29 research outputs found
Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space-time
Gravitational radiation of binary systems can be studied by using the
adiabatic approximation in General Relativity. In this approach a small
astrophysical object follows a trajectory consisting of a chained series of
bounded geodesics (orbits) in the outer region of a Kerr Black Hole,
representing the space time created by a bigger object. In our paper we study
the entire class of orbits, both of constant radius (spherical orbits), as well
as non-null eccentricity orbits, showing a number of properties on the physical
parameters and trajectories. The main result is the determination of the
geometrical locus of all the orbits in the space of physical parameters in Kerr
space-time. This becomes a powerful tool to know if different orbits can be
connected by a continuous change of their physical parameters. A discussion on
the influence of different values of the angular momentum of the hole is given.
Main results have been obtained by analytical methods.Comment: 26 pages, 12 figure
Forced motion near black holes
We present two methods for integrating forced geodesic equations in the Kerr
spacetime, which can accommodate arbitrary forces. As a test case, we compute
inspirals under a simple drag force, mimicking the presence of gas. We verify
that both methods give the same results for this simple force. We find that
drag generally causes eccentricity to increase throughout the inspiral. This is
a relativistic effect qualitatively opposite to what is seen in
gravitational-radiation-driven inspirals, and similar to what is observed in
hydrodynamic simulations of gaseous binaries. We provide an analytic
explanation by deriving the leading order relativistic correction to the
Newtonian dynamics. If observed, an increasing eccentricity would provide clear
evidence that the inspiral was occurring in a non-vacuum environment. Our two
methods are especially useful for evolving orbits in the adiabatic regime. Both
use the method of osculating orbits, in which each point on the orbit is
characterized by the parameters of the geodesic with the same instantaneous
position and velocity. Both methods describe the orbit in terms of the geodesic
energy, axial angular momentum, Carter constant, azimuthal phase, and two
angular variables that increase monotonically and are relativistic
generalizations of the eccentric anomaly. The two methods differ in their
treatment of the orbital phases and the representation of the force. In one
method the geodesic phase and phase constant are evolved together as a single
orbital phase parameter, and the force is expressed in terms of its components
on the Kinnersley orthonormal tetrad. In the second method, the phase constants
of the geodesic motion are evolved separately and the force is expressed in
terms of its Boyer-Lindquist components. This second approach is a
generalization of earlier work by Pound and Poisson for planar forces in a
Schwarzschild background.Comment: 28 pages, 2 figures, submitted to Phys. Rev. D; v2 has minor changes
for consistency with published version, plus a new section discussing the
relative advantages of the two approache
Core-Collapse Supernovae, Neutrinos, and Gravitational Waves
Core-collapse supernovae are among the most energetic cosmic cataclysms. They are prodigious emitters of neutrinos
and quite likely strong galactic sources of gravitational waves. Observation of both neutrinos and gravitational
waves from the next galactic or near extragalactic core-collapse supernova will yield a wealth of information on the
explosion mechanism, but also on the structure and angular momentum of the progenitor star, and on aspects of
fundamental physics such as the equation of state of nuclear matter at high densities and low entropies. In this contribution
to the proceedings of the Neutrino 2012 conference, we summarize recent progress made in the theoretical
understanding and modeling of core-collapse supernovae. In this, our emphasis is on multi-dimensional processes
involved in the explosion mechanism such as neutrino-driven convection and the standing accretion shock instability.
As an example of how supernova neutrinos can be used to probe fundamental physics, we discuss how the rise time
of the electron antineutrino flux observed in detectors can be used to probe the neutrino mass hierarchy. Finally, we
lay out aspects of the neutrino and gravitational-wave signature of core-collapse supernovae and discuss the power of
combined analysis of neutrino and gravitational wave data from the next galactic core-collapse supernova
Gravitational wave snapshots of generic extreme mass ratio inspirals
Using black hole perturbation theory, we calculate the gravitational waves
produced by test particles moving on bound geodesic orbits about rotating black
holes. The orbits we consider are generic - simultaneously eccentric and
inclined. The waves can be described as having radial, polar, and azimuthal
"voices", each of which can be made to dominate by varying eccentricity and
inclination. Although each voice is generally apparent in the waveform, the
radial voice is prone to overpowering the others. We also compute the radiative
fluxes of energy and axial angular momentum at infinity and through the event
horizon. These fluxes, coupled to a prescription for the radiative evolution of
the Carter constant, will be used in future work to adiabatically evolve
through a sequence of generic orbits. This will enable the calculation of
inspiral waveforms that, while lacking certain important features, will
approximate those expected from astrophysical extreme mass ratio captures
sufficiently well to aid development of measurement algorithms on a relatively
short timescale.Comment: Minor changes in response to comments from readers, referees, and
editors. Final version, as it will appear in Physical Review D. Raw data and
a small program which will convert the data into waveforms lasting for
arbitrary lengths of time can be found at
http://gmunu.mit.edu/sdrasco/snapshot
Geodesic equations and algebro-geometric methods
For an investigation of the physical properties of gravitational fields the
observation of massive test particles and light is very useful. The
characteristic features of a given space-time may be decoded by studying the
complete set of all possible geodesic motions. Such a thorough analysis can be
accomplished most effectively by using analytical methods to solve the geodesic
equation. In this contribution, the use of elliptic functions and their
generalizations for solving the geodesic equation in a wide range of well known
space-times, which are part of the general Pleba\'nski-Demia\'nski family of
solutions, will be presented. In addition, the definition and calculation of
observable effects like the perihelion shift will be presented and further
applications of the presented methods will be outlined.Comment: 8 pages, no figures; based on presentation at the conference
"Relativity and Gravitation: 100 Years after Einstein in Prague," Prague,
2012. Relativity and Gravitation, volume 157 of Springer Proceedings in
Physics, p 91. Springer International Publishing, 201
Lense-Thirring Precession in Pleba\'nski-Demia\'nski spacetimes
An exact expression of Lense-Thirring precession rate is derived for
non-extremal and extremal Pleba\'nski-Demia\'nski spacetimes. This formula is
used to find the exact Lense-Thirring precession rate in various axisymmetric
spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the
Kerr parameter vanishes in Pleba\'nski-Demia\'nski(PD) spacetime, the
Lense-Thirring precession does not vanish due to the existence of NUT charge.
To derive the LT precession rate in extremal Pleba\'nski-Demia\'nski we first
derive the general extremal condition for PD spacetimes. This general result
could be applied to get the extremal limit in any stationary and axisymmetric
spacetimes.Comment: 9 pages, Some special modifications are mad
Extreme Mass Ratio Inspirals: LISA's unique probe of black hole gravity
In this review article I attempt to summarise past and present-ongoing-work
on the problem of the inspiral of a small body in the gravitational field of a
much more massive Kerr black hole. Such extreme mass ratio systems, expected to
occur in galactic nuclei, will constitute prime sources of gravitational
radiation for the future LISA gravitational radiation detector. The article's
main goal is to provide a survey of basic celestial mechanics in Kerr spacetime
and calculations of gravitational waveforms and backreaction on the small
body's orbital motion, based on the traditional `flux-balance' method and the
Teukolsky black hole perturbation formalism.Comment: Invited review article, 45 pages, 23 figure
Correlated Gravitational Wave and Neutrino Signals from General-Relativistic Rapidly Rotating Iron Core Collapse
We present results from a new set of 3D general-relativistic hydrodynamic
simulations of rotating iron core collapse. We assume octant symmetry and focus
on axisymmetric collapse, bounce, the early postbounce evolution, and the
associated gravitational wave (GW) and neutrino signals. We employ a
finite-temperature nuclear equation of state, parameterized electron capture in
the collapse phase, and a multi-species neutrino leakage scheme after bounce.
The latter captures the important effects of deleptonization, neutrino cooling
and heating and enables approximate predictions for the neutrino luminosities
in the early evolution after core bounce. We consider 12-solar-mass and
40-solar-mass presupernova models and systematically study the effects of (i)
rotation, (ii) progenitor structure, and (iii) postbounce neutrino leakage on
dynamics, GW, and, neutrino signals. We demonstrate, that the GW signal of
rapidly rotating core collapse is practically independent of progenitor mass
and precollapse structure. Moreover, we show that the effects of neutrino
leakage on the GW signal are strong only in nonrotating or slowly rotating
models in which GW emission is not dominated by inner core dynamics. In rapidly
rotating cores, core bounce of the centrifugally-deformed inner core excites
the fundamental quadrupole pulsation mode of the nascent protoneutron star. The
ensuing global oscillations (f~700-800 Hz) lead to pronounced oscillations in
the GW signal and correlated strong variations in the rising luminosities of
antineutrino and heavy-lepton neutrinos. We find these features in cores that
collapse to protoneutron stars with spin periods <~ 2.5 ms and rotational
energies sufficient to drive hyper-energetic core-collapse supernova
explosions. Hence, joint GW + neutrino observations of a core collapse event
could deliver strong evidence for or against rapid core rotation. [abridged]Comment: 29 pages, 14 figures. Replaced with version matching published
versio
A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order
The motion of a small compact object in a background spacetime is
investigated in the context of a model nonlinear scalar field theory. This
model is constructed to have a perturbative structure analogous to the General
Relativistic description of extreme mass ratio inspirals (EMRIs). We apply the
effective field theory approach to this model and calculate the finite part of
the self force on the small compact object through third order in the ratio of
the size of the compact object to the curvature scale of the background (e.g.,
black hole) spacetime. We use well-known renormalization methods and
demonstrate the consistency of the formalism in rendering the self force finite
at higher orders within a point particle prescription for the small compact
object. This nonlinear scalar model should be useful for studying various
aspects of higher-order self force effects in EMRIs but within a comparatively
simpler context than the full gravitational case. These aspects include
developing practical schemes for higher order self force numerical
computations, quantifying the effects of transient resonances on EMRI waveforms
and accurately modeling the small compact object's motion for precise
determinations of the parameters of detected EMRI sources.Comment: 30 pages, 8 figure