arXiv subjects

Marcus Ansorg

Publications and source records attributed to Marcus Ansorg.

At least 19 recordsLinked to original sources

arXiv2019

Maximum Mass Of Differentially Rotating Strange Quark Stars

We present the first fully relativistic numerical calculations of differentially rotating Strange Quark Stars models for broad ranges of the maximum density and of the degree of differential rotation. Our simulations are performed with the very accurate and stable multi-domain spectral code FlatStar and use the MIT Bag model for describing strange quark matter. Our calculations based on a thorough exploration of the solution space show that the maximum mass of strange stars depends on both the degree of differential rotation and a type of solution, similarly to neutron stars described by a polytropic equations of state. The highest increase of the maximum mass (compared to the value for a non-rotating star) is obtained for models with a low degree of differential rotation. This highest mass is over four times larger than that of the equivalent non rotating configuration. Comparing our results with calculations done for realistic models of neutron stars, we conclude that with the help of differential rotation, strange stars can sustain masses much larger than stars made from nuclear matter for low degree of differential rotation which reinforces the hope of demonstrating, or of ruling out, the existence of strange matter through the observation by gravitational waves, by gamma rays or by neutrinos of the massive material object born from the merger of a compact binary system or during some supernova events.

astro-ph.HE↗

arXiv2018

Hyperboloidal slicing approach to quasi-normal mode expansions: the Reissner-Nordstr\"om case

We study quasi-normal modes of black holes, with a focus on resonant (or quasi-normal mode) expansions, in a geometric frame based on the use of conformal compactifications together with hyperboloidal foliations of spacetime. Specifically, this work extends the previous study of Schwarzschild in this geometric approach to spherically symmetric asymptotically flat black hole spacetimes, in particular Reissner-Nordstr\"om. The discussion involves, first, the non-trivial technical developments needed to address the choice of appropriate hyperboloidal slices in the extended setting as well as the generalization of the algorithm determining the coefficients in the expansion of the solution in terms of the quasi-normal modes. In a second stage, we discuss how the adopted framework provides a geometric insight into the origin of regularization factors needed in Leaver's Cauchy based foliations, as well as into the discussion of quasi-normal modes in the extremal black hole limit.

gr-qc↗

arXiv2016

A new view on the maximum mass of differentially rotating neutron stars

We study the main astrophysical properties of differentially rotating neutron stars described as stationary and axisymmetric configurations of a moderately stiff $Γ=2$ polytropic fluid. The high level of accuracy and of stability of our relativistic multidomain pseudo-spectral code enables us to explore the whole solution space for broad ranges of the degree of differential rotation, but also of the stellar density and oblateness. Staying within an astrophysicaly motivated range of rotation profiles, we investigate the characteristics of neutron stars with maximal mass for all types of families of differentially rotating relativistic objects identified in a previous article Ansorg, Gondek-Rosinsla, Villain (2009). We find that the maximum mass depends on both the degree of differential rotation and on the type of solution. It turns out that the maximum allowed mass can be up to 4 times higher than what it is for non-rotating stars with the same equation of state. Such values are obtained for a modest degree of differential rotation but for one of the newly discovered type of solutions. Since such configurations of stars are not that extreme, this result may have important consequences for the gravitational wave signal to expect from coalescing neutron star binaries or from some supernovae events.

astro-ph.HE↗

arXiv2016

Axisymmetric fully spectral code for hyperbolic equations

We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta ("SDIRK"-) method. The SDIRK-method also supplies the code with a good initial-guess. The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hole space-time in so-called hyperboloidal slices and reproduce some recent results available in the literature.

physics.comp-ph↗

arXiv2016

Spectral decomposition of black-hole perturbations on hyperboloidal slices

In this paper we present a spectral decomposition of solutions to relativistic wave equations described on horizon penetrating hyperboloidal slices within a given Schwarzschild-black-hole background. The wave equa- tion in question is Laplace-transformed which leads to a spatial differential equation with a complex parameter. For initial data which are analytic with respect to a compactified spatial coordinate, this equation is treated with the help of the Mathematica-package in terms of a sophisticated Taylor series analysis. Thereby, all ingredients of the desired spectral decomposition arise explicitly to arbitrarily prescribed accuracy, including quasi normal modes, quasi normal mode amplitudes as well as the jump of the Laplace-transform along the branch cut. Finally, all contributions are put together to obtain via the inverse Laplace transformation the spectral de- composition in question. The paper explains extensively this procedure and includes detailed discussions of relevant aspects, such as the definition of quasi normal modes and the question regarding the contribution of infinity frequencies modes to the early time response of the black hole.

gr-qc↗

arXiv2016

Pseudo-spectral construction of non-uniform black string solutions in five and six spacetime dimensions

In this paper, we describe in detail a scheme for the construction of highly accurate numerical solutions to Einstein's field equations in five and six spacetime dimensions corresponding to non-uniform black strings. The scheme consists of a sophistically adapted multi-domain pseudo-spectral method which incorporates a detailed understanding of the solution's behavior at the domain boundaries and at critical points. In particular, the five-dimensional case is exceedingly demanding as logarithmic terms appear which need to be treated with special care. The scheme resolves these issues and permits the investigation of unprecedentedly strong deformations of the black string horizon. As a consequence, we are able to study in detail the critical regime in phase diagrams displaying characteristic thermodynamic quantities such as mass and entropy. Our results show typical spiral curves in such diagrams which provides a strong support of previous numerical works.

gr-qc↗

arXiv2015

Highly Deformed Non-uniform Black Strings in Six Dimensions

We construct numerically static non-uniform black string solutions in six dimensions by using pseudo-spectral methods. An appropriately designed adaptation of the methods in regard of the specific behaviour of the field quantities in the vicinity of our numerical boundaries provides us with extremely accurate results, that allows us to get solutions with an unprecedented deformation of the black string horizon. Consequently, we are able to investigate in detail a critical regime within a suitable parameter diagram. In particular, we observe a clearly pronounced maximum in the mass curve, which is in accordance with the results of Kleihaus, Kunz and Radu from 2006. Interestingly, by looking at extremely distorted black strings, we find two further turning points of the mass, resulting in a spiral curve in the black string's phase diagram.

hep-th↗

arXiv2014

Convergence of Derivative Expansion in Supersymmetric Functional RG Flows

We confirm the convergence of the derivative expansion in two supersymmetric models via the functional renormalization group method. Using pseudo-spectral methods, high-accuracy results for the lowest energies in supersymmetric quantum mechanics and a detailed description of the supersymmetric analogue of the Wilson-Fisher fixed point of the three-dimensional Wess-Zumino model are obtained. The superscaling relation proposed earlier, relating the relevant critical exponent to the anomalous dimension, is shown to be valid to all orders in the supercovariant derivative expansion and for all $d \ge 2$.

hep-th↗

arXiv2014

Initial data for perturbed Kerr black holes on hyperboloidal slices

We construct initial data corresponding to a single perturbed Kerr black hole in vacuum. These data are defined on specific hyperboloidal ("ACMC-") slices on which the mean extrinsic curvature K asymptotically approaches a constant at future null infinity scri+. More precisely, we require that K obeys the Taylor expansion K=K0 + s^4 where K0 is a constant and s describes a compactified spatial coordinate such that scri+ is represented by s=0. We excise the singular interior of the black hole and assume a marginally outer trapped surface as inner boundary of the computational domain. The momentum and Hamiltonian constraints are solved by means of pseudo-spectral methods and we find exponential rates of convergence of our numerical solutions. Some physical properties of the initial data are studied with the calculation of the Bondi Mass, together with a multipole decomposition of the horizon. We probe the standard picture of gravitational collapse by assessing a family of Penrose-like inequalities and discuss in particular their rigidity aspects. Dynamical evolutions are planned in a future project.

gr-qc↗

arXiv2014

Axisymmetric constant mean curvature slices in the Kerr space-time

Recently, there have been efforts to solve Einstein's equation in the context of a conformal compactification of space-time. Of particular importance in this regard are the so called CMC-foliations, characterized by spatial hyperboloidal hypersurfaces with a constant extrinsic mean curvature K. However, although of interest for general space-times, CMC-slices are known explicitly only for the spherically symmetric Schwarzschild metric. This work is devoted to numerically determining axisymmetric CMC-slices within the Kerr solution. We construct such slices outside the black hole horizon through an appropriate coordinate transformation in which an unknown auxiliary function A is involved. The condition K=const. throughout the slice leads to a nonlinear partial differential equation for the function A, which is solved with a pseudo-spectral method. The results exhibit exponential convergence, as is to be expected in a pseudo-spectral scheme for analytic solutions. As a by-product, we identify CMC-slices of the Schwarzschild solution which are not spherically symmetric.

gr-qc↗

arXiv2011

Higher-dimensional puncture initial data

We calculate puncture initial data, corresponding to single and binary black holes with linear momenta, which solve the constraint equations of D dimensional vacuum gravity. The data are generated by a modification of the pseudo-spectral code presented in arXiv:gr-qc/0404056 and made available as the TwoPunctures thorn inside the Cactus computational toolkit. As examples, we exhibit convergence plots, the violation of the Hamiltonian constraint as well as the initial data for D=4,5,6,7. These initial data are the starting point to perform high energy collisions of black holes in D dimensions.

gr-qc↗

arXiv2011

Universal properties of distorted Kerr-Newman black holes

We discuss universal properties of axisymmetric and stationary configurations consisting of a central black hole and surrounding matter in Einstein-Maxwell theory. In particular, we find that certain physical equations and inequalities (involving angular momentum, electric charge and horizon area) are not restricted to the Kerr-Newman solution but can be generalized to the situation where the black hole is distorted by an arbitrary axisymmetric and stationary surrounding matter distribution.

gr-qc↗

arXiv2011

Application of initial data sequences to the study of Black Hole dynamical trapping horizons

Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial cuts of a single spacetime hypersurface foliated by (compact) marginally outer trapped surfaces. We present here some work in progress which makes use of uni-parametric sequences of (axisymmetric) binary black hole initial data for exploring the plausibility of this spacetime picture. The modelling of Einstein evolutions by sequences of initial data has proved to be a successful methodological tool in other settings for the understanding of certain qualitative features of evolutions in restricted physical regimes.

gr-qc↗

arXiv2011

The interior of axisymmetric and stationary black holes: Numerical and analytical studies

We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. First, we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms of a single-domain fully pseudo-spectral scheme. Thereafter, a rigorous mathematical approach is given, in which soliton methods are utilized to derive an explicit relation between the event horizon and an inner Cauchy horizon. This horizon arises as the boundary of the future domain of dependence of the event horizon. Our numerical studies provide strong evidence for the validity of the universal relation $\Ap\Am = (8πJ)^2$ where $\Ap$ and $\Am$ are the areas of event and inner Cauchy horizon respectively, and $J$ denotes the angular momentum. With our analytical considerations we are able to prove this relation rigorously.

gr-qc↗

arXiv2010

Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes

We study general S2xS1 Gowdy models with a regular past Cauchy horizon and prove that a second (future) Cauchy horizon exists, provided that a particular conserved quantity $J$ is not zero. We derive an explicit expression for the metric form on the future Cauchy horizon in terms of the initial data on the past horizon and conclude the universal relation $A\p A\f=(8πJ)^2$ where $A\p$ and $A\f$ are the areas of past and future Cauchy horizon respectively.

gr-qc↗

arXiv2009

Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory

We study the interior electrovacuum region of axisymmetric and stationary black holes with surrounding matter and find that there exists always a regular inner Cauchy horizon inside the black hole, provided the angular momentum $J$ and charge $Q$ of the black hole do not vanish simultaneously. In particular, we derive an explicit relation for the metric on the Cauchy horizon in terms of that on the event horizon. Moreover, our analysis reveals the remarkable universal relation $(8πJ)^2+(4πQ^2)^2=A^+ A^-$, where $A^+$ and $A^-$ denote the areas of event and Cauchy horizon respectively.

gr-qc↗

arXiv2009

On the Solution Space of Differentially Rotating Neutron Stars in General Relativity

A highly accurate, multi-domain spectral code is used in order to construct sequences of general relativistic, differentially rotating neutron stars in axisymmetry and stationarity. For bodies with a spheroidal topology and a homogeneous or an N=1 polytropic equation of state, we investigate the solution space corresponding to broad ranges of degree of differential rotation and stellar densities. In particular, starting from static and spherical configurations, we analyse the changes of the corresponding surface shapes as the rate of rotation is increased. For a sufficiently weak degree of differential rotation, the sequences terminate at a mass-shedding limit, while for moderate and strong rates of differential rotation, they exhibit a continuous parametric transition to a regime of toroidal fluid bodies. In this article, we concentrate on the appearance of this transition, analyse in detail its occurrence and show its relevance for the calculation of astrophysical sequences. Moreover, we find that the solution space contains various types of spheroidal configurations, which were not considered in previous work, mainly due to numerical limitations.

gr-qc↗

arXiv2009

The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory: study in terms of soliton methods

We use soliton methods in order to investigate the interior electrovacuum region of axisymmetric and stationary, electrically charged black holes with arbitrary surrounding matter in Einstein-Maxwell theory. These methods can be applied since the Einstein-Maxwell vacuum equations permit the formulation in terms of the integrability condition of an associated linear matrix problem. We find that there always exists a regular inner Cauchy horizon inside the black hole, provided the angular momentum $J$ and charge $Q$ of the black hole do not vanish simultaneously. Moreover, the soliton methods provide us with an explicit relation for the metric on the inner Cauchy horizon in terms of that on the event horizon. In addition, our analysis reveals the remarkable universal relation $(8πJ)^2+(4πQ^2)^2=A^+ A^-$, where $A^+$ and $A^-$ denote the reas of event and inner Cauchy horizon respectively.

gr-qc↗