arXiv subjects

Eanna E. Flanagan

Publications and source records attributed to Eanna E. Flanagan.

At least 55 records · Page 3Linked to original sources

arXiv2004

Quasi-local contribution to the gravitational self-force

The gravitational self-force on a point particle moving in a vacuum background spacetime can be expressed as an integral over the past worldline of the particle, the so-called tail term. In this paper, we consider that piece of the self-force obtained by integrating over a portion of the past worldline that extends a proper time $Δτ$ into the past, provided that $Δτ$ does not extend beyond the normal neighborhood of the particle. We express this ``quasi-local'' piece as a power series in the proper time interval $Δτ$. We argue from symmetries and dimensional considerations that the $O(Δτ^0)$ and $O(Δτ)$ terms in this power series must vanish, and compute the first two non-vanishing terms which occur at $O(Δτ^2)$ and $O(Δτ^3)$. The coefficients in the expansion depend only on the particle's four velocity and on the Weyl tensor and its derivatives at the particle's location. The result may be useful as a foundation for a practical computational method for gravitational self-forces in the Kerr spacetime, in which the portion of the tail integral in the distant past is computed numerically from a mode sum decomposition.

gr-qc↗

arXiv2004

The conformal frame freedom in theories of gravitation

It has frequently been claimed in the literature that the classical physical predictions of scalar tensor theories of gravity depend on the conformal frame in which the theory is formulated. We argue that this claim is false, and that all classical physical predictions are conformal-frame invariants. We also respond to criticisms by Vollick [gr-qc/0312041], in which this issue arises, of our recent analysis of the Palatini form of 1/R gravity.

gr-qc↗

arXiv2003

Higher order gravity theories and scalar tensor theories

We generalize the known equivalence between higher order gravity theories and scalar tensor theories to a new class of theories. Specifically, in the context of a first order or Palatini variational principle where the metric and connection are treated as independent variables, we consider theories for which the Lagrangian density is a function f of (i) the Ricci scalar computed from the metric, and (ii) a second Ricci scalar computed from the connection. We show that such theories can be written as tensor-multi-scalar theories with two scalar fields with the following features: (i) the two dimensional sigma-model metric that defines the kinetic energy terms for the scalar fields has constant, negative curvature; (ii) the coupling function determining the coupling to matter of the scalar fields is universal, independent of the choice of function f; and (iii) if both mass eigenstates are long ranged, then the Eddington post-Newtonian parameter has value 1/2. Therefore in order to be compatible with solar system experiments at least one of the mass eigenstates must be short ranged.

gr-qc↗

arXiv2003

Palatini form of 1/R gravity

It has been suggested that the recent acceleration of the expansion of the Universe is due a modified gravitational action consisting of the Einstein-Hilbert term plus a term proportional to the reciprocal of the Ricci scalar. Although the original version of this theory has been shown to be in conflict with solar system observations, a modified Palatini version of the theory, in which the metric and connection are treated as independent variables in the variational principle, has been suggested as a viable model of the cosmic acceleration. We show that this theory is equivalent to a type of scalar-tensor theory in which the scalar field kinetic energy term in absent from the action, and in which the scalar field is therefore not an independent dynamical degree of freedom. Integrating out the scalar field gives rise to additional interactions among the matter fields of the standard model of particle physics at a energy scale of order 10^(-3) eV (the geometric mean of the Hubble scale and the Planck scale), and so the theory is excluded by, for example, electron-electron scattering experiments.

astro-ph↗

arXiv2003

Simple sufficient conditions for the generalized covariant entropy bound

The generalized covariant entropy bound is the conjecture that the entropy of the matter present on any non-expanding null hypersurface L will not exceed the difference between the areas, in Planck units, of the initial and final spatial 2-surfaces bounding L. The generalized Bekenstein bound is a special case which states that the entropy of a weakly gravitating isolated matter system will not exceed the product of its mass and its width. Here we show that both bounds can be derived directly from the following phenomenological assumptions: that entropy can be computed by integrating an entropy current which vanishes on the initial boundary and whose gradient is bounded by the energy density. Though we note that any local description of entropy has intrinsic limitations, we argue that our assumptions apply in a wide regime. We closely follow the framework of an earlier derivation, but our assumptions take a simpler form, making their validity more transparent in some examples.

hep-th↗

arXiv2003

Saturation of the R-mode Instability

Rossby waves (r-modes) in rapidly rotating neutron stars are unstable because of the emission of gravitational radiation. We study saturation of this instability by nonlinear transfer of energy to stellar "inertial" oscillation modes. We present detailed calculations of stellar inertial modes in the WKB limit, their linear damping by bulk and shear viscosity, and the nonlinear coupling forces among these modes. The saturation amplitude is derived in the extreme limits of strong or weak driving by radiation reaction, as compared to the damping rate of low order inertial modes. We find the saturation energy is {\it extremely small}, at least four orders of magnitude smaller than that found by previous investigators. We discuss the consequences of this result for spin evolution of young neutron stars, and neutron stars being spun up by accretion in Low Mass X-ray Binaries.We also discuss the detection of these gravitational waves by LIGO.

astro-ph↗

arXiv2003

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

We address the issue of finding an optimal detection method for a discontinuous or intermittent gravitational wave stochastic background. Such a signal might sound something like popcorn popping. We derive an appropriate version of the maximum likelihood detection statistic, and compare its performance to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. The maximum likelihood statistic performs better than the cross-correlation statistic when the background is sufficiently non-Gaussian. For both ground and space based detectors, this results in a gain factor, ranging roughly from 1 to 3, in the minimum gravitational-wave energy density necessary for detection, depending on the duty cycle of the background. Our analysis is exploratory, as we assume that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. Before this detection method can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.

gr-qc↗

arXiv2002

Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise. II: Bayesian analyses

In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in weak signal limit. For stochastic signals, the resulting statistic consisted of a sum of an auto-correlation term and a cross-correlation term; it was necessary to discard by hand the auto-correlation term to obtain the correct, generalized cross-correlation statistic. In the present paper, we present an alternative Bayesian derivation of the same signal detection techniques. We compute the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the integrated signal-to-noise ratio is large compared to one, and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in the previous paper. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic auto-correlation term.

gr-qc↗

arXiv2001

Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise I: Frequentist analyses

Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as a stationary Gaussian process. However most experiments exhibit a non-Gaussian ``tail'' in the probability distribution. This ``excess'' of large signals can be a troublesome source of false alarms. This article derives an optimal (in the Neyman-Pearson sense, for weak signals) signal processing strategy when the detector noise is non-Gaussian and exhibits tail terms. This strategy is robust, meaning that it is close to optimal for Gaussian noise but far less sensitive than conventional methods to the excess large events that form the tail of the distribution. The method is analyzed for two different signal analysis problems: (i) a known waveform (e.g., a binary inspiral chirp) and (ii) a stochastic background, which requires a multi-detector signal processing algorithm. The methods should be easy to implement: they amount to truncation or clipping of sample values which lie in the outlier part of the probability distribution.

gr-qc↗

arXiv2001

Brane World Models With Bulk Scalar Fields

We examine several different types of five dimensional stationary spacetimes with bulk scalar fields and parallel 3-branes. We study different methods for avoiding the appearance of spacetime singularities in the bulk for models with and without cosmological expansion. For non-expanding models, we demonstrate that in general the Randall-Sundrum warp factor is recovered in the asymptotic bulk region, although elsewhere the warping may be steeper than exponential. We show that nonsingular expanding models can be constructed as long as the gradient of the bulk scalar field vanishes at zeros of the warp factor, which are then analogous to the particle horizons found in expanding models with a pure AdS bulk. Since the branes in these models are stabilized by bulk scalar fields, we expect there to be no linearly unstable radion modes. As an application, we find a specific class of expanding, stationary solutions with no singularities in the bulk in which the four dimensional cosmological constant and mass hierarchy are naturally very small.

hep-th↗

arXiv2001

Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.

gr-qc↗

arXiv2001

Detecting a non-Gaussian stochastic background of gravitational radiation

We derive a detection method for a stochastic background of gravitational waves produced by events where the ratio of the average time between events to the average duration of an event is large. Such a signal would sound something like popcorn popping. Our derivation is based on the somewhat unrealistic assumption that the duration of an event is smaller than the detector time resolution.

gr-qc↗

arXiv2000

An excess power statistic for detection of burst sources of gravitational radiation

We examine the properties of an excess power method to detect gravitational waves in interferometric detector data. This method is designed to detect short-duration (< 0.5 s) burst signals of unknown waveform, such as those from supernovae or black hole mergers. If only the bursts' duration and frequency band are known, the method is an optimal detection strategy in both Bayesian and frequentist senses. It consists of summing the data power over the known time interval and frequency band of the burst. If the detector noise is stationary and Gaussian, this sum is distributed as a chi-squared (non-central chi-squared) deviate in the absence (presence) of a signal. One can use these distributions to compute frequentist detection thresholds for the measured power. We derive the method from Bayesian analyses and show how to compute Bayesian thresholds. More generically, when only upper and/or lower bounds on the bursts duration and frequency band are known, one must search for excess power in all concordant durations and bands. Two search schemes are presented and their computational efficiencies are compared. We find that given reasonable constraints on the effective duration and bandwidth of signals, the excess power search can be performed on a single workstation. Furthermore, the method can be almost as efficient as matched filtering when a large template bank is required. Finally, we derive generalizations of the method to a network of several interferometers under the assumption of Gaussian noise.

gr-qc↗

arXiv2000

Proof of Classical Versions of the Bousso Entropy Bound and of the Generalized Second Law

Bousso has conjectured that in any spacetime satisfying Einstein's equation and satisfying the dominant energy condition, the "entropy flux" S through any null hypersurface L generated by geodesics with non-positive expansion starting from some spacelike 2 surface of area A must satisfy S<=A/4. This conjecture reformulates earlier conjectured entropy bounds of Bekenstein and also of Fischler and Susskind, and can be interpreted as a statement of the so-called holographic principle. We show that Bousso's entropy bound can be derived from either of two sets of hypotheses. The first set of hypotheses is (i) associated with each null surface L in spacetime there is an entropy flux 4-vector s^a_L whose integral over L is the entropy flux through L, and (ii) along each null geodesic generator of L, we have $|s^a_L k_a| \le π(λ_\infty - λ) T_{ab} k^a k^b$, where $T_{ab}$ is the stress-energy tensor, $λ$ is an affine parameter, $k^a = (d / dλ)^a$, and $λ_\infty$ is the value of affine parameter at the endpoint of the geodesic. The second (purely local) set of hypotheses is (i) there exists an absolute entropy flux 4-vector s^a such that the entropy flux through any null surface L is the integral of s^a over L, and (ii) this entropy flux 4-vector obeys the pointwise inequalities $(s_a k^a)^2 \le T_{ab} k^a k^b / (16 π)$ and $|k^a k^b \nabla_a s_b| \le πT_{ab} k^a k^b /4$ for any null vector k^a. Under the first set of hypotheses, we also show that a stronger entropy bound can be derived, which directly implies the generalized second law of thermodynamics.

hep-th↗

arXiv2000

A power filter for the detection of burst sources of gravitational radiation in interferometric detectors

We present a filter for detecting gravitational wave signals from burst sources. This filter requires only minimal advance knowledge of the expected signal: i.e. the signal's frequency band and time duration. It consists of a threshold on the total power in the data stream in the specified signal band during the specified time. This filter is optimal (in the Neyman-Pearson sense) for signal searches where only this minimal information is available.

gr-qc↗

arXiv1999

Can the post-Newtonian gravitational waveform of an inspiraling binary be improved by solving the energy balance equation numerically?

The detection of gravitational waves from inspiraling compact binaries using matched filtering depends crucially on the availability of accurate template waveforms. We determine whether the accuracy of the templates' phasing can be improved by solving the post-Newtonian energy balance equation numerically, rather than (as is normally done) analytically within the post-Newtonian perturbative expansion. By specializing to the limit of a small mass ratio, we find evidence that there is no gain in accuracy.

gr-qc↗

arXiv1999

Cosmological Expansion in the Randall-Sundrum Brane World Scenario

The cosmology of the Randall-Sundrum scenario for a positive tension brane in a 5-D Universe with localized gravity has been studied previously. In the radiation-dominated Universe, it was suggested that there are two solutions for the cosmic scale factor a(t) : the standard solution $a\sim t^{1/2}$, and a solution $a\sim t^{1/4}$, which is incompatible with standard big bang nucleosynthesis. In this note, we reconsider expansion of the Universe in this scenario. We derive and solve a first order, linear differential equation for H^2, the square of the expansion rate of the Universe, as a function of a. The differences between our equation for H^2 and the relationship found in standard cosmology are (i) there is a term proportional to density squared (a fact already known), which is small when the density is small compared to the brane tension, and (ii) there is a contribution which acts like a relativistic fluid. We show that this second contribution is due to gravitational degrees of freedom in the bulk. Thus, we find that there need not be any conflict between cosmology of the Randall-Sundrum scenario and the standard model of cosmology. We discuss how reheating at the end of inflation leads to the correct relationship between matter density and expansion rate, $H^2\to 8πGρ_m/3$, and the conditions that must be met for the expansion rate of the Universe to be close to its standard model value around the epoch of cosmological nucleosynthesis.

hep-ph↗

arXiv1999

A Cosmology of the Brane World

We develop a possible cosmology for a Universe with n additional spatial dimensions of variable scale, and an associated scalar field, the radion, which is distinct from the field responsible for inflation, the inflaton. Based on a particular ansatz for the effective potential for the inflaton and radion (which may emerge in string theory), we show that the early expansion of the Universe may proceed in three stages. First, the radion becomes trapped at a value much smaller than the size of the extra dimensions today. Second, the Universe expands exponentially, but with a Planck mass smaller than its present value. Because the Planck mass during inflation is small, density fluctuations in agreement with observations can arise naturally. Third, when inflation ends, the Universe reheats, and the radion becomes free to expand once more. During the third phase the Universe is ``radiation-dominated'' and tends toward a fixed-point evolutionary model in which the radion grows but the temperature remains unchanged. Ultimately, the radion becomes trapped once again at its present value, and a short period of exponential expansion, which we identify with the electroweak phase transition, ensues. Once this epoch is over, the Universe reheats to a temperature of order the electroweak scale, and the mature Universe evolves as in standard cosmological models. We show that the present day energy density in radions can be smaller than the closure density if the second inflationary epoch lasts about 8 e-foldings or more; the present-day radion mass turns out to be small (less than or of the order of an eV, depending on parameters). We argue that although our model envisages considerable time evolution in the Planck mass, substantial spatial fluctuations in Newton's constant are not produced.

hep-ph↗