fluid equations arise as the $c \to 0$ limit of the relativistic fluid equations and have recently experienced a surge of activity in the flat-space holography community. However, the rigorous mathematical well-posedness theory for these equations does not appear to have been previously studied. This paper is the third in a series in which we initiate the systematic analysis of the Carrollian fluid equations. In the present work we prove the global-in-time existence of bounded entropy solutions to the isentropic Carrollian fluid equations in one spatial dimension for a particular constitutive law ($γ= 3$). Our method is to use a vanishing viscosity approximation for which we establish a compensated compactness framework. Using this framework we also prove the compactness of entropy solutions in $L^\infty$, and establish a kinetic formulation of the problem. This global existence result in $L^\infty$ extends the $C^1$ theory presented in our companion paper ``One-Dimensional Carrollian Fluids II: $C^1$ Blow-up Criteria''.

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arXiv2024

One-dimensional Carrollian fluids II: $C^1$ blow-up criteria

The Carrollian fluid equations arise from the equations for relativistic fluids in the limit as the speed of light vanishes, and have recently experienced a surge of interest in the theoretical physics community in the context of asymptotic symmetries and flat-space holography. In this paper we initiate the rigorous systematic analysis of these equations by studying them in one space dimension in the $C^1$ setting. We begin by proposing a notion of isentropic Carrollian equations, and use this to reduce the Carrollian equations to a $2 \times 2$ system of conservation laws. Using the scheme of Lax, we then classify when $C^1$ solutions to the isentropic Carrollian equations exist globally, or blow up in finite time. Our analysis assumes a Carrollian analogue of a constitutive relation for the Carrollian energy density, with exponent in the range $γ\in (1,3]$.

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arXiv2023

Chern-Simons action and the Carrollian Cotton tensors

In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to Carrollian diffeomorphisms in a suitable frame, one discloses four sets of Cotton Carrollian relatives, which are conformal and obey Carrollian conservation equations. Each set of Carrollian Cotton tensors is alternatively obtained as the variation of a distinct Carroll-Chern-Simons action with respect to the degenerate metric and the clock form of a strong Carroll structure. The four Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original Chern-Simons ascendant. They inherit its anomalous behaviour under diffeomorphisms and Weyl transformations. The extremums of these Carrollian actions are commented and illustrated.

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arXiv2023

Flat from anti-de Sitter

Ricci-flat solutions to Einstein's equations in four dimensions are obtained as the flat limit of Einstein spacetimes with negative cosmological constant. In the limiting process, the anti-de Sitter energy--momentum tensor is expanded in Laurent series in powers of the cosmological constant, endowing the system with the infinite number of boundary data, characteristic of the asymptotically flat solution space. The governing flat Einstein dynamics is recovered as the limit of the original energy--momentum conservation law and from the additional requirement of the line-element finiteness, providing at each order the necessary set of flux-balance equations for the boundary data. This analysis is conducted using a covariant version of the Newman--Unti gauge designed for taking advantage of the boundary Carrollian structure emerging at vanishing cosmological constant and its Carrollian attributes such as the Cotton tensor.

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arXiv2023

Ehlers, Carroll, Charges and Dual Charges

We unravel the boundary manifestation of Ehlers' hidden Möbius symmetry present in four-dimensional Ricci-flat spacetimes that enjoy a time-like isometry and are Petrov-algebraic. This is achieved in a designated gauge, shaped in the spirit of flat holography, where the Carrollian three-dimensional nature of the null conformal boundary is manifest and covariantly implemented. The action of the Möbius group is local on the space of Carrollian boundary data, among which the Carrollian Cotton tensor plays a predominent role. The Carrollian and Weyl geometric tools introduced for shaping an appropriate gauge, as well as the boundary conformal group, which is $\text{BMS}_4$, allow to define electric/magnetic, leading/subleading towers of charges directly from the boundary Carrollian dynamics and explore their behaviour under the action of the Möbius duality group.

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arXiv2022

Relativistic Fluids, Hydrodynamic Frames and their Galilean versus Carrollian Avatars

We comprehensively study Galilean and Carrollian hydrodynamics on arbitrary backgrounds, in the presence of a matter/charge conserved current. For this purpose, we follow two distinct and complementary paths. The first is based on local invariance, be it Galilean or Carrollian diffeomorphism invariance, possibly accompanied by Weyl invariance. The second consists in analyzing the relativistic fluid equations at large or small speed of light, after choosing an adapted gauge, ADM-Zermelo for the former and Papapetrou-Randers for the latter. Unsurprisingly, the results agree, but the second approach is superior as it effortlessly captures more elaborate situations with multiple degrees of freedom. It furthermore allows to investigate the fate of hydrodynamic-frame invariance in the two limits at hand, and conclude that its breaking (in the Galilean) or its preservation (in the Carrollian) are fragile consequences of the behaviour of transport attributes at large or small $c$. Both methods do also agree on the doom of Noetherian currents generated in the relativistic theory by isometries: non-trivial currents are not always guaranteed in Newton-Cartan or Carroll spacetimes as a consequence of Galilean or Carrollian isometries. Comparison of Galilean and Carrollian fluid equations exhibits a striking but often superficial resemblance, which we comment in relation to black-hole horizon dynamics, awkwardly akin to Navier-Stokes equations. This congruity is authentic in one instance though and turns out then to describe Aristotelian dynamics, which is the last item in our agenda.

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arXiv2022

Holographic Lorentz and Carroll Frames

Relaxing the Bondi gauge, the solution space of three-dimensional gravity in the metric formulation has been shown to contain an additional free function that promotes the boundary metric to a Lorentz or Carroll frame, in asymptotically AdS or flat spacetimes. We pursue this analysis and show that the solution space also admits a finite symplectic structure, obtained taking advantage of the built-in ambiguities. The smoothness of the flat limit of the AdS symplectic structure selects a prescription in which the holographic anomaly appears in the boundary Lorentz symmetry, that rotates the frame. This anomaly turns out to be cohomologically equivalent to the standard holographic Weyl anomaly and survives in the flat limit, thus predicting the existence of quantum anomalies in conformal Carrollian field theories. We also revisit these results in the Chern--Simons formulation, where the prescription for the symplectic structure admitting a smooth flat limit follows from the variational principle, and we compute the charge algebra in the boundary conformal gauge.

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arXiv2020

Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence

In three-dimensional gravity, we discuss the relation between the Fefferman--Graham gauge, the Bondi gauge and the Eddington--Finkelstein type of gauge, often referred to as the derivative expansion, involved in the fluid/gravity correspondence. Starting with a negative cosmological constant, for each gauge, we derive the solution space and the residual gauge diffeomorphisms. We construct explicitly the diffeomorphisms that relate the various gauges, and establish the precise matching of their boundary data. We show that Bondi and Fefferman--Graham gauges are equivalent, while the fluid/gravity derivative expansion, originating from a partial gauge fixing, exhibits an extra unspecified function that encodes the boundary fluid velocity. The Bondi gauge turns out to describe a subspace of the derivative expansion's solution space, featuring a fluid in a specific hydrodynamic frame. We pursue our analysis with the Ricci-flat limit of the Bondi gauge and of the fluid/gravity derivative expansion. The relations between them persist in this limit, which is well-defined and non-trivial. Moreover, the flat limit of the derivative expansion maps to the ultra-relativistic limit on the boundary. This procedure allows to unravel the holographic properties of the Bondi gauge for vanishing cosmological constant, in terms of its boundary Carrollian dual fluid.

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arXiv2020

Gauges in Three-Dimensional Gravity and Holographic Fluids

Solutions to Einstein's vacuum equations in three dimensions are locally maximally symmetric. They are distinguished by their global properties and their investigation often requires a choice of gauge. Although analyses of this sort have been performed abundantly, several relevant questions remain. These questions include the interplay between the standard Bondi gauge and the Eddington--Finkelstein type of gauge used in the fluid/gravity holographic reconstruction of these spacetimes, as well as the Fefferman--Graham gauge, when available i.e. in anti de Sitter. The goal of the present work is to set up a thorough dictionary for the available descriptions with emphasis on the relativistic or Carrollian holographic fluids, which portray the bulk from the boundary in anti-de Sitter or flat instances. A complete presentation of residual diffeomorphisms with a preliminary study of their algebra accompanies the situations addressed here.

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arXiv2019

Two-dimensional fluids and their holographic duals

We describe the dynamics of two-dimensional relativistic and Carrollian fluids. These are mapped holographically to three-dimensional locally anti-de Sitter and locally Minkowski spacetimes, respectively. To this end, we use Eddington-Finkelstein coordinates, and grant general curved two-dimensional geometries as hosts for hydrodynamics. This requires to handle the conformal anomaly, and the expressions obtained for the reconstructed bulk metrics incorporate non-conformal-fluid data. We also analyze the freedom of choosing arbitrarily the hydrodynamic frame for the description of relativistic fluids, and propose an invariant entropy current compatible with classical and extended irreversible thermodynamics. This local freedom breaks down in the dual gravitational picture, and fluid/gravity correspondence turns out to be sensitive to dissipation processes: the fluid heat current is a necessary ingredient for reconstructing all Banados asymptotically anti-de Sitter solutions. The same feature emerges for Carrollian fluids, which enjoy a residual frame invariance, and their Barnich-Troessaert locally Minkowski duals. These statements are proven by computing the algebra of surface conserved charges in the fluid-reconstructed bulk three-dimensional spacetimes.

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arXiv2019

Carroll Structures, Null Geometry and Conformal Isometries

We study the concept of Carrollian spacetime starting from its underlying fiber-bundle structure. The latter admits an Ehresmann connection, which enables a natural separation of time and space, preserved by the subset of Carrollian diffeomorphisms. These allow for the definition of Carrollian tensors and the structure at hand provides the designated tools for describing the geometry of null hypersurfaces embedded in Lorentzian manifolds. Using these tools, we investigate the conformal isometries of general Carrollian spacetimes and their relationship with the BMS group.

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arXiv2018

Asymptotic Symmetries of Three-Dimensional Black Strings

We determine a consistent phase space for a theory consisting in the Einstein-Hilbert action coupled to matter fields (dilaton, one-form, two-form) and containing three-dimensional black strings (the Horne-Horowitz solution and generalizations thereof). The theory at hand is the low energy effective action for the bosonic sector of heterotic string theory. We find a consistent set of boundary conditions whose algebra of asymptotic charges consist in a single Virasoro algebra supplemented by three global $u(1)$ generators. We also discuss the thermodynamics of the zero-mode solutions and point out some peculiar features of this system.

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arXiv2018

Flat holography and Carrollian fluids

We show that a holographic description of four-dimensional asymptotically locally flat spacetimes is reached smoothly from the zero-cosmological-constant limit of anti-de Sitter holography. To this end, we use the derivative expansion of fluid/gravity correspondence. From the boundary perspective, the vanishing of the bulk cosmological constant appears as the zero velocity of light limit. This sets how Carrollian geometry emerges in flat holography. The new boundary data are a two-dimensional spatial surface, identified with the null infinity of the bulk Ricci-flat spacetime, accompanied with a Carrollian time and equipped with a Carrollian structure, plus the dynamical observables of a conformal Carrollian fluid. These are the energy, the viscous stress tensors and the heat currents, whereas the Carrollian geometry is gathered by a two-dimensional spatial metric, a frame connection and a scale factor. The reconstruction of Ricci-flat spacetimes from Carrollian boundary data is conducted with a flat derivative expansion, resummed in a closed form in Eddington-Finkelstein gauge under further integrability conditions inherited from the ancestor anti-de Sitter set-up. These conditions are hinged on a duality relationship among fluid friction tensors and Cotton-like geometric data. We illustrate these results in the case of conformal Carrollian perfect fluids and Robinson-Trautman viscous hydrodynamics. The former are dual to the asymptotically flat Kerr-Taub-NUT family, while the latter leads to the homonymous class of algebraically special Ricci-flat spacetimes.

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arXiv2018

All partial breakings in ${\cal N}=2$ supergravity with a single hypermultiplet

We consider partial supersymmetry breaking in ${\cal N}=2$ supergravity coupled to a single vector and a single hypermultiplet. This breaking pattern is in principle possible if the quaternion-Kähler space of the hypermultiplet admits (at least) one pair of commuting isometries. For this class of manifolds, explicit metrics exist and we analyse a generic electro-magnetic (dyonic) gauging of the isometries. An example of partial breaking in Minkowski spacetime has been found long ago by Ferrara, Girardello and Porrati, using the gauging of two translation isometries on $SO(4,1)/SO(4)$. We demonstrate that no other example of partial breaking of ${\cal N}=2$ supergravity in Minkowski spacetime exists. We also examine partial-breaking vacua in anti-de Sitter spacetime that are much less constrained and exist generically even for electric gaugings. On $SO(4,1)/SO(4)$, we construct the partially-broken solution and its global limit which is the Antoniadis-Partouche-Taylor model.

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