Gravitational radiation from corotating binary neutron stars of incompressible fluid in the first post-Newtonian approximation of general relativity

TL;DR

This paper analytically investigates gravitational radiation from corotating binary neutron stars with incompressible fluid, including first post-Newtonian corrections and finite size effects, revealing that 1PN effects slightly reduce finite size contributions.

Contribution

It provides the first analytical derivation of 1PN order gravitational radiation from corotating incompressible fluid neutron star binaries, incorporating finite size effects.

Findings

Finite size effects at 1PN order are only slightly smaller than Newtonian estimates.

The 1PN correction decreases the finite size effect in gravitational radiation.

Finite size effects are proportional to the ratio of gravitational radius to stellar radius.

Abstract

We analytically study gravitational radiation from corotating binary neutron stars composed of incompressible, homogeneous fluid in circular orbits. The energy and the angular momentum loss rates are derived up to the first post-Newtonian (1PN) order beyond the quadrupole approximation including effects of the finite size of each star of binary. It is found that the leading term of finite size effects in the 1PN order is only $O(GM_{\ast}/c^2 a_{\ast})$ smaller than that in the Newtonian order, where $GM_{\ast}/c^2 a_{\ast}$ means the ratio of the gravitational radius to the mean radius of each star of binary, and the 1PN term acts to decrease the Newtonian finite size effect in gravitational radiation.