Abstract:
The crucial role played by pressure in general relativity is explored in the mathematically simple context of a static spherically symmetric geometry. By keeping all pressure terms, the standard formalisms of rotation curve and gravitational lensing observations are extended to a first post-Newtonian order. It turns out that both post-Newtonian formalisms encode the gravitational field differently. Therefore, combined observations of rotation curves and gravitational lensing of the same galaxy can in principle be used to infer both the density and pressure profile of the galactic fluid, whereas the currently employed quasi-Newtonian formalisms only allow us to deduce the density profile.
If a suitable decomposition of the galaxy model is used to separate the dark matter from the galactic fluid, the newly introduced post-Newtonian formalism might allow us to make inferences about the equation of state of dark matter. While the Cold Dark Matter paradigm is currently favoured in the astrophysics and cosmology communities, the formalism presented herein offers an unprecedented way of being able to directly observe the equation of state, and therefore either confirm the CDM paradigm or gain new insight into the nature of galactic dark matter.
In a logically distinct analysis, I investigate the effects of negative pressure in compact objects, motivated by the recently introduced gravastar model. I find that gravastar like objects - which have an equation of state that exhibits negative pressure at the core of the object - can in principle mimic the external gravitational field of a black hole. Unlike a black hole, however, gravastars neither exhibit a pathological curvature singularity at the origin nor do they posess an event horizon. Instead they are mathematically well defined everywhere. Finally, another exotic option is considered as a mathematical alternative to black holes: The anti-gravastar, which is characterized by a core that has a negative mass-energy density.
