171 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.
Coordinates with Non-Singular Curvature for a Time Dependent Black Hole Horizon
A naive introduction of a dependency of the mass of a black hole on the
Schwarzschild time coordinate results in singular behavior of curvature
invariants at the horizon, violating expectations from complementarity. If
instead a temporal dependence is introduced in terms of a coordinate akin to
the river time representation, the Ricci scalar is nowhere singular away from
the origin. It is found that for a shrinking mass scale due to evaporation, the
null radial geodesics that generate the horizon are slightly displaced from the
coordinate singularity. In addition, a changing horizon scale significantly
alters the form of the coordinate singularity in diagonal (orthogonal) metric
coordinates representing the space-time. A Penrose diagram describing the
growth and evaporation of an example black hole is constructed to examine the
evolution of the coordinate singularity.Comment: 15 pages, 1 figure, additional citation
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.
Holomorphy, Minimal Homotopy and the 4D, N = 1 Supersymmetric Bardeen-Gross-Jackiw Anomaly
By use of a special homotopy operator, we present an explicit, closed-form
and simple expression for the left-right Bardeen-Gross-Jackiw anomalies
described as the proper superspace integral of a superfunction.Comment: 16 pp, LaTeX, Replacement includes addition comment on WZNW term and
one new referenc
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
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