Neutron stars are the most compact objects in the visible universe. As such they form intriguing laboratories of extreme physics. The density surpasses that of the atomic nucleus. The question arises what that does to matter. Does the star really consist mainly of neutrons, or are even neutrons not 'rigid' enough to withstand the pressure. We do not know yet, because we do not understand the theory of elementary particles completely to understand how they interact under these circumstances. Also, accurate measurements of neutron star sizes remain illusive, so we do not know the density with great accuracy. Hopefully, thermonuclear X-ray bursts will one day (soon) provide an answer. After all, they are the most luminous phenomenon on the neutron star surface. An important step forward would be the detection of spectral features in burst spectra and the measurement of their gravitational redshift, which is expected to be tens of percents. This is my current primary motive in research: hunt for particular kinds of bursts with the greatest X-ray telescopes of the day (Chandra and XMM-Newton), that have the highest probability of showing such features. These bursts are rare, which doesn't make it particularly easy.
The first X-ray source detected outside our solar system, Sco X-1 in 1962, is an X-ray binary. Such objects form the brightest stars in the X-ray sky. They are the most efficient power houses in our galaxy, generating a few hundred MeV out of every nucleon. Compare that to a few MeV through nuclear burning. Much is known about them today. However, new phenomena keep being discovered and some long-known behavior is still not understood. Regarding the latter, we basically do not understand in detail the variability of the radiation. This pertains to time scales of years (super-orbital modulations) as well as milliseconds (kHz quasi-periodic oscillations; burst oscillations). Herein, I find motive to continue research in this area.
I used to be involved in other areas of research, such as gamma-ray bursts, supergiant fast X-ray transients, stellar flares and coded aperture imaging. Although I haven't been active in these for some years, they are not completely out of my field of view.