arXiv subjects

Ben Kain

Publications and source records attributed to Ben Kain.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical wormholes

We numerically investigate the dynamical evolution of spherically symmetric charge free wormholes. We concentrate on two specific examples, both of which exhibit wormhole expansion and wormhole collapse: the Ellis-Bronnikov wormhole, which is sourced by a real massless ghost scalar field, and the quantum corrected Schwarzschild black hole in semiclassical gravity (which has a wormhole structure and is not a true black hole), which is sourced by a renormalized energy-momentum tensor. Despite their very different sources, we demonstrate that the dynamics of these two wormholes are remarkably similar. Our analysis focuses on diagrams for the areal radius and components of the energy-momentum tensor. This work also serves as a review, offering a detailed description of how to perform a spherically symmetric dynamical evolution using double null coordinates as well as a review of the static solutions for our two examples.

gr-qc↗

arXiv2025

Dynamical evolution and stability of quantum corrected Schwarzschild black holes in semiclassical gravity

The Schwarzschild solution describes a classical static black hole in general relativity. When general relativity is extended by including semiclassical corrections in the form of a renormalized energy-momentum tensor, the horizon of the Schwarzschild black hole disappears and is replaced by a wormhole. We study the stability of this quantum corrected static Schwarzschild solution in semiclassical gravity by using it as the initial data of a dynamical evolution. We find that the quantum corrected solution is unstable and that the wormhole can expand or collapse when perturbed. In vacuum, the wormhole expands, but in the presence of even a small amount of classical matter, the wormhole collapses, forming a horizon and evolving to an evaporating black hole.

gr-qc↗

arXiv2025

Quantum corrected Einstein-Yang-Mills black holes in semiclassical gravity

We study Einstein-Yang-Mills (EYM) black holes in semiclassical gravity by including in the field equations the expectation value of a renormalized energy-momentum tensor in the Polyakov approximation. We solve the field equations and the equations of motion self-consistently. This framework has previously been used to study vacuum solutions, i.e. quantum corrected Schwarzschild black holes. In our system, which contains black hole hair, we find quantum corrected solutions in which the classical horizon disappears and is replaced by a wormhole structure, similarly to what is found in vacuum. We also find quantum corrected solutions in which the classical horizon disappears, but there is no wormhole structure. Our results indicate that the inclusion of black hole hair in semiclassical gravity still leads to the disappearance of classical horizons for nonextremal black holes in static spherically symmetric systems.

gr-qc↗

arXiv2023

Rotating dark matter admixed neutron stars

We study rotating compact stars that are mixtures of the ordinary nuclear matter in a neutron star and fermionic dark matter. After deriving equations describing a slowly rotating system made up of an arbitrary number of perfect fluids, we specialize to the two-fluid case, where the first fluid describes ordinary matter and the second fluid describes dark matter. Electromagnetic observations of the moment of inertia and angular momentum directly probe ordinary matter and not dark matter. Upon taking this into account, we show that the I-Love-Q relations for dark matter admixed neutrons stars can deviate significantly from the standard single-fluid relationships.

gr-qc↗

arXiv2023

Probing the connection between entangled particles and wormholes in general relativity

Maldacena and Susskind conjectured that two entangled particles, which can be thought of as forming an Einstein-Podolsky-Rosen (EPR) pair, are connected by a nontraversable wormhole or Einstein-Rosen (ER) bridge. They named their conjecture ER = EPR. We present a concrete quantitative model for ER = EPR, in which two spin-1/2 particles in a singlet state are connected by a nontraversable wormhole in asymptotically flat general relativity. In our model, the fermions are described by the charged Dirac equation minimally coupled to gravity. This system has static wormhole solutions. We use these solutions as initial data and numerically evolve them forward in time. Our simulations show that black holes form, which are connected by the wormhole and which render the wormhole nontraversable. We also find that the wormhole throat shrinks, which places the particles in close proximity to one another and suggests an explanation for how the wormhole facilitates the nonlocal communication required by entanglement.

hep-th↗

arXiv2023

Einstein-Dirac-Maxwell wormholes in quantum field theory

Charged Dirac fields minimally coupled to gravity have spherically symmetric wormhole solutions known as Einstein-Dirac-Maxwell (EDM) wormholes. EDM wormholes do not make use of exotic matter and exist in asymptotically flat general relativity. We construct static spherically symmetric EDM wormhole configurations in quantum field theory using semiclassical approximations for gravity and the electromagnetic field. Our framework is able to describe a broader class of EDM wormholes than previously considered and, being constructed in quantum field theory, puts EDM wormholes on firmer theoretical ground.

gr-qc↗

arXiv2023

Are Einstein-Dirac-Maxwell wormholes traversable?

Einstein-Dirac-Maxwell wormholes are asymptotically flat static wormhole solutions in general relativity that do not make use of exotic matter. The asymmetric static solutions are smooth, are regular everywhere, and violate the null energy condition, which suggests that they are traversable. To determine if in fact they are traversable, we numerically evolve the static solutions forward in time. In all cases considered, our simulations indicate that black holes form that are connected by the wormhole. Although there exist null geodesics that travel through the wormhole, we find that they are trapped inside a black hole and are unable to travel arbitrarily far away. We conclude that Einstein-Dirac-Maxwell wormholes are not traversable.

gr-qc↗

arXiv2023

Einstein-Dirac system in semiclassical gravity

We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple independent Dirac fields to preserve spherical symmetry. We canonically quantize a single Dirac field in a static spherically symmetric curved spacetime background. Using the semiclassical gravity approximation, in which the Einstein field equations are sourced by the expectation value of the stress-energy-momentum tensor, we derive a system of equations whose solutions describe static spherically symmetric self-gravitating configurations of identical quantum spin-1/2 particles. We self-consistently solve these equations and present example configurations. Although limiting cases of our semiclassical system of equations reproduce the multi-field system of equations found in the literature, our system of equations is derived from the excitations of a single quantum field.

gr-qc↗

arXiv2022

Matter traveling through a wormhole

We revisit the numerical evolution of Ellis-Bronnikov-Morris-Thorne wormholes, which are constructed with a massless real ghost scalar field. For our simulations, we have developed a new code based on the standard 3+1 foliation of spacetime. We confirm that, for the massless symmetric wormhole, a pulse of regular scalar field causes the wormhole throat to collapse and form an apparent horizon, while a pulse of ghost scalar field can cause the wormhole throat to expand. As a new result, we show that it is possible for a pulse of regular matter to travel through the wormhole and then to send a light signal back before the wormhole collapses. We also evolve pulses of matter traveling through massive asymmetric wormholes, which has not previously been simulated.

gr-qc↗

arXiv2022

Dynamical evolution of fermion-boson stars with realistic equations of state

Fermion-boson stars are mixtures of the ordinary nuclear matter of a neutron star and bosonic dark matter. We dynamically evolve fermion-boson stars for the first time using a realistic equation of state for nuclear matter. We use our dynamical solutions to make a detailed study of the evolution of weakly and strongly perturbed static solutions. As examples of our findings, we identify a region of parameter space where weakly perturbed unstable static solutions migrate to a stable configuration and we determine the criteria under which strongly perturbed stable static solutions will always move to a stable configuration instead of collapsing to a black hole.

gr-qc↗

arXiv2022

Dynamical evolution of dark matter admixed neutron stars

We dynamically evolve for the first time dark matter admixed neutron stars with fermionic dark matter. These systems are mixtures of the ordinary nuclear matter of a neutron star and dark matter. To perform our dynamical evolutions, we derive the equations of motion, in conservation form, for spherically symmetric systems with an arbitrary number of perfect fluids. Using finite volume and high-resolution shock-capturing methods, we dynamically evolve the two-fluid case, with the first fluid modeling ordinary matter and the second fluid modeling dark matter. We use our dynamical solutions to study nonlinear stability, radial oscillation frequencies, and a dynamical formation process.

gr-qc↗

arXiv2021

Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice

We consider a Bogolibov-de Geenes (BdG) Hamiltonian, which is a non-Hermitian Hamiltonian with pseudo-Hermiticity, for a system of (pseudo) spin-$1/2$ bosons in a honeycomb lattice under the condition that the population difference between the two spin components, i.e., magnetization, is a constant. Such a system is capable of acting as a topological amplifier, under time-reversal symmetry, with stable bulk bands but unstable edge modes which can be populated at an exponentially fast rate. We quantitatively study the topological properties of this model within the framework of the 38-fold way for non-Hermitian systems. We find, through the symmetry analysis of the Bloch Hamiltonian, that this model is classified either as two copies of symmetry class AIII+$\eta_-$ or two copies of symmetry class A+$\eta$ depending on whether the (total) system is time-reversal-symmetric, where $\eta$ is the matrix representing pseudo-Hermiticity and $\eta_-$ indicates that pseudo-Hermiticity and chiral symmetry operators anticommute. We prove, within the context of non-Hermitian physics where eigenstates obey the bi-orthonormality relation, that a stable bulk is characterized by a single topological invariant, the Chern number for the Haldane model, independent of pairing interactions. We construct a convenient analytical description for the edge modes of the Haldane model in semi-infinite planes, which is expected to be useful for models built upon copies of the Haldane model across a broad array of disciplines. We adapt the theorem in our recent work [Phys. Rev. A 104, 013305 (2021)] to pseudo-Hermitian Hamiltonians that are less restrictive than BdG Hamiltonians and apply it to highlight that the vanishing of an unconventional commutator between number-conserving and number-nonconserving parts of the Hamiltonian indicates whether a system can be made to act as a topological amplifier.

cond-mat.quant-gas↗

arXiv2021

Fermion-charged-boson stars

Fermion-boson stars are starlike systems composed of the ordinary nuclear matter of a neutron star and bosonic dark matter. The bosonic dark matter has typically been taken to be a complex scalar field. A natural extension is for the complex scalar field to be charged. We make the simplest extension and gauge the scalar field under U(1). We therefore study fermion-charged-boson stars. We make a detailed study of the stability of this system by computing critical curves over the whole of parameter space. We then study how the fermion and boson sectors contribute to the total mass of the star. Finally, we present mass-radius diagrams, showing that an increase in charge can lead to more massive and more compact stars.

gr-qc↗

arXiv2021

Boson stars and their radial oscillations

We review the derivation of the pulsations equations for spherically symmetric boson stars and then make a thorough study of the radial oscillation frequencies for the fundamental and first excited modes. We do this for self-interacting boson stars and consider a range of values for the self-coupling constant. We also numerically evolve boson stars and Fourier transform the dynamic solutions. The Fourier transform gives an independent computation of the radial oscillation frequencies and allows us to verify our results obtained from the pulsation equations. We find excellent agreement between the two methods.

gr-qc↗

arXiv2021

Dark matter admixed neutron stars

Neutron stars could contain a mixture of ordinary nuclear matter and dark matter, such that dark matter could influence observable properties of the star, such as its mass and radius. We study these dark matter admixed neutron stars for two choices of dark matter: a free Fermi gas and mirror dark matter. In addition to solving the multi-fluid Tolman-Oppenheimer-Volkoff equations for static solutions and presenting mass-radius diagrams, we focus on two computations that are lacking in the literature. The first is a rigorous determination of stability over the whole of parameter space, which we do using two different methods. The first method is based on harmonic time-dependent perturbations to the static solutions and on solving for the radial oscillation frequency. The second method, which is less well-known, conveniently makes use of unperturbed, static solutions only. The second computation is of the radial oscillation frequency, for fundamental modes, over large swaths of parameter space.

gr-qc↗

arXiv2020

Selection Rule for Topological Amplifiers in Bogoliubov de Gennes Systems

Dynamical instability is an inherent feature of bosonic systems described by the Bogoliubov de Geenes (BdG) Hamiltonian. Since it causes the BdG system to collapse, it is generally thought that it should be avoided. Recently, there has been much effort to harness this instability for the benefit of creating a topological amplifier with stable bulk bands but unstable edge modes which can be populated at an exponentially fast rate. We present a theorem for determining the stability of states with energies sufficiently away from zero, in terms of an unconventional commutator between the number conserving part and number nonconserving part of the BdG Hamiltonian. We apply the theorem to a generalization of a model from Galilo et al. [Phys. Rev. Lett, 115, 245302(2015)] for creating a topological amplifier in an interacting spin-1 atom system in a honeycomb lattice through a quench process. We use this model to illustrate how the vanishing of the unconventional commutator selects the symmetries for a system so that its bulk states are stable against (weak) pairing interactions. We find that as long as time reversal symmetry is preserved, our system can act like a topological amplifier, even in the presence of an onsite staggered potential which breaks the inversion symmetry.

cond-mat.quant-gas↗

arXiv2020

Radial oscillations and stability of multiple-fluid compact stars

I derive a system of pulsation equations for compact stars made up of an arbitrary number of perfect fluids that can be used to study radial oscillations and stability with respect to small perturbations. I assume spherical symmetry and that the only inter-fluid interactions are gravitational. My derivation is in line with Chandrasekhar's original derivation for the pulsation equation of a single-fluid compact star and keeps the contributions from the individual fluids manifest. I illustrate solutions to the system of pulsations equations with one-, two-, and three-fluid examples.

gr-qc↗

arXiv2019

Perturbing the ground state of Dirac stars

Dirac stars are self-gravitating configurations of spin-1/2 fermions in which the fermions are described by the Dirac equation. After a detailed review of the derivation of the equations and their static solutions, we present an in-depth dynamical stability analysis of the ground state similar to previous studies for boson stars. We confirm that there exist both stable and unstable branches of static solutions and show that weakly perturbed Dirac stars from the unstable branch migrate to the stable branch. We also show that strongly perturbed Dirac stars from the stable branch migrate to the stable branch if their mass is below a critical value. If their mass is above the critical value they can migrate to the stable branch or collapse and form a black hole. For strongly perturbed Dirac stars from the unstable branch we show that the addition of even a small amount of mass leads to collapse, while if we decrease their mass they migrate to the stable branch.

gr-qc↗