Hyperbolic energy and Maskit gluings

We derive a formula for the energy of asymptotically locally hyperbolic (ALH) manifolds obtained by a gluing at infinity of two ALH manifolds. As an application we show that there exist three dimensional conformally compact ALH manifolds without boundary, with connected conformal infinity of higher genus, with constant negative scalar curvature and with negative mass.Comment: 43 pages, 7 figure

Warped Flatland

We study warped flat geometries in three-dimensional topologically massive gravity. They are quotients of global warped flat spacetime, whose isometries are given by the 2-dimensional centrally extended Poincar\'e algebra. The latter can be obtained as a certain scaling limit of Warped AdS3 space with a positive cosmological constant. We discuss the causal structure of the resulting spacetimes using projection diagrams. We study their charges and thermodynamics, together with asymptotic Killing vectors preserving a consistent set of boundary conditions including them. The asymptotic symmetry group is given by a Warped CFT algebra, with a vanishing current level. A generalization of the derivation of the Warped Cardy formula applies in this case, reproducing the entropy of the warped flat cosmological spacetimes.Comment: 44 pages, 4 figures, 1 Mathematica file, added clarifications, matches published versio

Near horizon boundary conditions for spin-3 gravity in flat space

The holographic principle proposes a solution to one of the most prominent problems of our time - the search for a consistent, quantized theory of gravity. According to this principle a theory of gravity in (d + 1) dimensions is equivalent to a quantum field theory (without gravity) in d dimensions. An important realization of this conjecture is the Anti-de-Sitter/conformal field theory (AdS/CFT) corre- spondence. However, since this correspondence is a strong-weak correspondence, it is hard to explicitly check the holographic principle by calculating observables on the field theory and the gravitational theory side. Conversely, higher-spin theories lead to weak-weak dualites, which can provide useful insights into aspects of the holographic principle [1-3]. Furthermore, since calculations in three dimensions may be done in the Chern-Simons formulation and are technically less challenging than in higher dimensions, it is often useful to restrict onself to three dimensions to clear up conceptional issues and obtain a better unde standing of the holographic principle. In this thesis, we construct a new set of boundary conditions for spin-3 gravity in three-dimensional flat space. This set of boundary conditions is inspired by the recent 'Soft Heisenberg hair'-proposal for Einstein gravity in three-dimensional Anti-de-Sitter space [4], which has subsequently been extended to flat space [5] and higher-spin gravity in AdS space [6]. In chapter 2 we discuss the peculiarities of restricting oneself to three dimensions and review the Chern- Simons formalism and the canonical analysis. In chapter 3 we discuss boundary conditions for gravity in three-dimensional AdS space and give a review of the Brown-Henneaux boundary conditions [7] and the near horizon boundary conditions proposed in [4]. In chapter 4 we motivate the respective near horizon boundary conditions for spin-3 gravity in three- dimensional flat space and compute the canonical boundary charges and the asymptotic symmetry algebra. As in previous, related work [4-6] the boundary conditions ensure regularity of the solutions (1) current independently of the charges. The asymptotic symmetry algebra is again given by a set of u algebras. We find that the vacuum descendants generated by the charges all have the same energy as the vacuum, i.e. they are higher-spin 'soft hair' in the sense of Hawking, Perry and Strominger [8]. Furthe more, we derive the entropy for solutions that are continuously connected to flat space cosmologies and find the same result as in the spin-2 case: the entropy is linear in the spin-2 zero-mode charges and inde- pendent from the spin-3 charges. Using twisted Sugawara-like constructions of the higher-spin currents we show that our simple result for entropy of higher-spin flat space cosmologies coincides precisely with the complicated earlier results expressed in terms of higher-spin zero-mode charges.7

Boundary conditions for extremal black holes from 2d gravity

We devise new boundary conditions for the near-horizon geometries of extremal BTZ and Kerr black holes, as well as for the ultra-cold limit of the Kerr-de Sitter black hole. These boundary conditions are obtained as the higher-dimensional uplift of recently proposed boundary conditions in two-dimensional gravity. Their asymptotic symmetries consist in the semi-direct product of a Virasoro and a current algebra, of which we determine the central extensions.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

New entropy formula for Kerr black holes

We introduce a new entropy formula for Kerr black holes inspired by recent results for 3-dimensional black holes and cosmologies with soft Heisenberg hair. We show that also Kerr–Taub–NUT black holes obey the same formula

New entropy formula for Kerr black holes

We introduce a new entropy formula for Kerr black holes inspired by recent results for 3-dimensional black holes and cosmologies with soft Heisenberg hair. We show that also Kerr–Taub–NUT black holes obey the same formula

Higher-spin flat space cosmologies with soft hair

We present and discuss near horizon boundary conditions for flat space higher-spin gravity in three dimensions. As in related work our boundary conditions ensure regularity of the solutions independently of the charges. The asymptotic symmetry algebra is given by a set of u(1) current algebras. The associated charges generate higher-spin soft hair. We derive the entropy for solutions that are continuously connected to flat space cosmologies and find the same result as in the spin-2 case: the entropy is linear in the spin-2 zero-mode charges and independent from the spin-3 charges. Using twisted Sugawara-like constructions of higher-spin currents we show that our simple result for entropy of higherspin flat space cosmologies coincides precisely with the complicated earlier results expressed in terms of higher-spin zero mode charges.SCOPUS: ar.jinfo:eu-repo/semantics/publishe