1,076 research outputs found
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A reason for unreason: returns based beliefs in game theory
Players cooperate in experiments more than game theory would predict. We introduce the ‘returns-based beliefs’ approach: the expected returns of a particular strategy in proportion to total expected returns of all strategies. Using a decision analytic solution concept, Luce’s (1959) probabilistic choice model, and ‘hyperpriors’ for ambiguity in players’ cooperability, our approach explains empirical observations in various classes of games including the Prisoner’s and Traveler’s Dilemmas. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2 × 2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts
Observing the Galaxy's massive black hole with gravitational wave bursts
An extreme-mass-ratio burst (EMRB) is a gravitational wave signal emitted
when a compact object passes through periapsis on a highly eccentric orbit
about a much more massive object, in our case a stellar mass object about a
10^6 M_sol black hole. EMRBs are a relatively unexplored means of probing the
spacetime of massive black holes (MBHs). We conduct an investigation of the
properties of EMRBs and how they could allow us to constrain the parameters,
such as spin, of the Galaxy's MBH. We find that if an EMRB event occurs in the
Galaxy, it should be detectable for periapse distances r_p < 65 r_g for a \mu =
10 M_sol orbiting object, where r_g = GM/c^2 is the gravitational radius. The
signal-to-noise ratio scales as \rho ~ -2.7 log(r_p/r_g) + log(\mu/M_sol) +
4.9. For periapses r_p < 10 r_g, EMRBs can be informative, and provide good
constraints on both the MBH's mass and spin. Closer orbits provide better
constraints, with the best giving accuracies of better than one part in 10^4
for both the mass and spin parameter.Comment: 25 pages, 17 figures, 1 appendix. One more typo fixe
Expectations for extreme-mass-ratio bursts from the Galactic Centre
When a compact object on a highly eccentric orbit about a much more massive
body passes through periapsis it emits a short gravitational wave signal known
as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects
orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs
provide a novel means of extracting information about the MBH; an EMRB from the
Galactic MBH could be highly informative regarding the MBH's mass and spin if
the orbital periapsis is small enough. However, to be a useful astronomical
tool EMRBs must be both informative and sufficiently common to be detectable
with a space-based interferometer. We construct a simple model to predict the
event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts
in a two year mission lifetime for LISA. Stellar mass black holes dominate the
event rate. Creating a sample of 100 mission realisations, we calculate what we
could learn about the MBH. On average, we expect to be able to determine the
MBH mass to ~1% and the spin to ~0.1 using EMRBs.Comment: 22 pages, 5 figures, 2 appendices. Minor changes to reflect published
versio
Astrometric Effects of Gravitational Wave Backgrounds with non-Luminal Propagation Speeds
A passing gravitational wave causes a deflection in the apparent astrometric positions of distant stars. The effect of the speed of the gravitational wave on this astrometric shift is discussed. A stochastic background of gravitational waves would result in a pattern of astrometric deflections which are correlated on large angular scales. These correlations are quantified and investigated for backgrounds of gravitational waves with sub- and super-luminal group velocities. The statistical properties of the correlations are depicted in two equivalent and related ways: as correlation curves and as angular power spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of enhancing (suppressing) the power in low-order angular modes. Analytical representations of the redshift-redshift and redshift-astrometry correlations are also derived. The potential for using this effect for constraining the speed of gravity is discussed
Importance of including small body spin effects in the modelling of intermediate mass-ratio inspirals. II Accurate parameter extraction of strong sources using higher-order spin effects
We improve the numerical kludge waveform model introduced in [1] in two ways.
We extend the equations of motion for spinning black hole binaries derived by
Saijo et al. [2] using spin-orbit and spin-spin couplings taken from
perturbative and post-Newtonian (PN) calculations at the highest order
available. We also include first-order conservative self-force corrections for
spin-orbit and spin-spin couplings, which are derived by comparison to PN
results. We generate the inspiral evolution using fluxes that include the most
recent calculations of small body spin corrections, spin-spin and spin-orbit
couplings and higher-order fits to solutions of the Teukolsky equation. Using a
simplified version of this model in [1], we found that small body spin effects
could be measured through gravitational wave observations from
intermediate-mass ratio inspirals (IMRIs) with mass ratio eta ~ 0.001, when
both binary components are rapidly rotating. In this paper we study in detail
how the spin of the small/big body affects parameter measurement using a
variety of mass and spin combinations for typical IMRIs sources. We find that
for IMRI events of a moderately rotating intermediate mass black hole (IMBH) of
ten thousand solar masses, and a rapidly rotating central supermassive black
hole (SMBH) of one million solar masses, gravitational wave observations made
with LISA at a fixed signal-to-noise ratio (SNR) of 1000 will be able to
determine the inspiralling IMBH mass, the central SMBH mass, the SMBH spin
magnitude, and the IMBH spin magnitude to within fractional errors of ~0.001,
0.001, 0.0001, and 9%, respectively. LISA can also determine the location of
the source in the sky and the SMBH spin orientation to within ~0.0001
steradians. We show that by including conservative corrections up to 2.5PN
order, systematic errors no longer dominate over statistical errors for IMRIs
with typical SNR ~1000.Comment: 21 pages, 7 figures. v2: three references added, edits in Sections
II-V, including additional results in Section V to address comments by the
referee. v3: mirrors version accepted to PR
Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals
We explore the ability of future low-frequency gravitational wave detectors
to measure the spin of stellar mass and intermediate mass black holes that
inspiral onto super-massive Kerr black holes (SMBHs). We develop a kludge
waveform model based on the equations of motion derived by Saijo et al. [Phys
Rev D 58, 064005, 1998] for spinning BH binaries, augmented with spin-orbit and
spin-spin couplings taken from perturbative and post-Newtonian (PN)
calculations, and the associated conservative self-force corrections, derived
by comparison to PN results. We model the inspiral phase using accurate fluxes
which include perturbative corrections for the spin of the inspiralling body,
spin-spin couplings and higher-order fits to solutions of the Teukolsky
equation. We present results of Monte Carlo simulations of parameter estimation
errors and of the model errors that arise when we omit conservative corrections
from the waveform template. For a source 5000+10^6 solar mass observed with an
SNR of 1000, LISA will be able to determine the two masses to within a
fractional error of ~0.001, measure the SMBH spin magnitude, q, and the spin
magnitude of the inspiralling BH to 0.0001, 10%, respectively, and determine
the location of the source in the sky and the SMBH spin orientation to within
0.0001 steradians. For a 10+10^6 solar mass system observed with SNR of 30,
LISA will not be able to determine the spin magnitude of the inspiralling BH,
although the measurement of the other waveform parameters is not significantly
degraded by the presence of spin. The model errors which arise from ignoring
conservative corrections become significant for mass-ratios above 0.0001, but
including these corrections up to 2PN order may be sufficient to reduce these
systematic errors to an acceptable level.Comment: 24 pages, 11 figures. v2 mirrors published version in PRD. Edits in
Sections V and VI in response to comments from refere
Recommended from our members
A Reason for Unreason: Returns-Based Beliefs in Game Theory
Players cooperate in experiments more than game theory would predict. We introduce the ‘returns-based beliefs’ approach: the expected returns of a particular strategy in proportion to total expected returns of all strategies. Using a decision analytic solution concept, Luce’s (1959) probabilistic choice model, and ‘hyperpriors’ for ambiguity in players’ cooperability, our approach explains empirical observations in various classes of games including the Prisoner’s and Traveler’s Dilemmas. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2 × 2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts
Electromagnetic Fields of Separable Space-Times
Carter derived the forms of the metric and the vector potentials of the
space-times in which the relativistic Schrodinger equation for the motion of a
charged particle separates. Here we show that on each `spheroidal' surface a
rotation rate exists such that relative to those rotating axes the electric and
magnetic fields are parallel and orthogonal to the spheroid which is thus an
equipotential in those axes. All the finite Carter separable systems without
magnetic monopoles or gravomagnetic NUT monopoles have the same gyromagnetic
ratio as the Dirac electron.Comment: 9 pages; accepted for publication in Class. Quantum Gra
Extreme-mass-ratio-bursts from extragalactic sources
Extreme-mass-ratio bursts (EMRBs) are a class of potentially interesting gravitational wave signals. They are produced when a compact object passes through periapsis on a highly eccentric orbit about a much more massive object; we consider stellar mass objects orbiting the massive black holes (MBHs) found in galactic centres. Such a system may emit many EMRBs before eventually completing the inspiral. There are several nearby galaxies that could yield detectable bursts. For a space-borne interferometer like the Laser Interferometer Space Antenna, sensitivity is greatest for EMRBs from MBHs of ∼106–107 M⊙, which could be detected out to ∼100 Mpc. Considering the examples of M32, NGC 4945 and NGC 4395 we investigate if extragalactic EMRB signals can provide information about their sources. This is possible, but only if the periapse radius of the orbit is small, of the order of rp ≲ 8rg, where rg = GM c− 2 is the gravitational radius of the MBH. This limits the utility of EMRBs as an astronomical tool. However, if we are lucky, we could place constraints on the mass and spin of nearby MBHs with 1 per cent precision
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