arXiv subjects

Philippos Papadopoulos

Publications and source records attributed to Philippos Papadopoulos.

At least 19 recordsLinked to original sources

arXiv2003

Axisymmetric core collapse simulations using characteristic numerical relativity

We present results from axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis of the global dynamics of the collapse. Contrary to traditional approaches based on the 3+1 formulation of the gravitational field equations, our framework uses a foliation based on a family of outgoing light cones, emanating from a regular center, and terminating at future null infinity. Such a coordinate system is well adapted to the study of interesting dynamical spacetimes in relativistic astrophysics such as stellar core collapse and neutron star formation. Perhaps most importantly this procedure allows for the unambiguous extraction of gravitational waves at future null infinity without any approximation, along with the commonly used quadrupole formalism for the gravitational wave extraction. Our results concerning the gravitational wave signals show noticeable disagreement when those are extracted by computing the Bondi news at future null infinity on the one hand and by using the quadrupole formula on the other hand. We have strong indication that for our setup the quadrupole formula on the null cone does not lead to physical gravitational wave signals. The Bondi gravitational wave signals extracted at infinity show typical oscillation frequencies of about 0.5 kHz.

gr-qc↗

arXiv2001

Simulating the dynamics of relativistic stars via a light-cone approach

We present new numerical algorithms for the coupled Einstein-perfect fluid system in axisymmetry. Our framework uses a foliation based on a family of light cones, emanating from a regular center, and terminating at future null infinity. This coordinate system is well adapted to the study of the dynamical spacetimes associated with isolated relativistic compact objects such as neutron stars. In particular, the approach allows the unambiguous extraction of gravitational waves at future null infinity and avoids spurious outer boundary reflections. The code can accurately maintain long-term stability of polytropic equilibrium models of relativistic stars. We demonstrate global energy conservation in a strongly perturbed neutron star spacetime, for which the total energy radiated away by gravitational waves corresponds to a significant fraction of the Bondi mass. As a first application we present results in the study of pulsations of axisymmetric relativistic stars, extracting the frequencies of the different fluid modes in fully relativistic evolutions of the Einstein-perfect fluid system and making a first comparison between the gravitational news function and the predicted wave using the approximations of the quadrupole formula.

gr-qc↗

arXiv2001

Non-linear radial oscillations of neutron stars: Mode-coupling results

The non-linear behaviour of oscillation modes in compact stars is a topic of considerable current interest. Accurate numerical studies of such phenomena are likely to require powerful new approaches to both fluid and spacetime computations. We propose that a key ingredient of such methods will be the non-linear evolution of deviations from the background stationary equilibrium star. We investigate the feasibility of this approach by applying it to non-linear radial oscillations of a neutron star, and explore numerically various non-linear features of this problem, for a large range of amplitudes. Quadratic and higher order mode coupling and non-linear transfer of energy is demonstrated and analysed in detail.

astro-ph↗

arXiv2001

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.

gr-qc↗

arXiv2001

Scalar field induced oscillations of neutron stars and gravitational collapse

We study the interaction of massless scalar fields with self-gravitating neutron stars by means of fully dynamic numerical simulations of the Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to spherical symmetry and the neutron stars are approximated by relativistic polytropes. Studying the nonlinear dynamics of isolated neutron stars is very effectively performed within the characteristic formulation of general relativity, in which the spacetime is foliated by a family of outgoing light cones. We are able to compactify the entire spacetime on a computational grid and simultaneously impose natural radiative boundary conditions and extract accurate radiative signals. We study the transfer of energy from the scalar field to the fluid star. We find, in particular, that depending on the compactness of the neutron star model, the scalar wave forces the neutron star either to oscillate in its radial modes of pulsation or to undergo gravitational collapse to a black hole on a dynamical timescale. The radiative signal, read off at future null infinity, shows quasi-normal oscillations before the setting of a late time power-law tail.

gr-qc↗

arXiv2001

Non-linear harmonic generation in finite amplitude black hole oscillations

The non-linear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an in-going light-cone framework. Localised, finite, perturbations of an isolated black hole are parametrised by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analysed to identify the strength of the non-linear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The relative efficiencies of down and up-scattering in harmonic space are computed for a range of couplings. Down-scattering, leading to smoothing out of angular structure is found to be equally or more efficient than the up-scatterings that would lead to increased rippling. The details of this non-linear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.

gr-qc↗

arXiv2001

Spherical collapse of supermassive stars: neutrino emission and gamma-ray bursts

We present the results of numerical simulations of the spherically symmetric gravitational collapse of supermassive stars (SMS). The collapse is studied using a general relativistic hydrodynamics code. The coupled system of Einstein and fluid equations is solved employing observer time coordinates, by foliating the spacetime by means of outgoing null hypersurfaces. The code contains an equation of state which includes effects due to radiation, electrons and baryons, and detailed microphysics to account for electron-positron pairs. In addition energy losses by thermal neutrino emission are included. We are able to follow the collapse of SMS from the onset of instability up to the point of black hole formation. Several SMS with masses in the range $5\times 10^5 M_{\odot}- 10^9 M_{\odot}$ are simulated. In all models an apparent horizon forms initially, enclosing the innermost 25% of the stellar mass. From the computed neutrino luminosities, estimates of the energy deposition by $ν\barν$-annihilation are obtained. Only a small fraction of this energy is deposited near the surface of the star, where, as proposed recently by Fuller & Shi (1998), it could cause the ultrarelativistic flow believed to be responsible for $γ$-ray bursts. Our simulations show that for collapsing SMS with masses larger than $5\times 10^5 M_{\odot}$ the energy deposition is at least two orders of magnitude too small to explain the energetics of observed long-duration bursts at cosmological redshifts. In addition, in the absence of rotational effects the energy is deposited in a region containing most of the stellar mass. Therefore relativistic ejection of matter is impossible.

astro-ph↗

arXiv2000

Imprints of accretion on gravitational waves from black holes

Black holes are superb sources of gravitational wave signals, for example when they are born in stellar collapse. We explore the subtleties that may emerge if mass accretion events increase significantly the mass of the black hole during its gravitational wave emission. We find the familiar damped-oscillatory radiative decay but now both decay rate and frequencies are modulated by the mass accretion rate. Any appreciable increase in the horizon mass during emission reflects on the instantaneous signal frequency, which shows a prominent negative branch in the dot[f](f) evolution diagram. The features of the frequency evolution pattern reveal key properties of the accretion event, such as the total accreted mass and the accretion rate. For slow accretion rates the frequency evolution follows verbatim the accretion rate, as expected from dimensional arguments. In view of the possibility of detection of black hole ``ringing'' by the upcoming gravitational wave experiments, the deciphering of the late time frequency dynamics may provide direct insight into otherwise obscured aspects of the black hole birth process.

gr-qc↗

arXiv2000

Black holes on the brane

We consider exact solutions for static black holes localized on a three-brane in five-dimensional gravity in the Randall-Sundrum scenario. We show that the Reissner-Nordstrom metric is an exact solution of the effective Einstein equations on the brane, re-interpreted as a black hole without electric charge, but with instead a tidal 'charge' arising via gravitational effects from the fifth dimension. The tidal correction to the Schwarzschild potential is negative, which is impossible in general relativity, and in this case only one horizon is admitted, located outside the Schwarzschild horizon. The solution satisfies a closed system of equations on the brane, and describes the strong-gravity regime. Current observations do not strongly constrain the tidal charge, and significant tidal corrections could in principle arise in the strong-gravity regime and for primordial black holes.

hep-th↗

arXiv2000

Null cone evolution of axisymmetric vacuum spacetimes

We present the details of an algorithm for the global evolution of asymptotically flat, axisymmetric spacetimes, based upon a characteristic initial value formulation using null cones as evolution hypersurfaces. We identify a new static solution of the vacuum field equations which provides an important test bed for characteristic evolution codes. We also show how linearized solutions of the Bondi equations can be generated by solutions of the scalar wave equation, thus providing a complete set of test beds in the weak field regime. These tools are used to establish that the algorithm is second order accurate and stable, subject to a Courant-Friedrichs-Lewy condition. In addition, the numerical versions of the Bondi mass and news function, calculated at scri on a compactified grid, are shown to satisfy the Bondi mass loss equation to second order accuracy. This verifies that numerical evolution preserves the Bianchi identities. Results of numerical evolution confirm the theorem of Christodoulou and Klainerman that in vacuum, weak initial data evolve to a flat spacetime. For the class of asymptotically flat, axisymmetric vacuum spacetimes, for which no nonsingular analytic solutions are known, the algorithm provides highly accurate solutions throughout the regime in which neither caustics nor horizons form.

gr-qc↗

arXiv2000

Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments

We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless (CT) approach that has improved stability properties in evolving weak and strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the range of resolutions used in our 3D simulations.

gr-qc↗

arXiv1999

Analysis of relativistic hydrodynamics in conservation form

Formulations of Eulerian general relativistic ideal hydrodynamics in conservation form are analyzed in some detail, with particular emphasis to geometric source terms. Simple linear transformations of the equations are introduced and the associated equivalence class is exploited for the optimization of such sources. A significant reduction of their complexity is readily possible in generic spacetimes. The local characteristic structure of the standard member of the equivalence class is analyzed for a general equation of state (EOS). This extends previous results restricted to the polytropic case. The properties of all other members of the class, in particular specialized forms employing Killing symmetries, are derivable from the standard form. Special classes of EOS are identified for both spacelike and null foliations, which lead to explicit inversion of the state vector and computational savings. The entire approach is equally applicable to spacelike or lightlike foliations and presents a complete proposal for numerical relativistic hydrodynamics on stationary or dynamic geometries.

gr-qc↗

arXiv1999

Numerical simulations of relativistic wind accretion on to black holes using Godunov-type methods

We have studied numerically the so-called Bondi-Hoyle (wind) accretion on to a rotating (Kerr) black hole in general relativity. We have used the Kerr-Schild form of the Kerr metric, free of coordinate singularities at the black hole horizon. The `test-fluid' approximation has been adopted, assuming no dynamical evolution of the gravitational field. We have used a recent formulation of the general relativistic hydrodynamic equations which casts them into a first-order hyperbolic system of conservation laws. Our studies have been performed using a Godunov-type scheme based on Marquina's flux-formula. We find that regardless of the value of the black hole spin the final accretion pattern is always stable, leading to constant accretion rates of mass and momentum. The flow is characterized by a strong tail shock which is increasingly wrapped around the central black hole as the hole angular momentum increases. The rotation induced asymmetry in the pressure field implies that besides the well known drag, the black hole will experience also a lift normal to the flow direction.

astro-ph↗

arXiv1999

Construction of Astrophysical Initial Data for Perturbations of Relativistic Stars

We develop a framework for constructing initial data sets for perturbations about spherically symmetric matter distributions. This framework facilitates setting initial data representing astrophysical sources of gravitational radiation involving relativistic stars. The procedure is based on Lichnerowicz-York's conformal approach to solve the constraints in Einstein's equations. The correspondence of these initial data sets in terms of the standard gauge perturbation variables in the Regge-Wheeler perturbation variables is established, and examples of initial data sets of merging neutron stars under the close-limit approximation are presented.

gr-qc↗

arXiv1999

Numerical hydrodynamics on light cones

Characteristic methods show excellent promise in the evolution of single black hole spacetimes. The effective coupling with matter fields may help the numerical exploration of important astrophysical systems such as neutron star black hole binaries. To this end we investigate formalisms for numerical relativistic hydrodynamics which can be adaptable to null (characteristic) foliations of the spacetime. The feasibility of the procedure is demonstrated with one-dimensional results on the evolution of self-gravitating matter accreting onto a dynamical black hole.

gr-qc↗

arXiv1999

Relativistic hydrodynamics on spacelike and null surfaces: Formalism and computations of spherically symmetric spacetimes

We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and fields are derived in the general case. A complete implementation of the formalism is developed in the case of spherical symmetry. The algorithm is tested in a number of different situations, predisposing for a range of possible applications. We consider the Riemann problem for a polytropic gas, with initial data given on a retarded/advanced time slice of Minkowski spacetime. We compute perfect fluid accretion onto a Schwarzschild black hole spacetime using ingoing null Eddington-Finkelstein coordinates. Tests of fluid evolution on dynamic background include constant density and TOV stars sliced along the radial null cones. Finally, we consider the accretion of self-gravitating matter onto a central black hole and the ensuing increase in the mass of the black hole horizon.

gr-qc↗

arXiv1998

Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Kerr black hole

In our program of studying numerically the so-called Bondi-Hoyle accretion in the fully relativistic regime, we present here first results concerning the evolution of matter accreting supersonically onto a rotating (Kerr) black hole. These computations generalize previous results where the non-rotating (Schwarzschild) case was extensively considered. We parametrize our initial data by the asymptotic conditions for the fluid and explore the dependence of the solution on the angular momentum of the black hole. Towards quantifying the robustness of our numerical results, we use two different geometrical foliations of the black hole spacetime, the standard form of the Kerr metric in Boyer-Lindquist coordinates as well as its Kerr-Schild form, which is free of coordinate singularities at the black hole horizon. We demonstrate some important advantages of using such horizon adapted coordinate systems. Our numerical study indicates that regardless of the value of the black hole spin the final accretion pattern is always stable, leading to constant accretion rates of mass and momentum. The flow is characterized by a strong tail shock, which, unlike the Schwarzschild case, is increasingly wrapped around the central black hole as the hole angular momentum increases. The rotation induced asymmetry in the pressure field implies that besides the well known drag, the black hole will experience also a lift normal to the flow direction. This situation exhibits some analogies with the Magnus effect of classical fluid dynamics.

astro-ph↗

arXiv1998

A "horizon adapted" approach to the study of relativistic accretion flows onto rotating black holes

We present a new geometrical approach to the study of accretion flows onto rotating (Kerr) black holes. Instead of Boyer-Lindquist coordinates, the standard choice in all existing numerical simulations in the literature, we employ the simplest example of a horizon adapted coordinate system, the Kerr-Schild coordinates. This choice eliminates boundary ambiguities and unphysical divergent behavior at the event horizon. Computations of Bondi-Hoyle accretion onto extreme Kerr black holes, performed here for the first time, demonstrate the key advantages of this procedure. We argue it offers the best approach to the numerical study of the, observationally, increasingly more accesible relativistic inner region around black holes.

astro-ph↗