Gravitational theory
Glossary
The Einstein equations can be solved within certain approximation schemes.
One may for instance assume that the compact objects in the binaries move slowly with respect to the speed of light ($v/c \ll 1$) and within weak gravitational fields (formally $G\ll1$). This gives rise to post-Newtonian (PN) schemes.
A second approximation that still expands expressions in weak fields, but this time for arbitrary velocities, is the post-Minkowskian (PM) approximation.
A third and final approximation is the small-mass-ratio (SMR) approximation, where one expands the Einstein equations in the asymmetry between the binary’s masses.
All these can be included in synergetic approaches such as the effective-one-body (EOB) formalism to extend their domain of validity. The idea is to cover a larger portion of the binary’s parameter space using the same relativistic information.
Projects
I have have explored how useful the PM approximation is to model LIGO-Virgo-type binaries. I find that successive orders in the PM approximation improve the description of the bound orbits detected in LIGO-Virgo analyses. This is not trivial, as PM information is usually obtained by studying scattering (and hence unbound orbits).
I have included SMR information into a EOB Hamiltonian for quasicircular nonspinning binaries, and compared the results against numerical-relativity simulations. We find excellent agreement, which suggests that self-force information may be a better base to model binaries than the PN approximation currently in use.
We have exploited inter-relationships between the PN, PM and SMR approximations to obtain high-order corrections in PN expansions of the binary’s conservative dynamics in a completely independent way to previous approaches. The method fully exploits concepts from PM theory and results from the self-force program, showcasing a deep relationship between the above approximations.