arXiv subjects

Nicolas Yunes

Publications and source records attributed to Nicolas Yunes.

185 records · Page 11Linked to original sources

arXiv2006

Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions

We construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in ADMTT coordinates. The specific matching procedure used here closely follows the calculation in gr-qc/0503011, and is performed in the so called buffer zone where both the post-Newtonian and the perturbed Schwarzschild approximations hold. The result is that both metrics agree in the buffer zone, up to the errors in the approximations. However, since isotropic coordinates are very similar to ADMTT coordinates, matching yields better results than in the previous calculation, where harmonic coordinates were used for the post-Newtonian 4-metric. In particular, not only does matching improve in the buffer zone, but due to the similarity between ADMTT and isotropic coordinates the two metrics are also close to each other near the black hole horizons. With the help of a transition function we also obtain a global smooth 4-metric which has errors on the order of the error introduced by the more accurate of the two approximations we match. This global smoothed out 4-metric is obtained in ADMTT coordinates which are not horizon penetrating. In addition, we construct a further coordinate transformation that takes the 4-metric from global ADMTT coordinates to new coordinates which are similar to Kerr-Schild coordinates near each black hole, but which remain ADMTT further away from the black holes. These new coordinates are horizon penetrating and lead, for example, to a lapse which is everywhere positive on the t=0 slice. Such coordinates may be more useful in numerical simulations.

gr-qc↗

arXiv2004

Universality of the subsolar mass distribution from critical gravitational collapse

Self-similarity induced by critical gravitational collapse is used as a paradigm to probe the mass distribution of subsolar objects. At large mass (solar mass and above) there is widespread agreement as to both the form and parameter values arising in the mass distribution of stellar objects. At subsolar mass there is still considerable disagreement as to the qualitative form of the mass distribution, let alone the specific parameter values characterizing that distribution. For the first time, the paradigm of critical gravitational collapse is applied to several concrete astrophysical scenarios to derive robust qualitative features of the subsolar mass distribution. We further contrast these theoretically derived ideas with the observational situation. In particular, we demonstrate that at very low mass the distribution is given by a power law, with an exponent opposite in sign to that observed in the high-mass regime. The value of this low-mass exponent is in principle calculable via dynamical systems theory applied to gravitational collapse. Qualitative agreement between theory, numerical experiments, and observational data is good, though quantitative issues remain troublesome.

astro-ph↗

arXiv2004

Testing Alternative Theories of Gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter ωof scalar-tensor theories of the Brans-Dicke type and on the Compton wavelength of the graviton λ_g in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA Sensitivity Curve Generator (SCG), available online. For a neutron star inspiralling into a 10^3 M_sun black hole in the Virgo Cluster, in a two-year integration, we find a lower bound ω> 3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error. Lower bounds on the graviton Compton wavelength ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year observations of massive binary black hole inspirals at cosmological distances (3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.

gr-qc↗

arXiv2004

Power-laws from critical gravitational collapse: The mass distribution of subsolar objects

Critical gravitational collapse and self similarity are used to probe the mass distribution of subsolar objects. We demonstrate that at very low mass the distribution is given by a power law, with an exponent opposite in sign to that observed at high-mass regime. We further show that the value of this low-mass exponent is in principle calculable via dynamical systems theory applied to gravitational collapse. Qualitative agreement between numerical experiments and observational data is good.

astro-ph↗

arXiv2002

Power laws, scale invariance, and generalized Frobenius series: Applications to Newtonian and TOV stars near criticality

We present a self-contained formalism for analyzing scale invariant differential equations. We first cast the scale invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-like power series with exponents that are integer multiples of the exponents arising in the linearized problem. This Frobenius-like series can be viewed as a variant of Liapunov's expansion theorem. As specific examples we apply these ideas to Newtonian and relativistic isothermal stars and demonstrate (both numerically and analytically) that the solution exhibits oscillatory power-law behaviour as the star approaches the point of collapse. These series solutions extend classical results. (Lane, Emden, and Chandrasekhar in the Newtonian case; Harrison, Thorne, Wakano, and Wheeler in the relativistic case.) We also indicate how to extend these ideas to situations where fixed points may not exist -- either due to ``monotone'' flow or due to the presence of limit cycles. Monotone flow generically leads to logarithmic deviations from scaling, while limit cycles generally lead to discrete self-similar solutions.

gr-qc↗