238 research outputs found
Global aspects of radiation memory
Gravitational radiation has a memory effect represented by a net change in
the relative positions of test particles. Both the linear and nonlinear sources
proposed for this radiation memory are of the "electric" type, or E mode, as
characterized by the even parity of the polarization pattern. Although
"magnetic" type, or B mode, radiation memory is mathematically possible, no
physically realistic source has been identified. There is an electromagnetic
counterpart to radiation memory in which the velocity of charged particles
obtain a net "kick". Again, the physically realistic sources of electromagnetic
radiation memory that have been identified are of the electric type. In this
paper, a global null cone description of the electromagnetic field is applied
to establish the non-existence of B mode radiation memory and the non-existence
of E mode radiation memory due to a bound charge distribution.Comment: Final version to be published in Class. Quantum Gra
The affine-null metric formulation of Einstein's equations
The details are presented of a new evolution algorithm for the characteristic
initial-boundary value problem based upon an affine parameter rather than the
areal radial coordinate used in the Bondi-Sachs formulation. The advantages
over the Bondi-Sachs version are discussed, with particular emphasis on the
application to the characteristic extraction of the gravitational waveform from
Cauchy simulations of general relativistic astrophysical systems.Comment: Version to appear in Physical Review
Spectral Cauchy Characteristic Extraction of strain, news and gravitational radiation flux
We present a new approach for the Cauchy-characteristic extraction of
gravitational radiation strain, news function, and the flux of the
energy-momentum, supermomentum and angular momentum associated with the
Bondi-Metzner-Sachs asymptotic symmetries. In Cauchy-characteristic extraction,
a characteristic evolution code takes numerical data on an inner worldtube
supplied by a Cauchy evolution code, and propagates it outwards to obtain the
space-time metric in a neighborhood of null infinity. The metric is first
determined in a scrambled form in terms of coordinates determined by the Cauchy
formalism. In prior treatments, the waveform is first extracted from this
metric and then transformed into an asymptotic inertial coordinate system. This
procedure provides the physically proper description of the waveform and the
radiated energy but it does not generalize to determine the flux of angular
momentum or supermomentum. Here we formulate and implement a new approach which
transforms the full metric into an asymptotic inertial frame and provides a
uniform treatment of all the radiation fluxes associated with the asymptotic
symmetries. Computations are performed and calibrated using the Spectral
Einstein Code (SpEC).Comment: 30 pages, 17 figure
Book Review : The Universe. Visions and Perspectives
I review the collection of essays which the editors Naresh Dadich and Ajit Kembhavi have assembled as a festschrift to honor Jayant Narlikar
The Merger of Small and Large Black Holes
We present simulations of binary black holes mergers in which, after the
common outer horizon has formed, the marginally outer trapped surfaces (MOTSs)
corresponding to the individual black holes continue to approach and eventually
penetrate each other. This has very interesting consequences according to
recent results in the theory of MOTSs. Uniqueness and stability theorems imply
that two MOTSs which touch with a common outer normal must be identical. This
suggests a possible dramatic consequence of the collision between a small and
large black hole. If the penetration were to continue to completion then the
two MOTSs would have to coalesce, by some combination of the small one growing
and the big one shrinking. Here we explore the relationship between theory and
numerical simulations, in which a small black hole has halfway penetrated a
large one.Comment: 17 pages, 11 figure
Testing the well-posedness of characteristic evolution of scalar waves
Recent results have revealed a critical way in which lower order terms affect
the well-posedness of the characteristic initial value problem for the scalar
wave equation. The proper choice of such terms can make the Cauchy problem for
scalar waves well posed even on a background spacetime with closed lightlike
curves. These results provide new guidance for developing stable characteristic
evolution algorithms. In this regard, we present here the finite difference
version of these recent results and implement them in a stable evolution code.
We describe test results which validate the code and exhibit some of the
interesting features due to the lower order terms.Comment: 22 pages, 15 figures Submitted to CQ
Boundary conditions for coupled quasilinear wave equations with application to isolated systems
We consider the initial-boundary value problem for systems of quasilinear
wave equations on domains of the form , where is
a compact manifold with smooth boundaries . By using an
appropriate reduction to a first order symmetric hyperbolic system with maximal
dissipative boundary conditions, well posedness of such problems is established
for a large class of boundary conditions on . We show that our
class of boundary conditions is sufficiently general to allow for a well posed
formulation for different wave problems in the presence of constraints and
artificial, nonreflecting boundaries, including Maxwell's equations in the
Lorentz gauge and Einstein's gravitational equations in harmonic coordinates.
Our results should also be useful for obtaining stable finite-difference
discretizations for such problems.Comment: 22 pages, no figure
An explicit harmonic code for black-hole evolution using excision
We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the well-posedness and numerical stability of the initial-boundary problem for the quasilinear wave equation. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code. Such tests range from the evolution of isolated black holes to the head-on collision of two black holes and then to a binary black hole inspiral and merger. Besides assessing the accuracy of the code, the inspiral and merger test has revealed that individual apparent horizons can touch and even intersect. This novel feature in the dynamics of the marginally trapped surfaces is unexpected but consistent with theorems on the properties of apparent horizons
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