A system of charged bosons at finite temperature and chemical potential is studied in a general-relativistic framework. We assume that the boson fields interact only gravitationally. At sufficiently low temperature the system exists in two phases: the gas and the condensate. By studying the condensation process numerically we determine the critical temperature $T_c$ at which the condensate emerges. As the temperature decreases, the system eventually settles down in the ground state of a cold boson star.
We derive the non-relativistic limit of a massive vector field. We show that the Cartesian spatial components of the vector behave as three identical, non-interacting scalar fields. We find classes of spherical, cylindrical, and planar self-gravitating vector solitons in the Newtonian limit. The gravitational properties of the lowest-energy vector solitons$mathrm{-}$the gravitational potential and density field$mathrm{-}$depend only on the net mass of the soliton and the vector particle mass. In particular, these self-gravitating, ground-state vector solitons are independent of the distribution of energy across the vector field components, and are indistinguishable from their scalar-field counterparts. Fuzzy Vector Dark Matter models can therefore give rise to halo cores with identical observational properties to the ones in scalar Fuzzy Dark Matter models. We also provide novel hedgehog vector soliton solutions, which cannot be observed in scalar-field theories. The gravitational binding of the lowest-energy hedgehog halo is about three times weaker than the ground-state vector soliton. Finally, we show that no spherically symmetric solitons exist with a divergence-free vector field.
We address the question whether a medium featuring $p + rho = 0$, dubbed $Lambda$- medium, has to be necessarily a cosmological constant. By using effective field theory, we show that this is not the case for a class of media comprising perfect fluids, solids and special super solids, providing an explicit construction. The low energy excitations are non trivial and lensing, the growth of large scale structures can be used to clearly distinguish $Lambda$-media from a cosmological constant.
We study a static system of self-gravitating radiations confined in a sphere by using numerical and analytical calculations. Due to the scaling symmetry of radiations, most of main properties of a solution can be represented as a segment of a solution curve on a plane of two-dimensional scale invariant variables. We define an `approximate horizon (AH) from the analogy with an apparent horizon. Any solution curve contains a unique point which corresponds to the AH. A given solution is uniquely labelled by three parameters representing the solution curve, the size of the AH, and the sphere size, which are an alternative of the data at the outer boundary. Various geometrical properties including the existence of an AH and the behaviors around the center can be identified from the parameters. We additionally present an analytic solution of the radiations on the verge of forming a blackhole. Analytic formulae for the central mass of the naked singularity are given.
We examine the dynamics of a self--gravitating magnetized neutron gas as a source of a Bianchi I spacetime described by the Kasner metric. The set of Einstein-Maxwell field equations can be expressed as a dynamical system in a 4-dimensional phase space. Numerical solutions of this system reveal the emergence of a point--like singularity as the final evolution state for a large class of physically motivated initial conditions. Besides the theoretical interest of studying this source in a fully general relativistic context, the resulting idealized model could be helpful in understanding the collapse of local volume elements of a neutron gas in the critical conditions that would prevail in the center of a compact object.
Both cosmological expansion and black holes are ubiquitous features of our observable Universe, yet exact solutions connecting the two have remained elusive. To this end, we study self-gravitating classical fields within dynamical spherically symmetric solutions that can describe black holes in an expanding universe. After attempting a perturbative approach of a known black-hole solution with scalar hair, we show by exact methods that the unique scalar field action with first-order derivatives that can source shear-free expansion around a black hole requires noncanonical kinetic terms. The resulting action is an incompressible limit of k-essence, otherwise known as the cuscuton theory, and the spacetime it describes is the McVittie metric. We further show that this solution is an exact solution to the vacuum Hov{r}ava-Lifshitz gravity with anisotropic Weyl symmetry.