21,613 research outputs found
Geometry of the quantum universe
A universe much like the (Euclidean) de Sitter space-time appears as
background geometry in the causal dynamical triangulation (CDT) regularization
of quantum gravity. We study the geometry of such universes which appear in the
path integral as a function of the bare coupling constants of the theory.Comment: 19 pages, 7 figures. Typos corrected. Conclusions unchange
Black Holes as Quantum Gravity Condensates
We model spherically symmetric black holes within the group field theory
formalism for quantum gravity via generalised condensate states, involving sums
over arbitrarily refined graphs (dual to 3d triangulations). The construction
relies heavily on both the combinatorial tools of random tensor models and the
quantum geometric data of loop quantum gravity, both part of the group field
theory formalism. Armed with the detailed microscopic structure, we compute the
entropy associated with the black hole horizon, which turns out to be
equivalently the Boltzmann entropy of its microscopic degrees of freedom and
the entanglement entropy between the inside and outside regions. We recover the
area law under very general conditions, as well as the Bekenstein-Hawking
formula. The result is also shown to be generically independent of any specific
value of the Immirzi parameter.Comment: 22 page
Oscillating Shells and Oscillating Balls in AdS
It has recently been reported that certain thin timelike shells undergo
oscillatory motion in AdS. In this paper, we compute two-point function of a
probe field in the geodesic approximation in such an oscillating shell
background. We confirm that the two-point function exhibits an oscillatory
behaviour following the motion of the shell. We show that similar oscillatory
dynamics is possible when the perfect fluid on the shell has a polytropic
equation of state. Moreover, we show that certain ball like configurations in
AdS also exhibit oscillatory motion and comment on how such a solution can be
smoothly matched to an appropriate exterior solution. We also demonstrate that
the weak energy condition is satisfied for these oscillatory configurations.Comment: 23 pages, 5 figures; v2: refs added; v3: JHEP versio
Conoids and Hyperbolic Paraboloids in Le Corbusier’s Philips Pavilion
The Philips Pavilion at the Brussels World Fair is the first of Le Corbusier’s architectural works to connect the evolution of his mathematical thought on harmonic series and modular coordination with the idea of three-dimensional continuity. This propitious circumstance was the consequence of his collaboration with Iannis Xenakis, whose profound interest in mathematical structures was improved on his becaming acquainted with the Modulor, while at the same time Le Corbusier encountered double ruled quadric surfaces. For the Philips Pavilion—the Poème Électronic—Corbusier entrusted Xenakis with a “mathematical translation” of his sketches, which represented the volume of a rounded bottle with a stomach-shaped plan. The Pavilion was designed as if it were an orchestral work in which lights, loudspeakers, film projections on curved surfaces, spectators’ shadows and their expression of wonder, objects hanging from the ceiling and the containing space itself were all virtual instrument
Static and dynamic properties of shell-shaped condensates
Static, dynamic, and topological properties of hollow systems differ from
those that are fully filled as a result of the presence of a boundary
associated with an inner surface. Hollow Bose-Einstein condensates (BECs)
naturally occur in various ultracold atomic systems and possibly within neutron
stars but have hitherto not been experimentally realized in isolation on Earth
because of gravitational sag. Motivated by the expected first realization of
fully closed BEC shells in the microgravity conditions of the Cold Atomic
Laboratory aboard the International Space Station, we present a comprehensive
study of spherically symmetric hollow BECs as well as the hollowing transition
from a filled sphere BEC into a thin shell through central density depletion.
We employ complementary analytic and numerical techniques in order to study
equilibrium density profiles and the collective mode structures of condensate
shells hosted by a range of trapping potentials. We identify concrete and
robust signatures of the evolution from filled to hollow structures and the
effects of the emergence of an inner boundary, inclusive of a dip in
breathing-mode-type collective mode frequencies and a restructuring of surface
mode structure across the transition. By extending our analysis to a
two-dimensional transition of a disk to a ring, we show that the collective
mode signatures are an essential feature of hollowing, independent of the
specific geometry. Finally, we relate our work to past and ongoing experimental
efforts and consider the influence of gravity on thin condensate shells. We
identify the conditions under which gravitational sag is highly destructive and
study the mode-mixing effects of microgravity on the collective modes of these
shells.Comment: 26 pages, 13 figure
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