arXiv subjects

V. Taghiloo

Publications and source records attributed to V. Taghiloo.

At least 19 recordsLinked to original sources

arXiv2026

Who Writes the Gravitational Second Law of Thermodynamics?

We define gravitational entropy as the manifestly integrable surface charge associated with local transverse Lorentz boosts, entirely bypassing the conventional reliance on spacetime diffeomorphisms. Any notion of entropy must satisfy the second law. To answer the question posed in the title, an analogy with Newtonian classical mechanics is instructive: Newton's second law of motion is written by inertial observers who are defined by the first law of mechanics. We show that the second law of gravitational thermodynamics is written by free-fall observers with path parameterization in which the non-affinity of the geodesics is equal to the expansion of their velocity vector field. We then provide a proof of the local second law by studying variations in entropy as viewed by this class of covariantly-defined causal free-fall observers. We show that the entropy variation is strictly non-decreasing, provided the matter sector satisfies the integrated strong energy condition along the observer path.

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arXiv2026

Dynamical Entropy Is a Noether Charge

Black hole thermodynamics for generic dynamical, non-equilibrium regimes remains a fundamental challenge. We establish dynamical entropy as the Noether charge associated with a generic evolving null surface subject to Dirichlet boundary conditions. We specify the symmetry generator associated with the dynamical entropy, which is a null vector on the null surface, upon requiring physically motivated geometric conditions that yield a notion of ``dynamical zeroth law.'' We prove that this Noether charge density satisfies the second law of thermodynamics strictly at each instant in time, bypassing the teleological final conditions traditionally required by event horizons. Thus, we extend and generalize the notion of dynamical entropy introduced in \cite{Hollands:2024vbe}, in some different ways: We do not impose background stationarity; our dynamical entropy and the associated second law are local in time and work for generic dynamical gravitational systems.

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arXiv2026

GR from RG, $2d$ Example: JT-Gravity Induced from Renormalization Group Flow

We demonstrate how the two-dimensional gravity emerges within ``GR from RG'' program initiated in \cite{Adami:2025pqr, Sheikh-Jabbari:2026uol}. To achieve this, we consider a generic 2d CFT with a 3d holographic description, which we assume to be well-described by pure Einstein-AdS$_3$ gravity in the bulk. We study the holographic RG flow for the 2d CFT action and show that the renormalization group (RG) corrected action at an arbitrary energy scale contains a 2d scalar-tensor gravity theory. In the simplest case, the flow induces Jackiw-Teitelboim (JT) gravity, where the bulk radial lapse function seeds the dynamical dilaton field of the JT gravity. We show that the standard T$\bar{\text{T}}$ deformation of the 2d CFT is recovered as a special case in the Fefferman-Graham limit where the lapse is fixed. We further establish the robustness of the RG induced gravity picture by verifying its consistency under holographic renormalization and by generalizing the result to a one-parameter family of boundary conditions. Our results provide a first-principles derivation of the JT gravity at a finite cutoff as an intrinsic manifestation of the holographic RG flow in a non-Fefferman-Graham gauge

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arXiv2026

GR from RG: Gravity Is Induced From Renormalization Group Flow In The Infrared

In this essay and utilizing the holographic Renormalization Group (RG) flow, we demonstrate how the effective action of a non-gravitating quantum field theory in the ultraviolet (UV) develops an Einstein-Hilbert term in the infrared (IR). That is, gravity is induced by the RG flow. An inherent outcome of holography that plays a crucial role in our analysis is the \textit{RG flow of boundary conditions}: the rigid Dirichlet conditions on the background metric in the UV become an admixture of Dirichlet and Neumann as we flow to the IR, thereby ``unfreezing'' the metric and transforming it from a non-dynamical background into a dynamical field. This mechanism, which is a conceptually new addition to the standard Wilsonian RG flow, also provides the mechanism to evade the Weinberg-Witten no-go theorem. Within the GR from RG picture outlined here, the search for a quantum theory of gravity by treating the metric as a fundamental field may be a hunt for a phantom--akin to seeking the atomic structure of water by quantizing the equations of hydrodynamics.

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arXiv2026

Geometric Aspects of Covariant Phase Space Formalism: Solution Space Slicings and Surface Charge Integrability

The Covariant Phase Space Formalism (CPSF) provides a robust framework for deriving symplectic structures and surface charges in diffeomorphism-invariant theories. By construction, the CPSF operates on two distinct manifolds: the spacetime and the Solution Phase Space (SPS). In this paper, we advance the formalism by establishing a strictly parallel geometric formulation for both manifolds. Within this framework, we systematically analyze diffeomorphisms and frame changes on both spaces. While spacetime diffeomorphisms have been extensively studied in the literature, transformations on the SPS have been largely overlooked; we rigorously define and investigate these as changes of slicing on SPS. We demonstrate that the standard Wald-Zoupas criterion for the integrability of surface charge variations is inherently slicing-dependent. To resolve this issue, we develop the Frobenius theorem on the SPS and use it to extends the Wald-Zoupas condition into an inherently slicing-independent criterion for integrability. The Frobenius theorem on the SPS also yields a rigorous and natural definition of fundamental geometric quantities on the solution space, specifically the SPS connection, torsion, and curvature. Furthermore, this geometric machinery naturally distinguishes between fundamentally different surface fluxes: "fake" fluxes are identified mathematically as pure gauge artifacts of the SPS connection, while "genuine" fluxes manifest as non-vanishing SPS torsion, which directly relates to the physical gravitational News tensor. Finally, we present a geometric formulation of the Liouville theorem on the SPS, offering a unified classification scheme for theories with and without propagating bulk degrees of freedom.

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arXiv2026

Freelance Fluid/Gravity Correspondence, 3d Analysis

Freelance holography program is an extension of gauge/gravity correspondence, where the gravity theory is defined on a portion of AdS with an arbitrary timelike boundary, with any desired boundary conditions. It is also known that gauge/gravity correspondence admits a fluid/gravity correspondence limit, where the gauge theory side is well described by a fluid. In this work, combining the two, we work through ``freelance fluid/gravity''. In particular, we study in detail the 2d fluid (3d Einstein gravity) case, where one has a good analytical control over the bulk equations due to their integrability and absence of viscosity in the 2d fluid. We study consistency and validity requirements for the freelance fluid/gravity and how the fluid changes along the renormalization group (RG) flow. We prove the $v_g$-theorem, stating that the group velocity of fluid waves $v_g$ is a decreasing function as we move toward the infrared region along the RG flow, regardless of the adopted boundary conditions. We also study examples of holographic fluid with various asymptotic boundary conditions.

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arXiv2026

Generalized Symmetries in Shallow Water

Recent developments have extended the concept of global symmetries in several directions, offering new perspectives across a wide range of physical systems. This work shows that generalized global symmetries naturally emerge in shallow water systems. In particular, we demonstrate that two subsystem symmetries-previously studied primarily in exotic field theories-arise intrinsically in the dynamics of shallow water flows. A central result is that the local conservation of potential vorticity follows directly from the first subsystem symmetry, revealing that the classic Kelvin circulation theorem is rooted in these symmetries. Notably, the associated charge algebra forms a Kac-Moody current algebra, with the level determined by the spatial variation of the Coriolis parameter. Beyond the first subsystem symmetry, we also identify a second one, construct the corresponding Noether charges, and explore their potential applications.

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arXiv2025

Gravitational Entropy And The Second Law of Thermodynamics for Causal Observers

It is well established that black holes possess entropy and behave as thermodynamic systems. Associating entropy with gravitational fields has not remained limited to black holes, necessitating the notion of the second law of thermodynamics in gravitating systems. There have been many ideas and attempts to prove the second law within gravitating systems starting from first principles. Within the covariant phase space formalism, we define gravitational entropy as the charge associated with the local boosts, detaching the gravitational entropy from horizons or trapped surfaces as well as from the diffeomorphisms as symmetry generators. Using this definition for the Einstein gravity case, we compute variations of the entropy along the path of any causal free-fall observer and establish that the entropy variations are always non-negative if the matter content satisfies the strong energy condition integrated along any segment of the observer's trajectory.

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arXiv2025

AdS$_3$ Freelance Holography, A Detailed Analysis

Freelance holography program is an extension of the gauge/gravity correspondence in which the boundary theory can reside on any timelike codimension-one surface in AdS space, and the boundary conditions on the bulk fields can be chosen arbitrarily. Freelance holography provides the framework for a systematic study of various boundary conditions and associated bulk geometries. In this work, we analyze in detail the AdS$_3$ freelance holography. One can explicitly solve for the bulk AdS$_3$ Einstein gravity equations of motion. For generic boundary conditions, the solutions are described by two arbitrary functions of one variable. We study holographic renormalization group (RG) flows, the interpolation between different boundary conditions at different boundaries and associated surface charges and their algebras.

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arXiv2025

Gravity Is Induced By Renormalization Group Flow

We revisit the holographic renormalization group (RG) setting in which a 4-dimensional ($4d$) quantum field theory at a finite cutoff corresponds to/is described by the Einstein gravity on a part of AdS$_{5}$ space, cutoff at a finite radius. This holographic setting has interesting and important implications for the $4d$ field theory: Deformation of the field theory by a certain combination involving the square of its energy-momentum tensor can be alternatively viewed as formulating the field theory on a background with a dynamical metric. Explicitly, starting with a non-gravitating $4d$ field theory in the UV, flowing to the IR, quantum effects that we compute using the classical $5d$ Einstein gravity theory, induce an effective $4d$ Einstein gravity theory. In other words, we show that gravity is not a fundamental force and is an effective description of quantum effects in the IR limit.

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arXiv2025

Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence

We explore AdS/CFT duality in the large $N$ limit, where the duality reduces to gauge/gravity correspondence, from the viewpoint of covariant phase space formalism (CPSF). In particular, we elucidate the role of the $W, Y$, and $Z$ freedoms (also known as ambiguities) in the CPSF and their meaning in the gauge/gravity correspondence. We show that $W$-freedom is associated with the choice of boundary conditions and slicing of solution space in the gravity side, which has been related to deformations by multi-trace operators in the gauge theory side. The gauge/gravity correspondence implies the equivalence of on-shell symplectic potentials on both sides, thereby the $Y$-freedom of the gravity side specifies the on-shell symplectic form of the gauge theory side. The $Z$-freedom, which determines the corner Lagrangian on the gravity side, establishes the boundary conditions and choice of slicing in the boundary theory and its solution space. We utilize these results to systematically formulate freelance holography in which boundary conditions of the fields on the gravity side are chosen freely and are not limited to Dirichlet boundary conditions, and discuss some examples with different boundary conditions.

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arXiv2025

Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence

We continue developing the freelance holography program, formulating gauge/gravity correspondence where the gravity side is formulated on a space bounded by a generic timelike codimension-one surface inside AdS and arbitrary boundary conditions are imposed on the gravity fields on the surface. Our analysis is performed within the Covariant Phase Space Formalism (CPSF). We discuss how a given boundary condition on the bulk fields on a generic boundary evolves as we move the boundary to another boundary inside AdS and work out how this evolution is encoded in deformations of the holographic boundary theory. Our analyses here extend the extensively studied T$\bar{\text{T}}$-deformation by relaxing the boundary conditions at asymptotic AdS or at the cutoff surface to be any arbitrary one (besides Dirichlet). We discuss some of the implications of our general freelance holography setting.

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arXiv2025

Charges in General Relativity and Black Hole Thermodynamics

We shed a new light on the longstanding problem of covariant charges in diffeomorphism invariant theories like General Relativity (GR) by noting the other important feature of the theory, the background independence. To this end, we develop covariant phase space formalism in which we allow for the boundaries of spacetime to have arbitrary fluctuations. Within this formalism we show non-covariance of charges appear in inevitable integration constants which also break background independence in the expression of charges. We then apply the same formalism to black hole thermodynamics. We generalize the seminal Iyer-Wald derivation the first law of bl1ack hole thermodynamics by relaxing the need for the assumptions at a bifurcation surface and asymptotic infinity, as well as addressing questions regarding the integrability of charges. We also present a first principles derivation of the Smarr relation within our framework.

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arXiv2024

Covariant Phase Space Formalism for Fluctuating Boundaries

We reconsider formulating $D$ dimensional gauge theories, with the focus on the case of gravity theories, in spacetimes with boundaries. We extend covariant phase space formalism to the cases in which boundaries are allowed to fluctuate. We analyze the symplectic form, the freedoms (ambiguities), and its conservation for this case. We show that boundary fluctuations render all the surface charges integrable. We study the algebra of charges and its central extensions, charge conservation, and fluxes. We briefly comment on memory effects and questions regarding semiclassical aspects of black holes in the fluctuating boundary setup.

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arXiv2024

Gravitational Stress Tensor and Current at Null Infinity in Three Dimensions

We develop the framework that reveals the intrinsic conserved stress tensor and current associated with the null infinity of a three-dimensional ($3d$) asymptotically flat spacetime. These are, respectively, canonical conjugates of degenerate metric and Ehresmann connection of the boundary Carrollian geometry. Their conservation reproduces the Bondi-mass and angular momentum conservation equations if the asymptotic boundary is endowed with a torsional affine connection that we specify. Our analysis and results shed further light on the $3d$ flat holography; the stress tensor and current give rise to an asymptotically flat fluid/gravity correspondence. The requirement of a well-defined $3d$ action principle yields Schwarzian action at null infinity governing the dynamics induced by reparametrizations over the celestial circle, in accord with the codimension $2$ holography of $3d$ flat spacetimes.

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arXiv2024

Heisenberg Soft Hair on Robinson-Trautman Spacetimes

We study 4 dimensional $(4d$) gravitational waves (GWs) with compact wavefronts, generalizing Robinson-Trautman (RT) solutions in Einstein gravity with an arbitrary cosmological constant. We construct the most general solution of the GWs in the presence of a causal, timelike, or null boundary when the usual tensor modes are turned off. Our solution space besides the shape and topology of the wavefront which is a generic compact, smooth, and orientable $2d$ surface $Σ$, is specified by a vector over $Σ$ satisfying the conformal Killing equation and two scalars that are arbitrary functions over the causal boundary, the boundary modes (soft hair). We work out the symplectic form over the solution space using covariant phase space formalism and analyze the boundary symmetries and charges. The algebra of surface charges is a Heisenberg algebra. Only the overall size of the compact wavefront and not the details of its shape appears in the boundary symplectic form and is canonical conjugate to the overall mass of the GW. Hence, the information about the shape of the wavefront can't be probed by the boundary observer. We construct a boundary energy-momentum tensor and a boundary current, whose conservation yields the RT equation for both asymptotically AdS and flat spacetimes. The latter provides a hydrodynamic description for our RT solutions.

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arXiv2023

Carrollian Structure of the Null Boundary Solution Space

We study pure $D$ dimensional Einstein gravity in spacetimes with a generic null boundary. We focus on the symplectic form of the solution phase space which comprises a $2D$ dimensional boundary part and a $2(D(D-3)/2+1)$ dimensional bulk part. The symplectic form is the sum of the bulk and boundary parts, obtained through integration over a codimension 1 surface (null boundary) and a codimension 2 spatial section of it, respectively. Notably, while the total symplectic form is a closed 2-form over the solution phase space, neither the boundary nor the bulk symplectic forms are closed due to the symplectic flux of the bulk modes passing through the boundary. Furthermore, we demonstrate that the $D(D-3)/2+1$ dimensional Lagrangian submanifold of the bulk part of the solution phase space has a Carrollian structure, with the metric on the $D(D-3)/2$ dimensional part being the Wheeler-DeWitt metric, and the Carrollian kernel vector corresponding to the outgoing Robinson-Trautman gravitational wave solution.

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arXiv2023

Fluid/p-form duality

In this study, we demonstrate that an inviscid fluid in a near-equilibrium state, when viewed in the Lagrangian picture in d+1 spacetime dimensions, can be reformulated as a (d-1)-form gauge theory. We construct a fluid/p-form dictionary and show that volume-preserving diffeomorphisms on the fluid side manifest as a U(1) gauge symmetry on the {(p+1)-form} gauge theory side. {Intriguingly, Kelvin's circulation theorem and the mass continuity equation respectively appear as the Gauss law and the Bianchi identity on the gauge theory side.} Furthermore, we show that at the level of the sources, the vortices in the fluid side correspond to the p-branes in the gauge theory side. We also consider fluid mechanics in the presence of boundaries and examine the boundary symmetries and corresponding charges from both the fluid and gauge theory perspectives.

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