The asymptotic structure of three-dimensional Carroll gravity with negative cosmological constant is studied. We formulate a consistent set of boundary conditions preserved by an infinite-dimensional extension of the AdS Carroll algebra, which turns out to be isomorphic to a precise generalized BMS algebra. This is described by four independent functions of the circle at infinity, generating spatial superrotations, Carroll superboosts, spatial supertranslations and time supertranslations. Remarkably, this asymptotic symmetry algebra contains as subalgebras to BMS (generated by spatial superrotations and time supertranslations) and the two-dimensional conformal algebra (spanned by spatial superrotations and spatial supertranslations). We also introduce a new solution — endowed with a Carroll extremal surface — that fulfills this set of asymptotic conditions. By taking advantage of the Chern-Simons formulation of the theory, Carroll thermal properties, obtained from regularity conditions, and entropy of the configuration are also addressed.

Chile

Luis Avilés

Belgium

Oscar Fuentealba

Iceland

Diego Hidalgo

Pablo Rodríguez

The conformal symmetry algebra in 2D (Diff(S 1)⊕Diff(S 1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, T and   <math> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \overline{T} $$ , closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS3 becomes a bona fide symmetry once the CFT2 is marginally deformed by the addition of a   <math> <msqrt> <mrow> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </mrow> </msqrt> </math>  $$ \sqrt{T\overline{T}} $$  term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT2 because its energy and momentum densities fulfill the BMS3 algebra. The deformation can also be described through the original CFT2 on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to T and   <math> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ \overline{T} $$ . BMS3 symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of N free bosons, which coincides with ultra-relativistic limits only for N = 1. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS3 (or flat) versions.

David Tempo

Ricardo Troncoso

Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite   <math> <msqrt> <mrow> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </mrow> </msqrt> </math>  $$ \sqrt{T\overline{T}} $$  deformations

The thermodynamic properties of the Bañados-Teitelboim-Zanelli black hole endowed with Korteweg–de Vries (KdV)-type boundary conditions are reconsidered. This family of boundary conditions is labeled by a non-negative integer <math><mi>n</mi></math>, and gives rise to a dual theory which possesses anisotropic Lifshitz scaling invariance with dynamical exponent <math><mi>z</mi><mo>=</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></math>. We show that from the scale invariance of the action for stationary and circularly symmetric spacetimes, an anisotropic version of the Smarr relation arises. Finally, we analyze the global and local thermal stability of the system and we found that the specific heat of the black hole is positive for all possible values of <math><mi>z</mi></math>, and at the self-dual temperature <math><msub><mi>T</mi><mi>s</mi></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>π</mi></mrow></mfrac><mo>(</mo><mfrac><mn>1</mn><mi>z</mi></mfrac><msup><mo>)</mo><mfrac><mi>z</mi><mrow><mi>z</mi><mo>+</mo><mn>1</mn></mrow></mfrac></msup></math>, there is a Hawking-Page phase transition between the BTZ black hole and thermal <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> spacetime.

Greece

Cristián Erices

Miguel Riquelme

BTZ black hole with Korteweg–de Vries-type boundary conditions: Thermodynamics revisited

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions.

Javier Matulich

Alfredo Pérez

Miguel Pino

Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

In this paper we study relativistic static traversable wormhole solutions which are a slight generalization of Schwarzschild wormholes. In order to do this we assume a shape function with a linear dependence on the radial coordinate r . This linear shape function generates wormholes whose asymptotic spacetime is not flat: they are asymptotically locally flat, since in the asymptotic limit r→∞ spacetimes exhibiting a solid angle deficit (or excess) are obtained. In particular, there exist wormholes which connect two asymptotically non-flat regions with a solid angle deficit. For these wormholes the size of their embeddings in a three-dimensional Euclidean space extends from the throat to infinity. A new phantom zero-tidal-force wormhole exhibiting such asymptotic is obtained. On the other hand, if a solid angle excess is present, the size of the wormhole embeddings depends on the amount of this angle excess, and the energy density is negative everywhere. We discuss the traversability conditions and study the impact of the β -parameter on the motion of a traveler when the wormhole throat is crossed. A description of the geodesic behavior for the wormholes obtained is also presented.

Mauricio Cataldo

Luis Liempi

Traversable Schwarzschild-like wormholes

In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p=ωρ for the isotropic pressure, independently of the form of the redshift function ϕ(r) . We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.