Carlos Peon Nieto

• University of Salamanca

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...

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 o(r+1,s+1) up to conjugation of the group O(r+1,s+1). The explicit classificat...

We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $\gamma$ of signature $(r,s)$ modulo conformal transformations of $\gamma$. 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 $...

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 I. Kerr-Schild–de Sitter are spacetimes of Kerr-Schild form with de Sitter background that solve the (Λ>0)-vacuum Einste...

We study the free data in the Fefferman–Graham expansion of asymptotically Einstein $$(n+1)$$ ( n + 1 ) -dimensional metrics with non-zero cosmological constant. We analyze the relation between the electric part of the rescaled Weyl tensor at $${\mathscr {I}}$$ I , D , and the free data at $${\mathscr {I}}$$ I , namely a certain traceless and trans...

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 $(\Lamb...

We show the existence of families of orthonormal, future directed bases which allow to cast every skew-symmetric endomorphism of ${\mathbb{M}}^{1,n}$ ( $\mathrm{S}\mathrm{k}\mathrm{e}\mathrm{w}\mathrm{E}\mathrm{n}\mathrm{d}\left({\mathbb{M}}^{1,n}\right)$ ) in a single canonical form depending on a minimal number of parameters. This canonical form...

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...

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 alge...

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,...

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 al...

We propose localization measures in phase space of the ground state of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu=2/\lambda$, to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary $U(4)$-isospin $\lambda$. We use a coherent state (Bargmann) representation of quantum states, as...

We propose localization measures in phase space of the ground state of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu=2/\lambda$, to characterize the three quantum phases (shortly denoted by spin, canted and ppin) for arbitrary $U(4)$-isospin $\lambda$. We use a coherent state (Bargmann) representation of quantum states, as...

We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu=2/\lambda$ and we also study the large $SU(4)$ isospin-$\lambda$ limit. The model Hamiltonian is an adaptation of the $\nu=2$ case [Phys. Rev. B71 (2005) 125318] to the many-body situation (arbitrary $\lambda$ flux quant...

We analyze the Hilbert space and ground state structure of bilayer quantum Hall (BLQH) systems at fractional filling factors $\nu=2/\lambda$ ($\lambda$ odd) and we also study the large $SU(4)$ isospin-$\lambda$ limit. The model Hamiltonian is an adaptation of the $\nu=2$ case [Z.F. Ezawa {\it et al.}, Phys. Rev. {B71} (2005) 125318] to the many-bod...

We revise the subject of -component fractional quantum Hall systems and its field-theoretic description in terms of -invariant nonlinear sigma models under a group-theoretical perspective. The Berry Lagrangian, which determines the dynamics and encodes the quantum commutation relations for the order parameter, is quantized and the Hilbert space is...