4,259 research outputs found
Quasi-local rotating black holes in higher dimension: geometry
With a help of a generalized Raychaudhuri equation non-expanding null
surfaces are studied in arbitrarily dimensional case. The definition and basic
properties of non-expanding and isolated horizons known in the literature in
the 4 and 3 dimensional cases are generalized. A local description of horizon's
geometry is provided. The Zeroth Law of black hole thermodynamics is derived.
The constraints have a similar structure to that of the 4 dimensional spacetime
case. The geometry of a vacuum isolated horizon is determined by the induced
metric and the rotation 1-form potential, local generalizations of the area and
the angular momentum typically used in the stationary black hole solutions
case.Comment: 32 pages, RevTex
Bending branes for DCFT in two dimensions
We consider a holographic dual model for defect conformal field theories
(DCFT) in which we include the backreaction of the defect on the dual geometry.
In particular, we consider a dual gravity system in which a two-dimensional
hypersurface with matter fields, the brane, is embedded into a
three-dimensional asymptotically Anti-de Sitter spacetime. Motivated by recent
proposals for holographic duals of boundary conformal field theories (BCFT), we
assume the geometry of the brane to be determined by Israel junction
conditions. We show that these conditions are intimately related to the energy
conditions for the brane matter fields, and explain how these energy conditions
constrain the possible geometries. This has implications for the holographic
entanglement entropy in particular. Moreover, we give exact analytical
solutions for the case where the matter content of the brane is a perfect
fluid, which in a particular case corresponds to a free massless scalar field.
Finally, we describe how our results may be particularly useful for extending a
recent proposal for a holographic Kondo model.Comment: 35 pages + appendices, 12 figures, v2: added references and a
paragraph on negative tension solutions, v3: updated reference
Ambitoric geometry I: Einstein metrics and extremal ambikaehler structures
We present a local classification of conformally equivalent but oppositely
oriented 4-dimensional Kaehler metrics which are toric with respect to a common
2-torus action. In the generic case, these "ambitoric" structures have an
intriguing local geometry depending on a quadratic polynomial q and arbitrary
functions A and B of one variable.
We use this description to classify Einstein 4-metrics which are hermitian
with respect to both orientations, as well a class of solutions to the
Einstein-Maxwell equations including riemannian analogues of the
Plebanski-Demianski metrics. Our classification can be viewed as a riemannian
analogue of a result in relativity due to R. Debever, N. Kamran, and R.
McLenaghan, and is a natural extension of the classification of selfdual
Einstein hermitian 4-manifolds, obtained independently by R. Bryant and the
first and third authors.
These Einstein metrics are precisely the ambitoric structures with vanishing
Bach tensor, and thus have the property that the associated toric Kaehler
metrics are extremal (in the sense of E. Calabi). Our main results also
classify the latter, providing new examples of explicit extremal Kaehler
metrics. For both the Einstein-Maxwell and the extremal ambitoric structures, A
and B are quartic polynomials, but with different conditions on the
coefficients. In the sequel to this paper we consider global examples, and use
them to resolve the existence problem for extremal Kaehler metrics on toric
4-orbifolds with second betti number b2=2.Comment: 31 pages, 1 figure, partially replaces arXiv:1010.099
Geometry of Generic Isolated Horizons
Geometrical structures intrinsic to non-expanding, weakly isolated and
isolated horizons are analyzed and compared with structures which arise in
other contexts within general relativity, e.g., at null infinity. In
particular, we address in detail the issue of singling out the preferred
normals to these horizons required in various applications. This work provides
powerful tools to extract invariant, physical information from numerical
simulations of the near horizon, strong field geometry. While it complements
the previous analysis of laws governing the mechanics of weakly isolated
horizons, prior knowledge of those results is not assumed.Comment: 37 pages, REVTeX; Subsections V.B and V.C moved to a new Appenedix to
improve the flow of main argument
Multipole Moments of Isolated Horizons
To every axi-symmetric isolated horizon we associate two sets of numbers,
and with , representing its mass and angular
momentum multipoles. They provide a diffeomorphism invariant characterization
of the horizon geometry. Physically, they can be thought of as the `source
multipoles' of black holes in equilibrium. These structures have a variety of
potential applications ranging from equations of motion of black holes and
numerical relativity to quantum gravity.Comment: 25 pages, 1 figure. Minor typos corrected, reference adde
Inviolable energy conditions from entanglement inequalities
Via the AdS/CFT correspondence, fundamental constraints on the entanglement
structure of quantum systems translate to constraints on spacetime geometries
that must be satisfied in any consistent theory of quantum gravity. In this
paper, we investigate such constraints arising from strong subadditivity and
from the positivity and monotonicity of relative entropy in examples with
highly-symmetric spacetimes. Our results may be interpreted as a set of energy
conditions restricting the possible form of the stress-energy tensor in
consistent theories of Einstein gravity coupled to matter.Comment: 25 pages, 3 figures, v2: refs added, expanded discussion of strong
subadditivity constraints in sections 2.1 and 4.
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