Master equation solutions in the linear regime of characteristic formulation of general relativity

From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and M\"adler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the $J$ metric variable of the Bondi-Sachs metric. Once $\beta$, another Bondi-Sachs potential, is obtained from the field equations, and $J$ is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, M\"adler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new solutions to the master equation for any multipolar moment $l$, with and without matter sources in terms only of the first kind Bessel's functions for the Minkowski, and in terms of the Confluent Heun's functions (Generalised Hypergeometric) for radiative (nonradiative) case in the Schwarzschild's background. We particularize our families of solutions for the known cases for $l=2$ reported previously in the literature and find complete agreement, showing the robustness of our results.Comment: 19 page

Gravitational radiation by point particle eccentric binary systems in the linearised characteristic formulation of general relativity

We study a binary system composed of point particles of unequal masses in eccentric orbits in the linear regime of the characteristic formulation of general relativity, generalising a previous study found in the literature in which a system of equal masses in circular orbits is considered. We also show that the boundary conditions on the time-like world tubes generated by the orbits of the particles can be extended beyond circular orbits. Concerning the power lost by the emission of gravitational waves, it is directly obtained from the Bondi's News function. It is worth stressing that our results are completely consistent, because we obtain the same result for the power derived by Peters and Mathews, in a different approach, in their seminal paper of 1963. In addition, the present study constitutes a powerful tool to construct extraction schemes in the characteristic formalism to obtain the gravitational radiation produced by binary systems during the inspiralling phase.Comment: 16 pages, 2 figures, DOI 10.1007/s10714-016-2038-

Point Particle Binary System with Components of Different Masses in the Linear Regime of the Characteristic Formulation of General Relativity

A study of binary systems composed of two point particles with different masses in the linear regime of the characteristic formulation of general relativity in a Minkowski background is provided. The present paper generalizes a previous study find in the literature. The boundary conditions at the world tubes generated by the particle's orbits are explored, when the metric variables are decomposed in spin-weighted spherical harmonics. The power lost by the emission of gravitational waves is computed using the News Bondi's functions. The power found is nothing but the well-known result for the power obtained by Peters and Mathews in a different approach. This agreement shows the consistency of the approach considered here. The contribution to the gravitational radiation of several multipole terms is also shown.Comment: 16 pages, 3 figure

Gravitational wave background from neutron star phase transition

We study the generation of a stochastic gravitational wave (GW) background produced by a population of neutron stars (NSs) which go over a hadron-quark phase transition in its inner shells. We obtain, for example, that the NS phase transition, in cold dark matter scenarios, could generate a stochastic GW background with a maximum amplitude of $h_{\rm BG} \sim 10^{-24}$, in the frequency band $\nu_{\rm{obs}} \simeq 20-2000 {\rm Hz}$ for stars forming at redshifts of up to $z\simeq 20.$ We study the possibility of detection of this isotropic GW background by correlating signals of a pair of Advanced LIGO observatories.Comment: 17 pages, 5 figure

A New Method to Calculate the Stochastic Background of Gravitational Waves Generated by Compact Binaries

In the study of gravitational waves (GWs), the stochastic background generated by compact binary systems are among the most important kinds of signals. The reason for such an importance has to do with their probable detection by the interferometric detectors [such as the Advanced LIGO (ALIGO) and Einstein Telescope (ET)] in the near future. In this paper we are concerned with, in particular, the stochastic background of GWs generated by double neutron star (DNS) systems in circular orbits during their periodic and quasi--periodic phases. Our aim here is to describe a new method to calculate such spectra, which is based on an analogy with a problem of Statistical Mechanics. Besides, an important characteristic of our method is to consider the time evolution of the orbital parameters.Comment: 10 pages, 2 figure

Stochastic Background of Gravitational Waves Generated by Eccentric Neutron Star Binaries

Binary systems emit gravitational waves in a well-known pattern; for binaries in circular orbits, the emitted radiation has a frequency that is twice the orbital frequency. Systems in eccentric orbits, however, emit gravitational radiation in the higher harmonics too. In this paper, we are concerned with the stochastic background of gravitational waves generated by double neutron star systems of cosmological origin in eccentric orbits. We consider in particular the long-lived systems, that is, those binaries for which the time to coalescence is longer than the Hubble time ($\sim 10$Gyr). Thus, we consider double neutron stars with orbital frequencies ranging from $10^{-8}$ to $2\times 10^{-6}$Hz. Although in the literature some papers consider the spectra generated by eccentric binaries, there is still space for alternative approaches for the calculation of the backgrounds. In this paper, we use a method that consists in summing the spectra that would be generated by each harmonic separately in order to obtain the total background. This method allows us to clearly obtain the influence of each harmonic on the spectra. In addition, we consider different distribution functions for the eccentricities in order to investigate their effects on the background of gravitational waves generated. At last, we briefly discuss the detectability of this background by space-based gravitational wave antennas and pulsar timing arrays.Comment: 6 pages, 5 figure

The rings of Chariklo under close encounters with the giant planets

The Centaur population is composed by minor bodies wandering between the giant planets and that frequently perform close gravitational encounters with these planets, which leads to a chaotic orbital evolution. Recently, the discovery of two well-defined narrow rings was announced around the Centaur 10199 Chariklo. The rings are assumed to be in the equatorial plane of Chariklo and to have circular orbits. The existence a well-defined system of rings around a body in such perturbed orbital region poses an interesting new problem. Are the rings of Chariklo stable when perturbed by close gravitational encounters with the giant planets? Our approach to address this question consisted of forward and backward numerical simulations of 729 clones of Chariklo, with similar initial orbits, for a period of 100 Myrs. We found, on average, that each clone suffers along its lifetime more than 150 close encounters with the giant planets within one Hill radius of the planet in question. We identified some extreme close encounters able to significantly disrupt or to disturb the rings of Chariklo. About 3% of the clones lose the rings and about 4% of the clones have the ring significantly disturbed. Therefore, our results show that in most of the cases (more than 90%) the close encounters with the giant planets do not affect the stability of the rings in Chariklo-like systems. Thus, if there is an efficient mechanism that creates the rings, then these structures may be common among these kinds of Centaurs.Comment: 11 pages. Accepted for publication in AP

The Gravitational Wave Background From Coalescing Compact Binaries: A New Method

Gravitational waves are perturbations in the spacetime that propagate at the speed of light. The study of such phenomenon is interesting because many cosmological processes and astrophysical objects, such as binary systems, are potential sources of gravitational radiation and can have their emissions detected in the near future by the next generation of interferometric detectors. Concerning the astrophysical objects, an interesting case is when there are several sources emitting in such a way that there is a superposition of signals, resulting in a smooth spectrum which spans a wide range of frequencies, the so-called stochastic background. In this paper, we are concerned with the stochastic backgrounds generated by compact binaries (i.e. binary systems formed by neutron stars and black holes) in the coalescing phase. In particular, we obtain such backgrounds by employing a new method developed in our previous studies.Comment: 8 pages, 2 figure

Forecast constraints on f(T)f(T) gravity with gravitational waves from compact binary coalescences

The direct detection of gravitational waves (GWs) opened a new chapter in the modern cosmology to probe possible deviations from the general relativity (GR) theory. In the present work, we investigate for the first time the modified GW form propagation from the inspiraling of compact binary systems within the context of $f(T)$ gravity in order to obtain new forecasts/constraints on the free parameter of the theory. First, we show that the modified waveform differs from the GR waveform essentially due to induced corrections on the GWs amplitude. Then, we discuss the forecasts on the $f(T)$ gravity assuming simulated sources of GWs as black hole binaries, neutron star binaries and black hole - neutron star binary systems, which emit GWs in the frequency band of the Advanced LIGO (aLIGO) interferometer and of the third generation Einstein Telescope (ET). We show that GWs sources detected within the aLIGO sensitivity can return estimates of the same order of magnitude of the current cosmological observations. On the other hand, detection within the ET sensitivity can improve by up to 2 orders of magnitude the current bound on the $f(T)$ gravity. Therefore, the statistical accuracy that can be achieved by future ground based GW observations, mainly with the ET detector (and planed detectors with a similar sensitivity), can allow strong bounds on the free parameter of the theory, and can be decisive to test the theory of gravitation.Comment: 13 pages, 9 captioned figures. Version published in PR

Formation of the G-ring arc

Since 2004, the images obtained by Cassini spacecraft's on-board cameras have revealed the existence of several small satellites in the Saturn system. Some of these small satellites are embedded in arcs of particles. While these satellites and their arcs are known to be in corotation resonances with Mimas, their origin remains unknown. This work investigates one possible process for capturing bodies into a corotation resonance, which involves raising the eccentricity of a perturbing body. Therefore, through numerical simulations and analytical studies, we show a scenario that the excitation of Mimas' eccentricity could capture particles in a corotation resonance and given a possible explanation for the origin for the arcs.Comment: 8 pages, 7 figures and 1 tabl