arXiv subjects

George Pappas

Publications and source records attributed to George Pappas.

At least 73 records · Page 4Linked to original sources

arXiv2018

Multipole moments and universal relations for scalarized neutron stars

In recent years there has been a surge of interest in what has come to be known as the `universal relations' between various global properties of neutron stars. These universal relations are equation of state independent relations between quantities such as the moment of inertia $I$, the tidal deformability or Love number $λ$, and the quadrupole $Q$ (I-Love-Q relations), or the relativistic multipole moments (3-hair relations). While I-Love-Q relations have been studied extensively in both general relativity and various alternatives, 3-hair relations have been studied only in general relativity. Recent progress on the definition of the multipole moments of a compact object in the case of scalar-tensor theories allows for the study of 3-hair relations in modified theories of gravity. Specifically, the aim of this work is to study them for scalarized stars in scalar-tensor theories with a massless scalar field that admit spontaneous scalarization. We find that the 3-hair relations between the mass and angular momentum moments that hold in general relativity hold for scalarized stars as well. The scalar moments also exhibit a universal behaviour, which is equation of state independent within one specific theory, but differs between different theories. Combining astrophysical observations one can in principle measure the different properties of scalarized neutron star and tell different theories apart.

gr-qc↗

arXiv2018

An Information Matrix Approach for State Secrecy

This paper studies the problem of remote state estimation in the presence of a passive eavesdropper. A sensor measures a linear plant's state and transmits it to an authorized user over a packet-dropping channel, which is susceptible to eavesdropping. Our goal is to design a coding scheme such that the eavesdropper cannot infer the plant's current state, while the user successfully decodes the sent messages. We employ a novel class of codes, termed State-Secrecy Codes, which are fast and efficient for dynamical systems. They apply linear time-varying transformations to the current and past states received by the user. In this way, they force the eavesdropper's information matrix to decrease with asymptotically the same rate as in the open-loop prediction case, i.e. when the eavesdropper misses all messages. As a result, the eavesdropper's minimum mean square error (mmse) for the unstable states grows unbounded, while the respective error for the stable states converges to the open-loop prediction one. These secrecy guarantees are achieved under minimal conditions, which require that, at least once, the user receives the corresponding packet while the eavesdropper fails to intercept it. Meanwhile, the user's estimation performance remains optimal. The theoretical results are illustrated in simulations.

eess.SY↗

arXiv2018

Cup products in the etale cohomology of number fields

This paper concerns cup product pairings in étale cohomology related to work of M. Kim and of W. McCallum and R. Sharifi. We will show that by considering Ext groups rather than cohomology groups, one arrives at a pairing which combines invariants defined by Kim with a pairing defined by McCallum and Sharifi. We also prove a formula for Kim's invariant in terms of Artin maps in the case of cyclic unramified Kummer extensions. One consequence is that for all $n > 1$, there are infinitely many number fields $F$ over which there are both trivial and non-trivial Kim invariants associated to cyclic groups of order $n$.

math.NT↗

arXiv2018

How well can ultracompact bodies imitate black hole ringdowns?

The ongoing observations of merging black holes by the instruments of the fledging gravitational wave astronomy has opened the way for testing the general relativistic Kerr black hole metric and, at the same time, for probing the existence of more speculative horizonless ultracompact objects. In this paper we quantify the difference that these two classes of objects may exhibit in the post-merger ringdown signal. By considering rotating systems in general relativity and assuming an eikonal limit and a third-order Hartle-Thorne slow rotation approximation, we provide the first calculation of the early ringdown frequency and damping time as a function of the body's multipolar structure. Using the example of a gravastar, we show that the main ringdown signal may differ as much as a few percent with respect to that of a Kerr black hole, a deviation that could be probed by near future Advanced LIGO/Virgo searches.

gr-qc↗

arXiv2017

Universal Relations and Alternative Gravity Theories

This is a review with the ambitious goal of covering the recent progress in: 1) universal relations (in general relativity and alternative theories of gravity), and 2) neutron star models in alternative theories. We also aim to be complementary to recent reviews in the literature that are covering the topic of universal relations of neutron stars.

gr-qc↗

arXiv2017

Post-Kerr black hole spectroscopy

One of the central goals of the newborn field of gravitational wave astronomy is to test gravity in the highly nonlinear, strong field regime characterizing the spacetime of black holes. In particular, "black hole spectroscopy" (the observation and identification of black hole quasinormal mode frequencies in the gravitational wave signal) is expected to become one of the main tools for probing the structure and dynamics of Kerr black holes. In this paper we take a significant step towards that goal by constructing a "post-Kerr" quasinormal mode formalism. The formalism incorporates a parametrized but general perturbative deviation from the Kerr metric and exploits the well-established connection between the properties of the spacetime's circular null geodesics and the fundamental quasinormal mode to provide approximate, eikonal limit formulae for the modes' complex frequencies. The resulting algebraic toolkit can be used in waveform templates for ringing black holes with the purpose of measuring deviations from the Kerr metric. As a first illustrative application of our framework, we consider the Johannsen-Psaltis deformed Kerr metric and compute the resulting deviation in the quasinormal mode frequency relative to the known Kerr result.

gr-qc↗

arXiv2017

Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers.

math.NT↗

arXiv2017

A National Research Agenda for Intelligent Infrastructure

Our infrastructure touches the day-to-day life of each of our fellow citizens, and its capabilities, integrity and sustainability are crucial to the overall competitiveness and prosperity of our country. Unfortunately, the current state of U.S. infrastructure is not good: the American Society of Civil Engineers' latest report on America's infrastructure ranked it at a D+ -- in need of $3.9 trillion in new investments. This dire situation constrains the growth of our economy, threatens our quality of life, and puts our global leadership at risk. The ASCE report called out three actions that need to be taken to address our infrastructure problem: 1) investment and planning in the system; 2) bold leadership by elected officials at the local and federal state; and 3) planning sustainability and resiliency in our infrastructure. While our immediate infrastructure needs are critical, it would be shortsighted to simply replicate more of what we have today. By doing so, we miss the opportunity to create Intelligent Infrastructure that will provide the foundation for increased safety and resilience, improved efficiencies and civic services, and broader economic opportunities and job growth. Indeed, our challenge is to proactively engage the declining, incumbent national infrastructure system and not merely repair it, but to enhance it; to create an internationally competitive cyber-physical system that provides an immediate opportunity for better services for citizens and that acts as a platform for a 21st century, high-tech economy and beyond.

cs.CY↗

arXiv2017

MOBILITY21: Strategic Investments for Transportation Infrastructure & Technology

America's transportation infrastructure is the backbone of our economy. A strong infrastructure means a strong America - an America that competes globally, supports local and regional economic development, and creates jobs. Strategic investments in our transportation infrastructure are vital to our national security, economic growth, transportation safety and our technology leadership. This document outlines critical needs for our transportation infrastructure, identifies new technology drivers and proposes strategic investments for safe and efficient air, ground, rail and marine mobility of people and goods.

cs.CY↗

arXiv2017

Generalized continuity equations from two-field Schrödinger Lagrangians

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents, and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of $\mathcal{PT}$ symmetric quantum mechanics and paraxial optics.

quant-ph↗

arXiv2016

An accurate metric for the spacetime around neutron stars

The problem of having an accurate description of the spacetime around neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a neutron star. Furthermore, an accurate appropriately parameterised metric, i.e., a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work we present such an approximate stationary and axisymmetric metric for the exterior of neutron stars, which is constructed using the Ernst formalism and is parameterised by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical properties of a neutron star spacetime as they are calculated numerically in general relativity. Because the metric is given in terms of an expansion, the expressions are much simpler and easier to implement, in contrast to previous approaches. For the parameterisation of the metric in general relativity, the recently discovered universal 3-hair relations are used to produce a 3-parameter metric. Finally, a straightforward extension of this metric is given for scalar-tensor theories with a massless scalar field, which also admit a formulation in terms of an Ernst potential.

gr-qc↗

arXiv2016

Bio-Inspired Framework for Allocation of Protection Resources in Cyber-Physical Networks

In this chapter, we consider the problem of designing protection strategies to contain spreading processes in complex cyber-physical networks. We illustrate our ideas using a family of bio-motivated spreading models originally proposed in the epidemiological literature, e.g., the Susceptible-Infected-Susceptible (SIS) model. We first introduce a framework in which we are allowed to distribute two types of resources in order to contain the spread, namely, (i) preventive resources able to reduce the spreading rate, and (ii) corrective resources able to increase the recovery rate of nodes in which the resources are allocated. In practice, these resources have an associated cost that depends on either the resiliency level achieved by the preventive resource, or the restoration efficiency of the corrective resource. We present a mathematical framework, based on dynamic systems theory and convex optimization, to find the cost-optimal distribution of protection resources in a network to contain the spread. We also present two extensions to this framework in which (i) we consider generalized epidemic models, beyond the simple SIS model, and (ii) we assume uncertainties in the contact network in which the spreading is taking place. We compare these protection strategies with common heuristics previously proposed in the literature and illustrate our results with numerical simulations using the air traffic network.

cs.SI↗

arXiv2016

Astrophysical applications of the post-Tolman-Oppenheimer-Volkoff formalism

The bulk properties of spherically symmetric stars in general relativity can be obtained by integrating the Tolman-Oppenheimer-Volkoff (TOV) equations. In previous work we developed a "post-TOV" formalism - inspired by parametrized post-Newtonian theory - which allows us to classify in a parametrized, phenomenological form all possible perturbative deviations from the structure of compact stars in general relativity that may be induced by modified gravity at second post-Newtonian order. In this paper we extend the formalism to deal with the stellar exterior, and we compute several potential astrophysical observables within the post-TOV formalism: the surface redshift $z_s$, the apparent radius $R_{\rm app}$, the Eddington luminosity at infinity $L_{\rm E}^\infty$ and the orbital frequencies. We show that, at leading order, all of these quantities depend on just two post-TOV parameters $μ_1$ and $χ$, and we discuss the possibility to measure (or set upper bounds on) these parameters.

gr-qc↗

arXiv2015

Diffusing Private Data over Networks

The emergence of social and technological networks has enabled rapid sharing of data and information. This has resulted in significant privacy concerns where private information can be either leaked or inferred from public data. The problem is significantly harder for social networks where we may reveal more information to our friends than to strangers. Nonetheless, our private information can still leak to strangers as our friends are their friends and so on. In order to address this important challenge, in this paper, we present a privacy-preserving mechanism that enables private data to be diffused over a network. In particular, whenever a user wants to access another users' data, the proposed mechanism returns a differentially private response that ensures that the amount of private data leaked depends on the distance between the two users in the network. While allowing global statistics to be inferred by users acting as analysts, our mechanism guarantees that no individual user, or a group of users, can harm the privacy guarantees of any other user. We illustrate our mechanism with two examples: one on synthetic data where the users share their GPS coordinates; and one on a Facebook ego-network where a user shares her infection status.

cs.DS↗

arXiv2015

Self-Trapping of Diskoseismic Corrugation Modes in Neutron Star Spacetimes

We examine the effects of higher-order multipole contributions of rotating neutron star (NS) spacetimes on the propagation of corrugation (c-)modes within a thin accretion disk. We find that the Lense-Thirring precession frequency, which determines the propagation region of the low-frequency fundamental corrugation modes, can experience a turnover allowing for c-modes to become self-trapped for sufficiently high dimensionless spin $j$ and quadrupole rotational deformability $α$. If such self-trapping c-modes can be detected, e.g. through phase-resolved spectroscopy of the iron line for a high-spin low-mass accreting neutron star, this could potentially constrain the spin-induced NS quadrupole and the NS equation of state.

astro-ph.HE↗

arXiv2015

Unified description of astrophysical properties of neutron stars independent of the equation of state

In recent years, a lot of work was done that has revealed some very interesting properties of neutron stars. One can relate the first few multipole moments of a neutron star, or quantities that can be derived from them, with relations that are independent of the equation of state (EoS). This is a very significant result that has great implications for the description of neutron stars and in particular for the description of the spacetime around them. Additionally, it was recently shown that there is a four parameter analytic spacetime, known as the two-soliton spacetime, which can accurately capture the properties of the geometry around neutron stars. This allows for the possibility of describing in a unified formalism the astrophysically relevant properties of the spacetime around a neutron star independently of the particulars of the EoS for the matter of the star. More precisely, the description of these astrophysical properties is done using an EoS omniscient spacetime that can describe the exterior of any neutron star. In the present work we investigate properties such as the location of the innermost stable circular orbit $R_{ISCO}$ (or the surface of the star when the latter overcomes the former), the various frequencies of perturbed circular equatorial geodesics, the efficiency of an accretion disc, its temperature distribution, and other properties associated with the emitted radiation from the disc, in a way that holds for all possible choices of a realistic EoS for the neutron star. Furthermore, we provide proof of principle that if one were to measure the right combinations of pairs of these properties, with the additional knowledge of the mass of the neutron star, one could determine the EoS of the star.

astro-ph.HE↗

arXiv2015

Post-Tolman-Oppenheimer-Volkoff formalism for relativistic stars

Besides their astrophysical interest, compact stars also provide an arena for understanding the properties of theories of gravity that differ from Einstein's general relativity. Numerous studies have shown that different modified theories of gravity can modify the bulk properties (such as mass and radius) of neutron stars for given assumptions on the microphysics. What is not usually stressed though is the strong degeneracy in the predictions of these theories for the stellar mass and radius. Motivated by this observation, in this paper we take an alternative route and construct a stellar structure formalism which, without adhering to any particular theory of gravity, describes in a simple parametrized form the departure from compact stars in general relativity. This "post-Tolman-Oppenheimer-Volkoff (TOV)" formalism for spherical static stars is inspired by the well-known parametrized post-Newtonian theory, extended to second post-Newtonian order by adding suitable correction terms to the fully relativistic TOV equations. We show how neutron star properties are modified within our formalism, paying special attention to the effect of each correction term. We also show that the formalism is equivalent to general relativity with an "effective" (gravity-modified) equation of state.

gr-qc↗

arXiv2015

Geodesic properties in terms of multipole moments in scalar-tensor theories of gravity

The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables that characterise geodesics in terms of the moments. These expressions provide some insight into how the structure of a scalarized compact object affects observables. They can also be used to understand how deviations from general relativity are imprinted on the observables.

gr-qc↗