Time-domain modeling of Extreme-Mass-Ratio Inspirals for the Laser Interferometer Space Antenna

Priscilla Canizares and Carlos F. Sopuerta

It is known that the majority of the galactic nuclei harbour a massive black hole (MBH), $M= 10^4-10^7 M_{odot}$ s. Such MBH can capture a stellar-mass compact object (SCO), $m = 1-50 M^{}_{odot}$, which ends up on a closer orbit to the MBH becoming gravitationally bounded to it. Subsequently, the orbit of the SCO shrinks due to the loss of energy and angular momentum through the emission of gravitational waves, which eventually makes the SCO plunge onto the MBH. The detection of gravitational wave signals produced during the inspiral phase of the SCO is the main goal of the future space-based gravitational-wave observatory LISA. However it will not be a straightforward task, due to the fact that the gravitational-wave signals from these so called Extreme-Mass-Ratio Inspiral (EMRI) systems will be buried in the detector instrumental noise and the gravitational wave foreground. Then, we will need accurate theoretical templates to dig out from the noise the relevant physical information, which means that we have to take into account the effect of the SCO gravitational field on its own trajectory. In other words, we have to compute the SCO gravitational back-reaction. In order to do so, this back reaction can be modeled as the action of a local {em self-force}. In this regard, the obtention of an efficient method to compute the self-force acting on a point-like object orbiting a massive black hole (MBH) is being object of an increasing interest due to its potential applicability on EMRIs. In this talk, we present a new time-domain technique to compute the self-force based on such model. The pseudospectral collocation method employed in our scheme, along with a multidomain spatial set-up, makes our approach a very suitable numerical tool to compute the self-force.