arXiv subjects

Thomas W. Baumgarte

Publications and source records attributed to Thomas W. Baumgarte.

At least 37 records · Page 2Linked to original sources

arXiv2023

Dynamical perturbations of black-hole punctures: effects of slicing conditions

While numerous numerical relativity simulations adopt a 1+log slicing condition, shock-avoiding slicing conditions form a viable and sometimes advantageous alternative. Despite both conditions satisfying similar equations, recent numerical experiments point to a qualitative difference in the behavior of the lapse in the vicinity of the black-hole puncture: for 1+log slicing, the lapse appears to decay approximately exponentially, while for shock-avoiding slices it performs approximately harmonic oscillation. Motivated by this observation, we consider dynamical coordinate transformations of the Schwarzschild spacetime to describe small perturbations of static trumpet geometries analytically. We find that the character of the resulting equations depends on the (unperturbed) mean curvature at the black-hole puncture: for 1+log slicing it is positive, predicting exponential decay in the lapse, while for shock-avoiding slices it vanishes, leading to harmonic oscillation. In addition to identifying the value of the mean curvature as the origin of these qualitative differences, our analysis provides insight into the dynamical behavior of black-hole punctures for different slicing conditions.

gr-qc↗

arXiv2023

Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves

We report on numerical simulations of critical phenomena near the threshold of black hole formation in the collapse of axisymmetric gravitational waves in vacuum. We discuss several new features of our numerical treatment, and then compare results obtained from families of quadrupolar and hexadecapolar initial data. Specifically, we construct (nonlinear) initial data from quadrupolar and hexadecapolar, time-symmetric wavelike solutions to the linearized Einstein equations (often referred to as Teukolsky waves), and evolve these using a shock-avoiding slicing condition. While our degree of fine-tuning to the onset of black-hole formation is rather modest, we identify several features of the threshold solutions formed for the two families. Both threshold solutions appear to display an at least approximate discrete self-similarity with an accumulation event at the center, and the characteristics of the threshold solution for the quadrupolar data are consistent with those found previously by other authors. The hexadecapolar threshold solution appears to be distinct from the quadrupolar one, providing further support to the notion that there is no universal critical solution for the collapse of vacuum gravitational waves.

gr-qc↗

arXiv2023

Bona-Massó slices of Reissner-Nordström spacetimes

Motivated by recent numerical relativity simulations of charged black holes and their interactions, we explore the properties of common slicing conditions in Reissner-Nordström spacetimes. Specifically, we consider different choices for the so-called Bona-Massó function, and construct static and spherically symmetric slices of the Reissner-Nordström spacetime satisfying the corresponding slicing conditions. For some of these functions the construction is entirely analytical, while for others we use numerical root-finding to solve quartic equations. Our solutions are parameterized by the charge-to-mass ratio $λ= Q/M$ and approach a unique slice, independent of the Bona-Massó functions considered here, in the extremal limit $λ\to 1$.

gr-qc↗

arXiv2022

Did a close tidal encounter cause the Great Dimming of Betelgeuse?

We assess whether gravity darkening, induced by a tidal interaction during a stellar fly-by, might be sufficient to explain the Great Dimming of Betelgeuse. Adopting several simple approximations, we calculate the tidal deformation and associated gravity darkening in a close tidal encounter, as well as the reduction in the radiation flux as seen by a distant observer. We show that, in principle, the duration and degree of the resulting stellar dimming can be used to estimate the minimum pericenter separation and mass of a fly-by object, which, even if it remains undetected otherwise, might be a black hole, neutron star, or white dwarf. Our estimates show that, while such fly-by events may occur in other astrophysical scenarios, where our analysis should be applicable, they likely are not large enough to explain the Great Dimming of Betelgeuse by themselves.

astro-ph.SR↗

arXiv2022

Shock-avoiding slicing conditions: tests and calibrations

While the 1+log slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop "gauge-shocks" in some examples. Alternative "shock-avoiding" slicing conditions suggested by Alcubierre prevent these pathologies in those examples, but have not yet been explored and tested very broadly. In this paper we compare the performance of shock-avoiding slicing conditions with those of 1+log slicing for a number of "text-book" problems, including black holes and relativistic stars. While, in some simulations, the shock-avoiding slicing conditions feature some unusual properties and lead to more "gauge-dynamics" than the 1+log slicing condition, we find that they perform quite similarly in terms of stability and accuracy, and hence provide a very viable alternative to 1+log slicing.

gr-qc↗

arXiv2022

Bona-Masso slicing conditions and the lapse close to black-hole punctures

We consider several families of functions $f(α)$ that appear in the Bona-Masso slicing condition for the lapse function $α$. Focusing on spherically symmetric and time-independent slices we apply these conditions to the Schwarzschild spacetime in order to construct analytical expressions for the lapse $α$ in terms of the areal radius $R$. We then transform to isotropic coordinates and determine the dependence of $α$ on the isotropic radius $r$ in the vicinity of the black-hole puncture. We propose generalizations of previously considered functions $f(α)$ for which, to leading order, the lapse is proportional to $r$ rather than a non-integer power of $r$. We also perform dynamical simulations in spherical symmetry and demonstrate advantages of the above choices in numerical simulations employing spectral methods.

gr-qc↗

arXiv2021

Accretion onto black holes inside neutron stars with piecewise-polytropic equations of state: analytic and numerical treatments

We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star.

astro-ph.HE↗

arXiv2021

Comparison of linear Brill and Teukolsky waves

Motivated by studies of critical phenomena in the gravitational collapse of vacuum gravitational waves we compare, at the linear level, two common approaches to constructing gravitational-wave initial data. Specifically, we construct analytical, linear Brill wave initial data and compare these with Teukolsky waves in an attempt to understand the different numerical behavior observed in dynamical (nonlinear) evolutions of these two different sets of data. In general, the Brill waves indeed feature higher multipole moments than the quadrupolar Teukolsky waves, which might have provided an explanation for the differences observed in the dynamical evolution of the two types of waves. However, we also find that, for a common choice of the Brill-wave seed function, all higher-order moments vanish identically, rendering the (linear) Brill initial data surprisingly similar to the Teukolsky data for a similarly common choice of its seed function.

gr-qc↗

arXiv2021

Relativistic Bondi accretion for stiff equations of state

We revisit Bondi accretion - steady-state, adiabatic, spherical gas flow onto a Schwarzschild black hole at rest in an asymptotically homogeneous medium - for stiff polytropic equations of state (EOSs) with adiabatic indices $Γ> 5/3$. A general relativistic treatment is required to determine their accretion rates, for which we provide exact expressions. We discuss several qualitative differences between results for soft and stiff EOSs - including the appearance of a minimum steady-state accretion rate for EOSs with $Γ\geq 5/3$ - and explore limiting cases in order to examine these differences. As an example we highlight results for $Γ= 2$, which is often used in numerical simulations to model the EOS of neutron stars. We also discuss a special case with this index, the ultra-relativistic `causal' EOS, $P = ρ$. The latter serves as a useful limit for the still undetermined neutron-star EOS above nuclear density. The results are useful, for example, to estimate the accretion rate onto a mini-black hole residing at the center of a neutron star.

astro-ph.HE↗

arXiv2021

Critical phenomena in the gravitational collapse of electromagnetic dipole and quadrupole waves

We report on critical phenomena in the gravitational collapse of electromagnetic waves. Generalizing earlier results that focused on dipole electromagnetic waves, we here compare with quadrupole waves in axisymmetry. We perform numerical simulations of dipole and quadrupole wave initial data, fine-tuning both sets of data to the onset of black hole formation in order to study the critical solution and related critical phenomena. We observe that different multipole moments have different symmetries, indicating that the critical solution for electromagnetic waves cannot be unique, at least not globally. This is confirmed in our numerical simulations: while dipole data lead to a single center of collapse, at the center of symmetry, quadrupole data feature two separate centers of collapse on the symmetry axis, above and below the center of symmetry -- reminiscent of similar findings reported for critical collapse of vacuum gravitational waves. While the critical solution for neither the dipole nor the quadrupole data is exactly self-similar, we find that their approximate echoing periods appear to differ, as do the critical exponents. We discuss whether the centers of collapse found for dipole and quadrupole data might all have the same properties, which would suggest a "local uniqueness" of the critical solution. Instead, we provide some evidence -- including the differing echoing periods and critical exponents -- suggesting that the critical solutions are distinct even locally. We speculate on the implications of our findings for critical phenomena in the collapse of vacuum gravitational waves, which share with electromagnetic waves the absence of a spherically symmetric critical solution.

gr-qc↗

arXiv2021

Accretion onto a small black hole at the center of a neutron star

We revisit the system consisting of a neutron star that harbors a small, possibly primordial, black hole at its center, focusing on a nonspinning black hole embedded in a nonrotating neutron star. Extending earlier treatments, we provide an analytical treatment describing the rate of secular accretion of the neutron star matter onto the black hole, adopting the relativistic Bondi accretion formalism for stiff equations of state that we presented elsewhere. We use these accretion rates to sketch the evolution of the system analytically until the neutron star is completely consumed. We also perform numerical simulations in full general relativity for black holes with masses up to nine orders of magnitude smaller than the neutron star mass, including a simulation of the entire evolution through collapse for the largest black hole mass. We construct relativistic initial data for these simulations by generalizing the black hole puncture method to allow for the presence of matter, and evolve these data with a code that is optimally designed to resolve the vastly different length scales present in this problem. We compare our analytic and numerical results, and provide expressions for the lifetime of neutron stars harboring such endoparasitic black holes.

astro-ph.HE↗

arXiv2021

Neutron Stars Harboring a Primordial Black Hole: Maximum Survival Time

We explore in general relativity the survival time of neutron stars that host an endoparasitic, possibly primordial, black hole at their center. Corresponding to the minimum steady-state Bondi accretion rate for adiabatic flow that we found earlier for stiff nuclear equations of state (EOSs), we derive analytically the maximum survival time after which the entire star will be consumed by the black hole. We also show that this maximum survival time depends only weakly on the stiffness for polytropic EOSs with $Γ\geq 5/3$, so that this survival time assumes a nearly universal value that depends on the initial black hole mass alone. Establishing such a value is important for constraining the contribution of primordial black holes in the mass range $10^{-16} M_\odot \lesssim M \lesssim 10^{-10} M_\odot$ to the dark-matter content of the Universe.

astro-ph.HE↗

arXiv2020

Relativistic radiation hydrodynamics in a reference-metric formulation

We adopt a two-moment formalism, together with a reference-metric approach, to express the equations of relativistic radiation hydrodynamics in a form that is well-suited for numerical implementations in curvilinear coordinates. We illustrate the approach by employing a gray opacity in an optically thick medium. As numerical demonstrations we present results for two test problems, namely stationary, slab-symmetric solutions in flat spacetimes, including shocks, and heated Oppenheimer-Snyder collapse to a black hole. For the latter, we carefully analyze the transition from an initial transient to a post-transient phase that is well described by an analytically-known diffusion solution. We discuss the properties of the numerical solution when rendered in moving-puncture coordinates.

gr-qc↗

arXiv2020

Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit

We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamics (GRMHD) in a 3+1 split of spacetime in spherical coordinates without symmetry assumptions. The spacetime evolution is performed using reference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and conformal Z4 system with constraint damping. We have developed a reference-metric version of the Valencia formulation of GRMHD with a vector potential method, guaranteeing the absence of magnetic monopoles during the evolution. In our framework, every dynamical field (both spacetime and matter) is evolved using its components in an orthonormal basis with respect to the spherical reference-metric. Furthermore, all geometric information about the spherical coordinate system is encoded in source terms appearing in the evolution equations. This allows for the straightforward extension of Cartesian high-resolution shock-capturing finite volume codes to use spherical coordinates with our framework. To this end, we have adapted GRHydro, a Cartesian finite volume GRMHD code already available in the Einstein Toolkit, to use spherical coordinates. We present the full evolution equations of the framework, as well as details of its implementation in the Einstein Toolkit. We validate SphericalNR by demonstrating it passes a variety of challenging code tests in static and dynamical spacetimes.

gr-qc↗

arXiv2019

Critical phenomena in the gravitational collapse of electromagnetic waves

We numerically investigate the threshold of black-hole formation in the gravitational collapse of electromagnetic waves in axisymmetry. We find approximate power-law scaling $ρ_{\rm max}\sim (η_*-η)^{-2γ}$ of the maximum density in the time evolution of near-subcritical data with $γ\simeq 0.145$, where $η$ is the amplitude of the initial data. We directly observe approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of $Δ\simeq 0.55$. The critical solution is approximately the same for two families of initial data, providing some evidence of universality. Neither the discrete self-similarity nor the universality, however, are exact. We speculate that the absence of an exactly discrete self-similarity might be caused by the interplay of electromagnetic and gravitational wave degrees of freedom, or by the presence of higher-order angular multipoles, or both, and discuss implications of our findings for the critical collapse of vacuum gravitational waves.

gr-qc↗

arXiv2019

Critical phenomena in gravitational collapse with two competing massless matter fields

In the gravitational collapse of matter beyond spherical symmetry, gravitational waves are necessarily present. On the other hand, gravitational waves can collapse to a black hole even without matter. One might therefore wonder whether the interaction and competition between the matter fields and gravitational waves affects critical phenomena at the threshold of black hole formation. As a toy model for this, we study type II critical collapse with two matter fields in spherical symmetry, namely a scalar field and a Yang-Mills field. On their own, both display discrete self-similarity (DSS) in type II critical collapse, and we can take either one of them as a toy model for gravitational waves. To our surprise, in numerical time evolutions we find that, for sufficiently good fine-tuning, the scalar field always dominates on sufficiently small scales. We explain our results by the conjectured existence of a "quasi-discretely self-similar" (QSS) solution shared by the two fields, equal to the known Yang-Mills critical solution at infinitely large scales and the known scalar field critical solution (the Choptuik solution) at infinitely small scales, with a gradual transition from one field to the other. This QSS solution itself has only one unstable mode, and so acts as the critical solution for any mixture of scalar field and Yang-Mills initial data.

gr-qc↗

arXiv2019

Dark matter heating of gas accreting onto Sgr A$^*$

We study effects of heating by dark matter (DM) annihilation on black hole gas accretion. We observe that, for reasonable assumptions about DM densities in spikes around supermassive black holes, as well as DM masses and annihilation cross-sections within the standard WIMP model, heating by DM annihilation may have an appreciable effect on the accretion onto Sgr A$^*$ in the Galactic center. Motivated by this observation we study the effects of such heating on Bondi accretion, i.e. spherically symmetric, steady-state Newtonian accretion onto a black hole. We consider different adiabatic indices for the gas, and different power-law exponents for the DM density profile. We find that typical transonic solutions with heating have a significantly reduced accretion rate. However, for many plausible parameters, transonic solutions do not exist, suggesting a breakdown of the underlying assumptions of steady-state Bondi accretion. Our findings indicate that heating by DM annihilation may play an important role in the accretion onto supermassive black holes at the center of galaxies, and may help explain the low accretion rate observed for Sgr A$^*$.

astro-ph.HE↗

arXiv2019

Maximally Rotating Supermassive Stars at the Onset of Collapse: Effects of Gas Pressure

The "direct collapse" scenario has emerged as a promising evolutionary track for the formation of supermassive black holes early in the Universe. In an idealized version of such a scenario, a uniformly rotating supermassive star spinning at the mass-shedding (Keplerian) limit collapses gravitationally after it reaches a critical configuration. Under the assumption that the gas is dominated by radiation pressure, this critical configuration is characterized by unique values of the dimensionless parameters $J/M^2$ and $R_p/M$, where $J$ is the angular momentum, $R_p$ the polar radius, and $M$ the mass. Motivated by a previous perturbative treatment we adopt a fully nonlinear approach to evaluate the effects of gas pressure on these dimensionless parameters for a large range of masses. We find that gas pressure has a significant effect on the critical configuration even for stellar masses as large as $M \simeq 10^6 M_{\odot}$. We also calibrate two approximate treatments of the gas pressure perturbation in a comparison with the exact treatment, and find that one commonly used approximation in particular results in increasing deviations from the exact treatment as the mass decreases, and the effects of gas pressure increase. The other approximation, however, proves to be quite robust for all masses $M \gtrsim 10^4 M_{\odot}$.

astro-ph.HE↗