Antonios Tsokaros

GW170817, general relativistic magnetohydrodynamic simulations, and the neutron star maximum mass

Recent numerical simulations in general relativistic magnetohydrodynamics (GRMHD) provide useful constraints for the interpretation of the GW170817 discovery. Combining the observed data with these simulations leads to a bound on the maximum mass of a cold, spherical neutron star (the TOV limit): Mmaxsph≲2.74/β , where β is the ratio of the maximum mass of a uniformly rotating neutron star (the supramassive limit) over the maximum mass of a nonrotating star. Causality arguments allow β to be as high as 1.27, while most realistic candidate equations of state predict β to be closer to 1.2, yielding Mmaxsph in the range 2.16-2.28M⊙. A minimal set of assumptions based on these simulations distinguishes this analysis from previous ones, but leads a to similar estimate. There are caveats, however, and they are enumerated and discussed. The caveats can be removed by further simulations and analysis to firm up the basic argument.

A general sudden cosmological singularity

We construct an asymptotic series for a general solution of the Einstein equations near a sudden singularity. The solution is quasi isotropic and contains nine independent arbitrary functions of the space coordinates as required by the structure of the initial value problem.

Asymptotics of flat, radiation universes in quadratic gravity

Abstract We consider the asymptotics of flat, radiation-dominated isotropic universes in four-dimensional theories with quadratic curvature corrections which may arise when contributions related to the string parameter α ′ are switched on. We show that all such universes are singular initially, and calculate all early time asymptotics using the method of asymptotic splittings. We also examine the late time asymptotic behaviour of these models and show that there are no solutions which diverge as e t 2 , the known radiation solution of general relativity is essentially the only late time asymptotic possibility in these models.

Numerical method for binary black hole/neutron star initial data: Code test

A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Greens function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Greens functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field, are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix 1.

The initial state of generalized radiation universes

We use asymptotic methods to study the early time stability of isotropic and homogeneous solutions filled with radiation which are close initially to the exact, flat, radiation solution in quadratic lagrangian theories of gravity. For such models, we analyze all possible modes of approach to the initial singularity and prove the essential uniqueness and stability of the resulting asymptotic scheme in all cases except perhaps that of the conformally invariant BachWeyl gravity. We also provide a formal series representation valid near the initial singularity of the general solution of these models and show that this is dominated at early times by a form in which both curvature and radiation play a subdominant role. We also discuss the implications of these results for the generic initial state of the theory.

Binary black hole circular orbits computed with cocal

Results are presented for binary black hole circular orbits computed using cocal, the Compact Object CALculator. Using the 3 + 1 decomposition, we solve five equations under the assumptions of conformal flatness and maximal slicing. Excision is used, and the appropriate apparent horizon boundary conditions are applied. The orbital velocity is determined by imposing a Schwarzschild behavior at infinity. A sequence of equal-mass black holes is obtained, and its main physical characteristics are calculated.

New code for equilibriums and quasiequilibrium initial data of compact objects. II. Convergence tests and comparisons of binary black hole initial data

Cocal is a code for computing equilibriums or quasiequilibrium initial data of single or binary compact objects based on finite difference methods. We present the results of supplementary convergence tests of cocal code using time symmetric binary black hole data (Brill-Lindquist solution). Then, we compare the initial data of binary black holes on the conformally flat spatial slice obtained from cocal and KADATH, where KADATH is a library for solving a wide class of problems in theoretical physics including relativistic compact objects with spectral methods. Data calculated from the two codes converge nicely towards each other, for close as well as largely separated circular orbits of binary black holes. Finally, as an example, a sequence of equal mass binary black hole initial data with corotating spins is calculated and compared with data in the literature.

Modeling differential rotations of compact stars in equilibriums

Outcomes of numerical relativity simulations of massive core collapses or binary neutron star mergers with moderate masses suggest formations of rapidly and differentially rotating neutron stars. Subsequent fall back accretion may also amplify the degree of differential rotations. We propose new formulations for modeling differential rotations of those compact stars, and present selected solutions of differentially rotating, stationary, and axisymmetric compact stars in equilibriums. For the cases when rotating stars reach break-up velocities, the maximum masses of such rotating models are obtained.

Asymptotic vacua with higher derivatives

Abstract We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.

THE FORMAL CONSTRUCTION OF SUDDEN COSMOLOGICAL SINGULARITIES

Solutions of the Friedmann-Lemaitre cosmological equations of general relativity have been found with finite-time singularities that are everywhere regular, have regular Hubble expansion rate, and obey the strong-energy conditions but possess pressure and acceleration singularities at finite time that are not associated with geodesic incompleteness. We show how these solutions with sudden singularities can be constructed using fractional series methods and find the limiting form of the equation of state on approach to the singularity.