6,744 research outputs found

### Metric perturbations from eccentric orbits on a Schwarzschild black hole: I. Odd-parity Regge-Wheeler to Lorenz gauge transformation and two new methods to circumvent the Gibbs phenomenon

We calculate the odd-parity, radiative ($\ell \ge 2$) parts of the metric
perturbation in Lorenz gauge caused by a small compact object in eccentric
orbit about a Schwarzschild black hole. The Lorenz gauge solution is found via
gauge transformation from a corresponding one in Regge-Wheeler gauge. Like the
Regge-Wheeler gauge solution itself, the gauge generator is computed in the
frequency domain and transferred to the time domain. The wave equation for the
gauge generator has a source with a compact, moving delta-function term and a
discontinuous non-compact term. The former term allows the method of extended
homogeneous solutions to be applied (which circumvents the Gibbs phenomenon).
The latter has required the development of new means to use frequency domain
methods and yet be able to transfer to the time domain while avoiding Gibbs
problems. Two new methods are developed to achieve this: a partial annihilator
method and a method of extended particular solutions. We detail these methods
and show their application in calculating the odd-parity gauge generator and
Lorenz gauge metric perturbations. A subsequent paper will apply these methods
to the harder task of computing the even-parity parts of the gauge generator.Comment: 17 pages, 9 figures, Updated with one modified figure and minor
changes to the text. Added DOI and Journal referenc

### Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole

We calculate the gravitational perturbations produced by a small mass in
eccentric orbit about a much more massive Schwarzschild black hole and use the
numerically computed perturbations to solve for the metric. The calculations
are initially made in the frequency domain and provide Fourier-harmonic modes
for the gauge-invariant master functions that satisfy inhomogeneous versions of
the Regge-Wheeler and Zerilli equations. These gravitational master equations
have specific singular sources containing both delta function and
derivative-of-delta function terms. We demonstrate in this paper successful
application of the method of extended homogeneous solutions, developed recently
by Barack, Ori, and Sago, to handle source terms of this type. The method
allows transformation back to the time domain, with exponential convergence of
the partial mode sums that represent the field. This rapid convergence holds
even in the region of $r$ traversed by the point mass and includes the
time-dependent location of the point mass itself. We present numerical results
of mode calculations for certain orbital parameters, including highly accurate
energy and angular momentum fluxes at infinity and at the black hole event
horizon. We then address the issue of reconstructing the metric perturbation
amplitudes from the master functions, the latter being weak solutions of a
particular form to the wave equations. The spherical harmonic amplitudes that
represent the metric in Regge-Wheeler gauge can themselves be viewed as weak
solutions. They are in general a combination of (1) two differentiable
solutions that adjoin at the instantaneous location of the point mass (a result
that has order of continuity $C^{-1}$ typically) and (2) (in some cases) a
delta function distribution term with a computable time-dependent amplitude.Comment: 25 pages, 5 figures, Updated with minor change

### Time Dependence of Particle Creation from Accelerating Mirrors

Particle production due to a quantized, massless, minimally coupled scalar
field in two-dimensional flat spacetime with an accelerating mirror is
investigated, with a focus on the time dependence of the process. We analyze
first the classes of trajectories previously investigated by Carlitz and Willey
and by Walker and Davies. We then analyze four new classes of trajectories, all
of which can be expressed analytically and for which several ancillary
properties can be derived analytically. The time dependence is investigated
through the use of wave packets for the modes of the quantized field that are
in the out vacuum state. It is shown for most of the trajectories studied that
good time resolution of the particle production process can be obtained.Comment: 21 pages, 5 figure

### Mirror Reflections of a Black Hole

An exact correspondence between a black hole and an accelerating mirror is
demonstrated. It is shown that for a massless minimally coupled scalar field
the same Bogolubov coefficients connecting the "in" and "out" states occur for
a (1+1)D flat spacetime with a particular perfectly reflecting accelerating
boundary trajectory and a (1+1)D curved spacetime in which a null shell
collapses to form a black hole. Generalization of the latter to the (3+1)D case
is discussed. The spectral dynamics is computed in both (1+1)-dimensional
spacetimes along with the energy flux in the spacetime with a mirror. It is
shown that the approach to equilibrium is monotonic, asymmetric in terms of the
rate, and there is a specific time which characterizes the system when it is
the most out-of-equilibrium.Comment: 25 pages, 7 figure

### Trumpet Initial Data for Boosted Black Holes

We describe a procedure for constructing initial data for boosted black holes
in the moving-punctures approach to numerical relativity that endows the
initial time slice from the outset with trumpet geometry within the black hole
interiors. We then demonstrate the procedure in numerical simulations using an
evolution code from the Einstein Toolkit that employs 1+log slicing. The
Lorentz boost of a single black hole can be precisely specified and multiple,
widely separated black holes can be treated approximately by superposition of
single hole data. There is room within the scheme for later improvement to
re-solve (iterate) the constraint equations in the multiple black hole case.
The approach is shown to yield an initial trumpet slice for one black hole that
is close to, and rapidly settles to, a stationary trumpet geometry. Initial
data in this new approach is shown to contain initial transient (or "junk")
radiation that is suppressed by as much as two orders of magnitude relative to
that in comparable Bowen-York initial data.Comment: 18 pages, 18 figure

### Black Hole - Moving Mirror II: Particle Creation

There is an exact correspondence between the simplest solution to Einstein's
equations describing the formation of a black hole and a particular moving
mirror trajectory. In both cases the Bogolubov coefficients in 1+1 dimensions
are identical and can be computed analytically. Particle creation is
investigated by using wave packets. The entire particle creation history is
computed, incorporating the early-time non-thermal emission due to the
formation of the black hole (or the early-time acceleration of the moving
mirror) and the evolution to a Planckian spectrum.Comment: Contribution to MG14 Proceedings, 5 pages, 4 figure

### Highly eccentric inspirals into a black hole

We model the inspiral of a compact stellar-mass object into a massive
nonrotating black hole including all dissipative and conservative
first-order-in-the-mass-ratio effects on the orbital motion. The techniques we
develop allow inspirals with initial eccentricities as high as $e\sim0.8$ and
initial separations as large as $p\sim 50$ to be evolved through many thousands
of orbits up to the onset of the plunge into the black hole. The inspiral is
computed using an osculating elements scheme driven by a hybridized self-force
model, which combines Lorenz-gauge self-force results with highly accurate flux
data from a Regge-Wheeler-Zerilli code. The high accuracy of our hybrid
self-force model allows the orbital phase of the inspirals to be tracked to
within $\sim0.1$ radians or better. The difference between self-force models
and inspirals computed in the radiative approximation is quantified.Comment: Updated to reflect published versio

### Evolution of small-mass-ratio binaries with a spinning secondary

We calculate the evolution and gravitational-wave emission of a spinning
compact object inspiraling into a substantially more massive (non-rotating)
black hole. We extend our previous model for a non-spinning binary [Phys. Rev.
D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force.
For spin-aligned binaries we calculate the dephasing of the inspiral and
associated waveforms relative to models that do not include spin-curvature
effects. We find this dephasing can be either positive or negative depending on
the initial separation of the binary. For binaries in which the spin and
orbital angular momentum are not parallel, the orbital plane precesses and we
use a more general osculating element prescription to compute inspirals.Comment: 17 pages, 6 figure

### Black Hole - Moving Mirror I: An Exact Correspondence

An exact correspondence is shown between a new moving mirror trajectory in
(1+1)D and a spacetime in (1+1)D in which a black hole forms from the collapse
of a null shell. It is shown that the Bogolubov coefficients between the "in"
and "out" states are identical and the exact Bogolubov coefficients are
displayed. Generalization to the (3+1)D black hole case is discussed.Comment: Contribution to MG14 Proceedings, 5 pages, 1 figur

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