arXiv subjects

Javier Peraza

Publications and source records attributed to Javier Peraza.

15 recordsLinked to original sources

arXiv2026

Higher-spin algebras from soft theorems I: the wedge condition

In this article we use the sub$^n$-soft graviton theorems to construct the map $\Top$ from the spin-graded set of holomorphic functions on local celestial sphere patches to differential operators acting on the asymptotic data for massless particles at $\scrip$, in analogy with previous results in the literature for the sub$^n$-soft photon theorems. The result is an explicit closed-form formula. We show that the wedge subalgebras for both Yang-Mills and gravity are the natural domain on which $\Top$ becomes a representation.

hep-th↗

arXiv2026

Periodic Analogs of Multiple Black Holes Solutions

In this article, we extend the numerical studies developed in [arXiv:2210.12898] to construct periodic stationary axisymmetric solutions containing multiple horizons in each fundamental domain. As a direct application, we consider periodic stationary axisymmetric solutions with two identical equidistant counter-rotating horizons. These solutions can be parametrized by the period $L$, the mass $M$, and the absolute value of the angular momentum $|J| >0$. We provide strong numerical evidence for the existence of such configurations, without any restriction in terms of the distance between horizons. This is in sharp contrast with the non-zero total angular momentum case, as it was recently established in \cite{Peraza:2024uto} that static single-horizon periodic solutions cannot be put into rotation if $L < 4M$. It is shown that these solutions do not have any struts on the axis, and it is also explicitly shown that, by taking non-equidistant horizons, struts develop between the black holes. Other global properties of the solutions are also presented.

gr-qc↗

arXiv2025

Boundary Actions and Loop Groups: A Geometric Picture of Gauge Symmetries at Null Infinity

In previous work arXiv:2407.13556, we proposed an extended phase space structure at null infinity accommodating large gauge symmetries for sub$^n$-leading soft theorems in Yang-Mills, via dressing fields arising in the Stueckelberg procedure. Here, we give an explicit boundary action controlling the dynamics of these fields. This allows for a derivation from first principles of the associated charges, together with an explicit renormalization procedure when taking the limit to null and spatial infinity, matching with charges proposed in previous work. Using the language of fibre bundles, we relate the existence of Stueckelberg fields to the notion of extension/reduction of the structure group of a principal bundle, thereby deriving their transformation rules in a natural way, thus realising them as Goldstone-like objects. Finally, this allows us to give a geometric picture of the gauge transformation structure at the boundary, via a loop group coming from formal expansions in the coordinate transversal to the boundary.

hep-th↗

arXiv2025

Periodic Kerr solution as an infinite soliton chain

We combine numerical analysis with the inverse scattering method to study the periodic analog of Kerr solution. The periodic analog of the Schwarzschild solution is known to be regular and exhibit Kasner asymptotic behaviour for an arbitrary size of event horizon not exceeding the period. The previous numerical analysis of the rotating version of the periodic Schwarzschild black hole in [arXiv:2210.12898] based on the heat flow, together with analytical results in [arXiv:2407.16960] shows that there exist obstructions to putting the periodic Schwarzschild solution in rotation in a certain parameter range. In this paper we apply an efficient numerical approach based on the inverse scattering method, interpreting the periodic Kerr solution as an infinite chain of solitons. This allows to completely describe the existence domain in the space of physical parameters (the period, mass and the angular momentum); we study the dependence of Kasner exponent and the shape of the ergosphere on parameters of the problem.

gr-qc↗

arXiv2024

Static vacuum 3+1 black holes that cannot be put into stationary rotation

We prove that some of the static Myers/Korotkin-Nicolai (MKN) vacuum 3+1 static black holes cannot be put into stationary rotation. Namely, they cannot be deformed into axisymmetric stationary vacuum black holes with non-zero angular momentum. We also prove that this occurs in particular for those MKN solutions for which the distance along the axis between the two poles of the horizon is sufficiently small compared to the square root of its area. The MKN solutions, sometimes called periodic Schwarzschild, are physically regular, have no struts or singularities, but are asymptotically Kasner. The static rigidity presented here appears to be the first in the literature of General Relativity.

gr-qc↗

arXiv2024

Infinite-dimensional hierarchy of recursive extensions for all sub$^n$-leading soft effects in Yang-Mills

Building on our proposal in arXiv:2405.06629, we present in detail the construction of the extended phase space for Yang-Mills at null infinity, containing the asymptotic symmetries and the charges responsible for sub$^n$-leading soft theorems at all orders. The generality of the procedure allows it to be directly applied to the computation of both tree and loop-level soft limits. We also give a detailed study of Yang-Mills equations under the radial expansion, giving a thorough construction of the radiative phase space for decays compatible with tree-level amplitudes for both light-cone and radial gauges. This gives rise to useful recursion relations at all orders between the field strength and the vector gauge coefficients. We construct the sub$^n$-leading charges recursively, and show a hierarchical truncation such that each charge subalgebra is closed, and their action in the extended phase space is canonical. We relate these results with the infinite-dimensional algebras that have been recently introduced in the context of conformal field theories at null infinity. We also apply our method to the computation of non-universal terms in the sub-leading charges arising in theories with higher derivative interaction terms.

hep-th↗

arXiv2024

A General Hierarchy of Charges at Null Infinity via the Todd Polynomials

We give a general procedure for constructing an extended phase space for Yang-Mills theory at null infinity, capable of handling the asymptotic symmetries and construction of charges responsible for sub$^n$-leading soft theorems at all orders. The procedure is coordinate and gauge-choice independent, and can be fed into the calculation of both tree and loop-level soft limits. We find a hierarchy in the extended phase space controlled by the Bernoulli numbers arising in Todd genus computations. We give an explicit example of a calculation at tree level, in radial gauge, where we also uncover recursion relations at all orders for the equations of motion and charges.

hep-th↗

arXiv2023

Renormalized electric and magnetic charges for $O(r^n)$ large gauge symmetries

In this work we present the construction of a renormalized symplectic form on an extended phases space where the higher order large gauge transformations act canonically. The expressions of the sub$^n$-leading electric charges associated to each $O(r^n)$ LGT are then obtained, in agreement with the expressions previously proposed in arXiv:1810.04619 by means of the tree-level sub$^n$-leading formulas. We also present the duality extension of the extended phase space, computing the full electromagnetic charge algebra, showing a tower of central extensions.

hep-th↗

arXiv2022

Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity

Working in the self-dual sector for Yang-Mills and gravity, we show how to construct an extended phase space at null infinity, to all orders in the radial expansion. This formalises the symmetry origin of the infrared behaviour of these theories to all sub-leading orders. As a corollary, we also derive a double copy mapping from a subset of YM gauge transformations to a subset of diffeomorphisms to all orders in the transformation parameters, which to our knowledge has not been presented before in the literature.

hep-th↗

arXiv2022

Periodic analogues of the Kerr solutions: a numerical study

In recent years black hole configurations with non standard topology or with non-standard asymptotic have gained considerable attention. In this article we carry out numerical investigations aimed to find periodic coaxial configurations of co-rotating 3+1 vacuum black holes, for which existence and uniqueness has not yet been theoretically proven. The aimed configurations would extend Myers/Korotkin-Nicolai's family of non-rotating (static) coaxial arrays of black holes. We find that numerical solutions with a given value for the area A and for the angular momentum J of the horizons appear to exist only when the separation between consecutive horizons is larger than a certain critical value that depends only on A and |J|. We also establish that the solutions have the same Lewis's cylindrical asymptotic as Stockum's infinite rotating cylinders. Below the mentioned critical value the rotational energy appears to be too big to sustain a global equilibrium and a singularity shows up at a finite distance from the bulk. This phenomenon is a relative of Stockum's asymptotic's collapse, manifesting when the angular momentum (per unit of axial length) reaches a critical value compared to the mass (per unit of axial length), and that results from a transition in the Lewis's class of the cylindrical exterior solution. This remarkable phenomenon seems to be unexplored in the context of coaxial arrays of black holes. Ergospheres and other global properties are also presented in detail.

gr-qc↗

arXiv2022

Lie algebras of curves and loop-bundles on surfaces

W. Goldman and V. Turaev defined a Lie bialgebra structure on the $\mathbb Z$-module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes of its fundamental group). We develop a generalization of this construction replacing homotopies by thin homotopies, based on the combinatorial approach given by M. Chas. We use it to give a geometric proof of a characterization of simple curves in terms of the Goldman-Turaev bracket, which was conjectured by Chas.

math.GT↗

arXiv2021

Charge algebra for non-abelian large gauge symmetries at $O(r)$

Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are $O(1)$ in the large $r$ expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with $O(r)$ gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with $O(r)$ gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which $O(1)$ and $O(r)$ charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.

hep-th↗

arXiv2020

On the classical and quantum Geroch group

The Geroch group is an infinite dimensional transitive group of symmetries of classical cylindrically symmetric gravitational waves which acts by non-canonical transformations on the phase space of these waves. Here this symmetry is rederived and the unique Poisson bracket on the Geroch group which makes its action on the gravitational phase space Lie-Poisson is obtained. Two possible notions of asymptotic flatness are proposed that are compatible with the Poisson bracket on the phase space, and corresponding asymptotic flatness preserving subgroups of the Geroch group are defined which turn out to be compatible with the Poisson bracket on the group. A quantization of the Geroch group is proposed that is similar to, but distinct from, the $\mathfrak{sl}_2$ Yangian, and a certain action of this quantum Geroch group on gravitational observables is shown to preserve the commutation relations of Korotkin and Samtleben's quantization of asymptotically flat cylindrically symmetric gravitational waves. The action also preserves three of the additional conditions that define their quantization. It is conjectured that the action preserves the remaining two conditions (asymptotic flatness and a unit determinant condition on a certain basic field) as well and is, in fact, a symmetry of their model. Our results on the quantum theory are formal, but a possible rigorous formulation based on algebraic quantum theory is outlined.

gr-qc↗

arXiv2020

Generalized BMS charge algebra

It has been argued that the symmetries of gravity at null infinity should include a Diff$(S^2)$ factor associated to diffeomorphisms on the celestial sphere. However, the standard phase space of gravity does not support the action of such transformations. Building on earlier work by Laddha and one of the authors, we present an extension of the phase space of gravity at null infinity on which Diff$(S^2)$ acts canonically. The Poisson brackets of supertranslation and Diff$(S^2)$ charges reproduce the generalized BMS algebra introduced in arXiv:1408.2228 .

gr-qc↗

arXiv2019

A complete classification of S1-symmetric static vacuum black holes

In a seminal paper of 1917, H. Weyl presented a remarkable reduction of the static axisymmetric vacuum Einstein equations, serving as a relatively straightforward technique to generate and explore new solutions. Weyl's reduction was used by Myers in 1987, and independently by Korotkin-Nicolai in 1994, to construct a new family of static and axisymmetric solutions with compact non-empty horizon, however with non-trivial topology and asymptotically Kasner. This family, together with the Schwarzschild and the Boost families, remained until now as the only known S1-symmetric static black hole solutions, namely, (metrically complete) S1-symmetric static vacuum solutions with compact and non-empty horizon. In this article we prove that, indeed, these three families exhaust all the examples of S1-symmetric static vacuum black holes.

gr-qc↗