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As the era of gravitational-wave astronomy has well and truly begun, gravitational radiation from rotating neutron stars remains elusive. Rapidly spinning neutron stars are the main targets for continuous-wave searches since, according to general relativity, provided they are asymmetrically deformed, they will emit gravitational waves. It is believed that detecting such radiation will unlock the answer to why no pulsars have been observed to spin close to the break-up frequency. We review existing studies on the maximum mountain that a neutron star crust can support, critique the key assumptions and identify issues relating to boundary conditions that need to be resolved. In light of this discussion, we present a new scheme for modelling neutron star mountains. The crucial ingredient for this scheme is a description of the fiducial force which takes the star away from sphericity. We consider three examples: a source potential which is a solution to Laplaces equation, another solution which does not act in the core of the star and a thermal pressure perturbation. For all the cases, we find that the largest quadrupoles are between a factor of a few to two orders of magnitude below previous estimates of the maximum mountain size.
Rapidly spinning, deformed neutron stars have long been considered potential gravitational-wave emitters. However, so far only upper limits on the size of the involved quadrupole deformations have been obtained. For this reason, it is pertinent to as
Finite size effects in a neutron star merger are manifested, at leading order, through the tidal deformabilities (Lambdas) of the stars. If strong first-order phase transitions do not exist within neutron stars, both neutron stars are described by th
Although the main features of the evolution of binary neutron star systems are now well established, many details are still subject to debate, especially regarding the post-merger phase. In particular, the lifetime of the hyper-massive neutron stars
The discovery of a radioactively powered kilonova associated with the binary neutron star merger GW170817 was the first - and still only - confirmed electromagnetic counterpart to a gravitational-wave event. However, observations of late-time electro
We report the discovery and initial follow-up of a double neutron star (DNS) system, PSR J1946$+$2052, with the Arecibo L-Band Feed Array pulsar (PALFA) survey. PSR J1946$+$2052 is a 17-ms pulsar in a 1.88-hour, eccentric ($e , =, 0.06$) orbit with a