143 research outputs found
Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit
We report our rederivation of the equations of motion for relativistic
compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order
approximation to general relativity using the strong field point particle limit
to describe self-gravitating stars instead of the Dirac delta functional. The
computation is done in harmonic coordinates. Our equations of motion describe
the orbital motion of the binary consisting of spherically symmetric
non-rotating stars. The resulting equations of motion fully agree with the 3.5
PN equations of motion derived in the previous works. We also show that the
locally defined energy of the star has a simple relation with its mass up to
the 3.5 PN order.Comment: 38 pages, no figures. Accepted for publication in Phys. Rev.
Energy in ghost-free massive gravity theory
The detailed calculations of the energy in the ghost-free massive gravity
theory is presented. The energy is defined in the standard way within the
canonical approach, but to evaluate it requires resolving the Hamiltonian
constraints, which are known, in general, only implicitly. Fortunately, the
constraints can be explicitly obtained and resolved in the spherically
symmetric sector, which allows one to evaluate the energy. It turns out that
the energy is positive for globally regular and asymptotically flat fields
constituting the "physical sector" of the theory. In other cases the energy can
be negative and even unbounded from below, which suggests that the theory could
be still plagued with ghost instability. However, a detailed inspection reveals
that the corresponding solutions of the constraints are either not globally
regular or not asymptotically flat. Such solutions cannot describe initial data
triggering ghost instability of the physical sector. This allows one to
conjecture that the physical sector could actually be protected from the
instability by a potential barrier separating it from negative energy states.Comment: 35 pages, minor improvements, an appendix adde
Three dimensional numerical relativity: the evolution of black holes
We report on a new 3D numerical code designed to solve the Einstein equations
for general vacuum spacetimes. This code is based on the standard 3+1 approach
using cartesian coordinates. We discuss the numerical techniques used in
developing this code, and its performance on massively parallel and vector
supercomputers. As a test case, we present evolutions for the first 3D black
hole spacetimes. We identify a number of difficulties in evolving 3D black
holes and suggest approaches to overcome them. We show how special treatment of
the conformal factor can lead to more accurate evolution, and discuss
techniques we developed to handle black hole spacetimes in the absence of
symmetries. Many different slicing conditions are tested, including geodesic,
maximal, and various algebraic conditions on the lapse. With current
resolutions, limited by computer memory sizes, we show that with certain lapse
conditions we can evolve the black hole to about , where is the
black hole mass. Comparisons are made with results obtained by evolving
spherical initial black hole data sets with a 1D spherically symmetric code. We
also demonstrate that an ``apparent horizon locking shift'' can be used to
prevent the development of large gradients in the metric functions that result
from singularity avoiding time slicings. We compute the mass of the apparent
horizon in these spacetimes, and find that in many cases it can be conserved to
within about 5\% throughout the evolution with our techniques and current
resolution.Comment: 35 pages, LaTeX with RevTeX 3.0 macros. 27 postscript figures taking
7 MB of space, uuencoded and gz-compressed into a 2MB uufile. Also available
at http://jean-luc.ncsa.uiuc.edu/Papers/ and mpeg simulations at
http://jean-luc.ncsa.uiuc.edu/Movies/ Submitted to Physical Review
Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable
A quantization method based on replacement of c-number by c-number
parameterized by an unbiased hidden random variable is developed. In contrast
to canonical quantization, the replacement has straightforward physical
interpretation as statistical modification of classical dynamics of ensemble of
trajectories, and implies a unique operator ordering. We then apply the method
to develop quantum measurement without wave function collapse \'a la pilot-wave
theory.Comment: 14 pages, accepted in Physica
Transient analysis of arm locking controller
Arm locking is one of the key technologies to suppress the laser phase noise
in spaced-based gravitational waves observatories. Since arm locking was
proposed, phase margin criterion was always used as the fundamental design
strategy for the controller development. In this paper, we find that this
empirical method from engineering actually cannot guarantee the arm locking
stability. Therefore, most of the advanced arm locking controllers reported so
far may have instable problems. After comprehensive analysis of the single arm
locking's transient responses, strict analytical stability criterions are
summarized for the first time. These criterions are then generalized to dual
arm locking, modified-dual arm locking and common arm locking, and special
considerations for the design of arm locking controllers in different
architectures are also discussed. It is found that PI controllers can easily
meet our stability criterions in most of the arm locking systems. Using a
simple high gain PI controller, it is possible to suppress the laser phase
noise by 5 orders of magnitude within the science band. Our stability
criterions can also be used in other feedback systems, where several modules
with different delays are connected in parallel.Comment: 24 pages, 24 figure
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