The classical equations of motion for an axion with potential V (φ) = m 2 a f 2 a [1 − cos(φ/fa)] possess quasi-stable, localized, oscillating solutions, which we refer to as "axion stars". We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an "axion star stability diagram", parameterized by the initial ADM mass, MADM, and axion decay constant, fa. We identify three regions of the parameter space: i) long-lived oscillating axion star solutions, with a base frequency, ma, modulated by self-interactions, ii) collapse to a BH and iii) complete dispersal due to gravitational cooling and interactions. We locate the boundaries of these three regions and an approximate "triple point" (MTP, fTP) ∼ (2.4M 2 pl /ma, 0.3M pl ). For fa below the triple point BH formation proceeds during winding (in the complex U (1) picture) of the axion field near the dispersal phase. This could prevent astrophysical BH formation from axion stars with fa M pl . For larger fa fTP, BH formation occurs through the stable branch and we estimate the mass ratio of the BH to the stable state at the phase boundary to be O(1) within numerical uncertainty. We discuss the observational relevance of our findings for axion stars as BH seeds, which are supermassive in the case of ultralight axions. For the QCD axion, the typical BH mass formed from axion star collapse is MBH ∼ 3.4(fa/0.6M pl ) 1.2 M .

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We consider the effects of inhomogeneous initial conditions in both the scalar field profile and the extrinsic curvature on different inflationary models. In particular, we compare the robustness of small field inflation to that of large field inflation, using numerical simulations with Einstein gravity in 3+1 dimensions. We find that small field inflation can fail in the presence of subdominant gradient energies, suggesting that it is much less robust to inhomogeneities than large field inflation, which withstands dominant gradient energies. However, we also show that small field inflation can be successful even if some regions of spacetime start out in the region of the potential that does not support inflation. In the large field case, we confirm previous results that inflation is robust if the inflaton occupies the inflationary part of the potential. Furthermore, we show that increasing initial scalar gradients will not form sufficiently massive inflation-ending black holes if the initial hypersurface is approximately flat. Finally, we consider the large field case with a varying extrinsic curvature K, such that some regions are initially collapsing. We find that this may again lead to local black holes, but overall the spacetime remains inflationary if the spacetime is open, which confirms previous theoretical studies.

In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured BergerRigoutsos grid generation. The code supports non-trivial "many-boxes-in-many-boxes" mesh hierarchies and massive parallelism through the Message Passing Interface (MPI). GRChombo evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3 + 1 setting, whilst also significantly simplifying the process of setting up the mesh for these problems. We show that GRChombo can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.

Extending our previous work on the robustness of inflation to perturbations in the scalar field, we investigate the effects of perturbations in the transverse traceless part of the extrinsic curvature on the evolution of an inhomogeneous inflaton field. Focusing on small field models, we show that these additional metric inhomogeneities initially reduce the total number of e-folds as the amplitude increases, but that the reduction saturates and even reverses above a certain amplitude. We present an argument that this is due to the presence of a large initial Hubble friction when metric perturbations are large.