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The dependence of the final fate of supermassive star (SMS) cores on their mass and angular momentum is studied with simple modeling. SMS cores in the hydrogen burning phase encounter the general relativistic instability during the stellar evolution if the mass is larger than $\sim 3 \times 10^4M_\odot$. Spherical SMS cores in the helium burning phase encounter the general relativistic instability prior to the onset of the electron-positron pair instability if the mass is larger than $\sim 1\times 10^4M_\odot$. For rapidly rotating SMS cores, these values for the threshold mass are enhanced by up to a factor of $\sim 5$, and thus, for SMSs with mass smaller than $\sim 10^4M_\odot$ the collapse is triggered by the pair-instability, irrespective of the rotation. After the onset of the general relativistic instability, SMS cores in the hydrogen burning phase with reasonable metallicity are likely to collapse to a black hole irrespective of the degree of rotation, whereas the SMS cores in the helium burning phase could explode via nuclear burning with no black hole formation, as previous works demonstrate., Comment: 13 pages, 6 figures. Submitted to ApJ

We perform new general relativistic hydrodynamics simulations for collapses of rotating supermassive star cores with an approximate nuclear burning up to carbon and a detailed equation of state. For all the models we investigate, the energy generation by nuclear burning plays only a minor role, leading to the formation of a black hole without a nuclear-powered explosion. For rotating models, however, the stellar explosion associated with shock heating is driven from a torus, which forms after the black hole formation. The explosion energy is up to $10^{-4}$ of the mass energy of the supermassive star cores ($\sim 10^{55}-10^{56}$ erg). We find that, even if we increase the rotational angular momentum of the progenitor, the ejecta mass saturates at $\sim 1$\% of the total mass of the initial stellar core. The average ejecta velocity also saturates at $\approx 20\%$ of the speed of light. As a result, the ejecta kinetic energy is approximately proportional to the initial mass of the supermassive star core for the rapidly rotating case. We also perform viscous hydrodynamics simulations for exploring the evolution of the remnant torus. Although the viscous heating drives an outflow from the torus, we find that its effect is subdominant in terms of the kinetic energy because of the small velocity ($\approx 0.07c$) of the ejecta component., Comment: 21 pages, 11 figures, submitted to ApJ

Einstein-Cartan gravity is a close historical sibling of general relativity that allows for spacetime torsion. As a result, angular momentum couples to spacetime geometry in a similar way to energy. While consequences of this are well studied on cosmological scales, their role in neutron star physics is largely under-explored. We study the effects that torsion, sourced by either microphysical spin or macroscopic angular momentum, has on neutron stars. For this, we use a simplified polytropic model to quantify the microphysical coupling to torsion. We also derive expressions to model rotation-induced torsion effects and estimate the consequences for rotating neutron stars with different rotation rates. We find that the presence of torsion in general leads to neutron stars with smaller radii and masses, but higher central densities. Realistic models for microphysical spin lead to torsion effects that have no relevant influence on the neutron star structure. Rotation-induced torsion effects however, can decrease the radius by up to $900\,m$, which is comparable to the increase due to centrifugal forces. Depending on which effect dominates, this leads to a torsion-induced spin-up or spin-down of the neutron star. We conclude that torsion effects due to rotation can not be neglected and are large enough to be tested using current or near-future technology., Comment: 17+1 pages, 4 figures. v2: updated to match published version

Current boson star models are largely restricted to global symmetries and lower spin fields. In this work, we generalize these systems of self-gravitating bosonic fields to allow for arbitrary totally antisymmetric tensor fields and arbitrary internal gauge symmetries. We construct a generalized formalism for Yang-Mills-like theories, which allows for arbitrary k-form fields, instead of just vector fields. The k-form fields have gauge symmetries described by semisimple, compact Lie groups. We further derive equations of motion for the k-form fields and connection coefficients of the Lie group. Extensions and applications are also discussed. We present a novel way to fix the group connection using a spacetime connection. As an example, we derive explicitly the connection coefficients for SU(2) in a spherically symmetric spacetime using rectangular vielbeins. The combination of methods presented leads to a powerful, adaptable and practical framework. As a proof of concept, we derive ordinary differential equations for a 0-form field with a SU(2) symmetry. Our framework can be used to model self-gravitating (multi) particle states with internal symmetries, such as pion condensates or dark matter. It is also suited as a tool to approach open problems in modified gravity and string theory., Comment: 58 pages including appendix, both authors are first authors

Dark matter could accumulate around neutron stars in sufficient amounts to affect their global properties. In this work, we study the effect of a specific model for dark matter -- a massive and self-interacting vector (spin-1) field -- on neutron stars. We describe the combined systems of neutron stars and vector dark matter using Einstein-Proca theory coupled to a nuclear-matter term, and find scaling relations between the field and metric components in the equations of motion. We construct equilibrium solutions of the combined systems, compute their masses and radii and also analyse their stability and higher modes. The combined systems admit dark matter (DM) core and cloud solutions. Core solutions compactify the neutron star component and tend to decrease the total mass of the combined system. Cloud solutions have the inverse effect. Electromagnetic observations of certain cloud-like configurations would appear to violate the Buchdahl limit. This could make Buchdahl-limit violating objects smoking gun signals for dark matter in neutron stars. The self-interaction strength is found to significantly affect both mass and radius. We also compare fermion Proca stars to objects where the dark matter is modelled using a complex scalar field. We find that fermion Proca stars tend to be more massive and geometrically larger than their scalar field counterparts for equal boson masses and self-interaction strengths. Both systems can produce degenerate masses and radii for different amounts of DM and DM particle masses., Comment: 20 pages, 11 figures, supersedes arXiv:2308.12174. v2: Content matches published version in Particles (open access) https://www.mdpi.com/2571-712X/7/1/4

It is believed that dark matter (DM) could accumulate inside neutron stars and significantly change their masses, radii and tidal properties. We study what effect bosonic dark matter, modelled as a massive and self-interacting scalar or vector field, has on neutron stars. We derive equations to compute the tidal deformability of the full Einstein-Hilbert-Klein-Gordon system self-consistently, and probe the influence of the scalar field mass and self-interaction strength on the total mass and tidal properties of the combined system, called fermion boson stars (FBS). We are the first to combine Proca stars with neutron stars to mixed systems of fermions and a vector field in Einstein-Proca theory, which we name fermion Proca stars (FPS). We construct equilibrium solutions of FPS, compute their masses, radii and analyse them regarding their stability and higher modes. We find that FPS tend to be more massive and geometrically larger than FBS for equal boson masses and self-interaction strengths. Both FBS and FPS admit DM core and DM cloud solutions and we find that they can produce degenerate results. Core solutions compactify the neutron star component and lower their tidal deformability, cloud solutions have the inverse effect. Electromagnetic observations of certain cloud-like configurations would appear to violate the Buchdahl limit. The self-interaction strength is found to significantly affect both mass and tidal deformability. We discuss observational constraints and the connection to anomalous detections. We also show how models with an effective equation of state compare to the self-consistent solution of FBS and find the self-interaction strength where both solutions converge sufficiently., Comment: Master thesis, 104 pages, 29 figures

In this work we investigate the tidal deformability of a neutron star admixed with dark matter, modeled as a massive, self-interacting, complex scalar field. We derive the equations to compute the tidal deformability of the full Einstein-Hilbert-Klein-Gordon system self-consistently, and probe the influence of the scalar field mass and self-interaction strength on the total mass and tidal properties of the combined system. We find that dark matter core-like configurations lead to more compact objects with smaller tidal deformability, and dark matter cloud-like configurations lead to larger tidal deformability. Electromagnetic observations of certain cloud-like configurations would appear to violate the Buchdahl limit. The self-interaction strength is found to have a significant effect on both mass and tidal deformability. We discuss observational constraints and the connection to anomalous detections. We also investigate how this model compares to those with an effective bosonic equation of state and find the interaction strength where they converge sufficiently., Comment: 14 pages, 7 figures; Accepted for publication