4,558 research outputs found
An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
We present an introduction to dynamical trapping horizons as quasi-local
models for black hole horizons, from the perspective of an Initial Value
Problem approach to the construction of generic black hole spacetimes. We focus
on the geometric and structural properties of these horizons aiming, as a main
application, at the numerical evolution and analysis of black hole spacetimes
in astrophysical scenarios. In this setting, we discuss their dual role as an
"a priori" ingredient in certain formulations of Einstein equations and as an
"a posteriori" tool for the diagnosis of dynamical black hole spacetimes.
Complementary to the first-principles discussion of quasi-local horizon
physics, we place an emphasis on the "rigidity" properties of these
hypersurfaces and their role as privileged geometric probes into near-horizon
strong-field spacetime dynamics.Comment: 37 pages, 5 figures. Notes prepared for the course at the 2011
Shanghai Asia-Pacific School and Workshop on Gravitation (Shanghai Normal
University, February 10-14, 2011
Finite VEVs from a Large Distance Vacuum Wave Functional
We show how to compute vacuum expectation values from derivative expansions
of the vacuum wave functional. Such expansions appear to be valid only for
slowly varying fields, but by exploiting analyticity in a complex scale
parameter we can reconstruct the contribution from rapidly varying fields.Comment: 39 pages, 16 figures, LaTeX2e using package graphic
Bounds on area and charge for marginally trapped surfaces with cosmological constant
We sharpen the known inequalities and between the area and the electric charge of a stable marginally
outer trapped surface (MOTS) of genus g in the presence of a cosmological
constant . In particular, instead of requiring stability we include
the principal eigenvalue of the stability operator. For we obtain a lower and an upper bound for in terms of as well as the upper bound for the charge, which reduces to in the stable case . For
there remains only a lower bound on . In the spherically symmetric, static,
stable case one of the area inequalities is saturated iff the surface gravity
vanishes. We also discuss implications of our inequalities for "jumps" and
mergers of charged MOTS.Comment: minor corrections to previous version and to published versio
PT-symmetry from Lindblad dynamics in a linearized optomechanical system
We analyze a lossy linearized optomechanical system in the red-detuned regime under the rotating wave approximation. This so-called optomechanical state transfer protocol provides effective lossy frequency converter (quantum beam-splitter-like) dynamics where the strength of the coupling between the electromagnetic and mechanical modes is controlled by the optical steady-state amplitude. By restricting to a subspace with no losses, we argue that the transition from mode-hybridization in the strong coupling regime to the damped-dynamics in the weak coupling regime, is a signature of the passive parity-time (PT) symmetry breaking transition in the underlying non-Hermitian quantum dimer. We compare the dynamics generated by the quantum open system (Langevin or Lindblad) approach to that of the PT-symmetric Hamiltonian, to characterize the cases where the two are identical. Additionally, we numerically explore the evolution of separable and correlated number states at zero temperature as well as thermal initial state evolution at room temperature. Our results provide a pathway for realizing non-Hermitian Hamiltonians in optomechanical systems at a quantum level
Painlevé-II approach to binary black hole merger dynamics: universality from integrability
The binary black hole merger waveform is both simple and universal. Adoptingan effective asymptotic description of the dynamics, we aim at accounting forsuch universality in terms of underlying (effective) integrable structures.More specifically, under a ``wave-mean flow'' perspective, we propose that fastdegrees of freedom corresponding to the observed waveform would be subject toeffective linear dynamics, propagating on a slowly evolving background subjectto (effective) non-linear integrable dynamics. The Painlev\'e property of thelatter would be implemented in terms of the so-called Painlev\'e-IItranscendent, providing a structural link between i) orbital (in particular,EMRI) dynamics in the inspiral phase, ii) self-similar solutions of non-lineardispersive Korteweg-de Vries-like equations (namely, the `modified Korteweg-deVries' equation) through the merger and iii) the matching with the isospectralfeatures of black hole quasi-normal modes in late ringdown dynamics. Moreover,the Painlev\'e-II equation provides also a `non-linear turning point' problem,extending the linear discussion in the recently introduced Airy approach tobinary black hole merger waveforms. Under the proposed integrabilityperspective, the simplicity and universality of the binary black hole mergerwaveform would be accounted to by the `hidden symmetries' of the underlyingintegrable (effective) dynamics. In the spirit of asymptotic reasoning, andconsidering Ward's conjecture linking integrability and self-dual Yang-Millsstructures, it is tantalizing to question if such universal patterns wouldreflect the actual full integrability of a (self-dual) sector of generalrelativity, ultimately responsible for the binary black hole waveform patterns.<br
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