Binary black hole mergers inf(R)theory

Abstract

In the near future, gravitational wave detection is set to become an important observational tool for astrophysics. It will provide us with an excellent means to distinguish different gravitational theories. In effective form, many gravitational theories can be cast into an f (R) theory. In this article, we study the dynamics and gravitational waveform of an equal-mass binary black hole system in f (R) theory. We reduce the equations of motion in f (R) theory to the Einstein-Klein-Gordon coupled equations. In this form, it is straightforward to modify our existing numerical relativistic codes to simulate binary black hole mergers in f (R) theory. We considered binary black holes surrounded by a shell of scalar field. We solve the initial data numerically using the Olliptic code. The evolution part is calculated using the extended AMSS-NCKU code. Both codes were updated and tested to solve the problem of binary black holes in f (R) theory. Our results show that the binary black hole dynamics in f (R) theory is more complex than in general relativity. In particular, the trajectory and merger time are strongly affected. Via the gravitational wave, it is possible to constrain the quadratic part parameter of f (R) theory in the range |a2| < 10 11 m 2 . In principle, a gravitational wave detector can distinguish between a merger of binary black hole in f (R) theory and the respective merger in general relativity. Moreover, it is possible to use gravitational wave detection to distinguish between f (R) theory and a non self-interacting scalar field model in general relativity.

Coalescence of binary neutron stars in a scalar-tensor theory of gravity

“…We derive the scalar-wave luminosity from the scalar dipole moment integrating Eq. (22). The relevant term in the wave zone is φ → d : i n i =r where n i is the unit spatial vector pointing along the radial direction, and d i is the scalar dipole moment with magnitude…”

“…To reach this goal, the two-body dynamics and gravitational-wave emission in modified theories have been computed analytically, in an approximated way, via the post-Newtonian framework [7,[16][17][18] and more recently, also numerically, solving the field equations with all the nonlinearities [19][20][21][22]. Here we focus on the scalar-tensor theory by Damour and Esposito-Farése (DEF) [10][11][12] and study its strong-field dynamical regime by performing numericalrelativity simulations of coalescing binary neutron stars.…”

On the hyperbolicity and stability of $$3+1$$ 3 + 1 formulations of metric f(R) gravity

“…In fact, with the exception of [83], the Cauchy problem of f (R) has mostly been studied by utilizing this equivalence, see [23,44] for examples involving numerical applications. However, such dynamical equivalence should be interpreted with caution [48,20,28,56].…”

Gravitational wave astronomy: chance and challenge to fundamental physics and astrophysics

“…The invoked difficulty is how to construct corresponding theoretical model for GW data analysis end. Leaving alone the numerical stability problem, the more serious problem is how to relate the matter field involved in the fundamental physical law to the astrophysical objects [12]. On the experiment side, there is also a challenge about how to determine the polarization modes [13].…”

“…Currently, the idea is firstly solving the direct problem to construct the corresponding theoretical model for GW sources based on specific fundamental physics law. Then based on such theoretical model, the matured GW data analysis technique, matched filtering method, can be adapted to treat the corresponding inverse problem [12]. The invoked difficulty is how to construct corresponding theoretical model for GW data analysis end.…”