arXiv subjects

Carlos Peón-Nieto

Publications and source records attributed to Carlos Peón-Nieto.

8 recordsLinked to original sources

arXiv2026

Asymptotics of Killing horizons: A Characterization in de Sitter Spacetime

We prove that (n + 1)-dimensional de Sitter spacetime is locally the unique $(Λ> 0)$-vacuum spacetime whose Killing horizons intersect the conformal boundary $\mathscr{I}$. The intersection occurs at the isolated essential zeros of the extension of the Killing vector field to $\mathscr{I}$. We then reconstruct all de Sitter Killing vector fields from their boundary value and obtain a characterization of those admitting a Killing horizon in terms of a conformal invariant $σ$: $σ<0$ characterizes non-degenerate bifurcate horizons, whereas $σ= 0$ yields degenerate non-bifurcate horizons. Finally, we derive an intrinsic, conformally invariant formula for the surface gravity of the horizons in de Sitter, $κ^2 = |σ|$.

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arXiv2025

Conformal Einstein equation and symplectic flux with a positive cosmological constant

We analyze the conformal Einstein equation with a positive cosmological constant to extract fall-off conditions of the gravitational fields. The fall-off conditions are consistent with a finite, non-trivial presymplectic current on the future boundary of de Sitter. Hence our result allows a non-zero gravitational flux across the boundary of the de Sitter. We present an explicit gauge-free computation to show that the Gibbons-Hawking boundary term, counterterm in the action, and fall-off condition of gravitational field in conformal Einstein equation are crucial to reproduce the finite symplectic flux.

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arXiv2025

Classification of $Λ\neq 0$-vacuum algebraically special spacetimes with conformally flat $\mathscr I$ from Weyl tensor expansion

We introduce a general algebraic decomposition of Riemann-like and Weyl-like tensors with respect to a non-null vector $u$. We derive Gauss, Codazzi and Ricci-type identities for the Weyl tensor, that allow to relate the components of the spacetime Weyl tensor with intrinsic quantities of the hypersurfaces orthogonal to $u$. Restricting to the case of $Λ$-vacuum spacetimes (with $Λ\neq 0$ and any dimension) admiting a conformal compactification, we then study the behaviour of the Weyl tensor near $\mathscr I$ by means of an asymptotic expansion {\it à la} Fefferman-Graham, where the first terms are explicitly computed. We use these tools to characterize four dimensional algebraically special spacetimes with locally conformally flat $\mathscr{I}$, showing they match exactly the so-called {\it Kerr-de Sitter-like class with conformally flat $\scri$}, thus providing a geometric characterization of this class of spacetimes.

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arXiv2022

Covariant classification of conformal Killing vectors of locally conformally flat $n$-manifolds with an application to Kerr-de Sitter

We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $γ$ of signature $(r,s)$ modulo conformal transformations of $γ$. This is done in terms of endomorphisms in the pseudo-orthogonal Lie algebra $\mathfrak{o}(r+1,s+1)$ up to conjugation of the its group $O(r+1,s+1)$. The explicit classification is worked out in full for the Riemannian $γ$ case ($r = 0, s = n$). As an application of this result, we prove that the set of five dimensional, $(Λ>0)$-vacuum, algebraically special metrics with non-degenerate optical matrix, previously studied by Bernardi de Freitas, Godazgar and Reall, is in one-to-one correspondence with the metrics in the Kerr-de Sitter-like class. This class exists in all dimensions and its defining properties involve only properties at $\mathscr{I}$. The equivalence between two seemingly unrelated classes of metrics points towards interesting connections between the algebraically special type of the bulk spacetime and the conformal geometry at null infinity

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arXiv2021

Free data at spacelike $\mathscr{I}$ and characterization of Kerr-de Sitter in all dimensions

We study the free data in the Fefferman-Graham expansion of asymptotically Einstein metrics with non-zero cosmological constant. We prove that if $\mathscr{I}$ is conformally flat, the rescaled Weyl tensor at $\mathscr{I}$ agrees up to a constant with the free data at $\mathscr{I}$ , namely the traceless part of the $n$-th order coefficient of the expansion. In the non-conformally flat case, the rescaled Weyl tensor is generically divergent at $\mathscr{I}$ but one can still extract the free data in terms of the difference of the Weyl tensors of suitably constructed metrics, in full generality when the spacetime dimension $D$ is even and provided the so-called obstruction tensor at $\mathscr{I}$ is identically zero when $D$ is odd. These results provide a geometric definition of the data, particularly relevant for the asymptotic Cauchy problem of even dimensional Einstein metrics with positive $Λ$ and also for the odd dimensional analytic case irrespectively of the sign of $Λ$. We establish a Killing initial data equation at spacelike $\mathscr{I}$ in all dimension for analytic data. These results are used to find a geometric characterization of the Kerr-de Sitter metrics in all dimensions in terms of its geometric data at null infinity.

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arXiv2021

Classification of Kerr-de Sitter-like spacetimes with conformally flat $\mathscr{I}$ in all dimensions

Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat $\mathscr{I}$. Kerr-Schild-de Sitter are spacetimes of Kerr-Schild form with de Sitter background that solve the $(Λ>0)$-vacuum Einstein equations and admit a smooth conformal compactification sharing $\mathscr{I}$ with the background metric. Kerr-de Sitter-like metrics with conformally flat $\mathscr{I}$ are a generalization of the Kerr-de Sitter metrics, defined originally in four spacetime dimensions and extended here to all dimensions in terms of their initial data at null infinity. We explicitly construct all metrics in this class as limits or analytic extensions of Kerr-de Sitter. The structure of limits is inferred from corresponding limits of the asymptotic data, which appear to be hard to guess from the spacetime metrics.

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arXiv2020

Skew-symmetric endomorphisms in $\mathbb{M}^{1,n}$: A unified canonical form with applications to conformal geometry

We show the existence of families of orthonormal, future directed bases which allow to cast every skew-symmetric endomorphism of $\mathbb{M}^{1,n}$ ($\mathrm{SkewEnd}(\mathbb{M}^{1,n})$) in a single canonical form depending on a minimal number of parameters. This canonical form is shared by every pair of elements in $\mathrm{SkewEnd}(\mathbb{M}^{1,n})$ differing by an orthochronous Lorentz transformation, i.e. it defines the orbits of the orthochronous Lorentz group under the adjoint action on its algebra. Using this form, we obtain the quotient topology of $\mathrm{SkewEnd}(\mathbb{M}^{1,n})/O^+(1,n)$. From known relations between $\mathrm{SkewEnd}(\mathbb{M}^{1,n})$ and the conformal Killing vector fields (CKVFs) of the sphere $\mathbb{S}^n$, a canonical form for CKVFs follows immediately. This form is used to find adapted coordinates to an arbitrary CKVF that covers all cases at the same time. We do the calculation for even $n$ and obtain the case of odd $n$ as a consequence. Finally, we employ the adapted coordinates to obtain a wide class of TT-tensors for $n=3$, which provide Cauchy data at conformally flat null infinity $\mathscr{I}$. Specifically, this class of data is characterized for generating $Λ>0$-vacuum spacetimes with two-symmetries, one of which axial, admitting a conformally flat $\mathscr{I}$. The class of data is infinite dimensional, depending on two arbitrary functions of one variable as well as a number of constants. Moreover, it contains the data for the Kerr-de Sitter spacetime, which we explicitly identify within.

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arXiv2020

Skew-symmetric endomorphisms in $\mathbb{M}^{1,3}$: A unified canonical form with applications to conformal geometry

We derive a canonical form for skew-symmetric endomorphisms $F$ in Lorentzian vector spaces of dimension three and four which covers all non-trivial cases at once. We analyze its invariance group, as well as the connection of this canonical form with duality rotations of two-forms. After reviewing the relation between these endomorphisms and the algebra of conformal Killing vectors of $\mathbb{S}^2$, $\mathrm{CKill}(\mathbb{S}^2)$, we are able to also give a canonical form for an arbitrary element $ ξ\in \mathrm{CKill}(\mathbb{S}^2)$ along with its invariance group. The construction allows us to obtain explicitly the change of basis that transforms any given $F$ into its canonical form. For any non-trivial $ ξ$ we construct, via its canonical form, adapted coordinates that allow us to study its properties in depth. Two applications are worked out: we determine explicitly for which metrics, among a natural class of spaces of constant curvature, a given $ξ$ is a Killing vector and solve all local TT (traceless and transverse) tensors that satisfy the Killing Initial Data equation for $ξ$. In addition to their own interest, the present results will be a basic ingredient for a subsequent generalization to arbitrary dimensions.

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