97 research outputs found
Bondi-Sachs Energy-Momentum for the CMC Initial Value Problem
The constraints on the asymptotic behavior of the conformal factor and
conformal extrinsic curvature imposed by the initial value equations of general
relativity on constant mean extrinsic curvature (CMC) hypersurfaces are
analyzed in detail. We derive explicit formulas for the Bondi-Sachs energy and
momentum in terms of coefficients of asymptotic expansions on CMC hypersurfaces
near future null infinity. Precise numerical results for the Bondi-Sachs
energy, momentum, and angular momentum are used to interpret physically
Bowen-York solutions of the initial value equations on conformally flat CMC
hypersurfaces of the type obtained earlier by Buchman et al. [Phys. Rev. D
80:084024 (2009)].Comment: version to be published in Phys. Rev.
Black hole initial data on hyperboloidal slices
We generalize Bowen-York black hole initial data to hyperboloidal constant
mean curvature slices which extend to future null infinity. We solve this
initial value problem numerically for several cases, including unequal mass
binary black holes with spins and boosts. The singularity at null infinity in
the Hamiltonian constraint associated with a constant mean curvature
hypersurface does not pose any particular difficulties. The inner boundaries of
our slices are minimal surfaces. Trumpet configurations are explored both
analytically and numerically.Comment: version for publication in Phys. Rev.
Radiation fields in the Schwarzschild background
Scalar, electromagnetic, and gravitational test fields in the Schwarzschild background are examined with the help of the general retarded solution of a single master wave equation. The solution for each multipole is generated by a single arbitrary function of retarded time, the retarded multipole moment. We impose only those restrictions on the time dependence of the multipole moment which are required for physical regularity. We find physically well-behaved solutions which (i) do not satisfy the Penrose peeling theorems at past null infinity and/or (ii) do not have well-defined Newman-Penrose quantities. Even when the NP quantities exist, they are not measurable; they represent an "average" multipole moment over the infinite past, and their conservation is essentially trivial
Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
We present a new evolution system for Einstein's field equations which is
based on tetrad fields and conformally compactified hyperboloidal spatial
hypersurfaces which reach future null infinity. The boost freedom in the choice
of the tetrad is fixed by requiring that its timelike leg be orthogonal to the
foliation, which consists of constant mean curvature slices. The rotational
freedom in the tetrad is fixed by the 3D Nester gauge. With these conditions,
the field equations reduce naturally to a first-order constrained symmetric
hyperbolic evolution system which is coupled to elliptic equations for the
gauge variables. The conformally rescaled equations are given explicitly, and
their regularity at future null infinity is discussed. Our formulation is
potentially useful for high accuracy numerical modeling of gravitational
radiation emitted by inspiraling and merging black hole binaries and other
highly relativistic isolated systems.Comment: Corrected factor of 2 errors in Eqs. (A8) and (A9) and a few typos;
final versio
The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
We study the near horizon limit of a four dimensional extreme rotating black
hole. The limiting metric is a completely nonsingular vacuum solution, with an
enhanced symmetry group SL(2,R) x U(1). We show that many of the properties of
this solution are similar to the AdS_2 x S^2 geometry arising in the near
horizon limit of extreme charged black holes. In particular, the boundary at
infinity is a timelike surface. This suggests the possibility of a dual quantum
mechanical description. A five dimensional generalization is also discussed.Comment: 21 page
Andreev Reflections in Micrometer-Scale Normal-Insulator-Superconductor Tunnel Junctions
Understanding the subgap behavior of Normal-Insulator-Superconductor (NIS)
tunnel junctions is important in order to be able to accurately model the
thermal properties of the junctions. Hekking and Nazarov developed a theory in
which NIS subgap current in thin-film structures can be modeled by multiple
Andreev reflections. In their theory, the current due to Andreev reflections
depends on the junction area and the junction resistance area product. We have
measured the current due to Andreev reflections in NIS tunnel junctions for
various junction sizes and junction resistance area products and found that the
multiple reflection theory is in agreement with our data
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