Dr. Christian Reisswig

Formation of a supermassive black hole binary system in supermassive star collapse

Christian — Mon, 29 Dec 2014 07:48:55 +0000

Supermassive stars are hypothetical objects with masses between 10,000 and 1e8 solar masses that are kept in hydrostatic equilibrium by radiation pressure (unlike ordinary main sequence stars that are powered by nuclear fusion). Even though such a star has never been observed, they are hypothesized to have existed in the very early Universe at high redshifts when the first stars and galaxies have formed (an era of the Universe that is not yet accessible to telescopes). The collapse of supermassive stars is a possible way of explaining the puzzling existence of supermassive BHs at those high redshifts (z > 7). Recently, I have shown that it is possible to form a merging BBH system during the collapse of a single supermassive star. The formation of two BHs is made possible by a non-axisymmetric instability encountered by rapidly rotating and radiation pressure dominated collapsing stars that leads to fragmentation. Electron-positron pair creation at high temperatures above 10^9 K causes further loss of pressure, and accelerates the collapse in each fluid fragment, eventually forming an event horizon around each fragment. Since the formation of a pair of BHs from just one supermassive star gives rise to very powerful gravitational radiation that can be seen from the edge of our universe with space-borne GW observatories, an observed GW signal may inform cosmology about the possible formation processes of supermassive BHs when the universe was less than 1 Gyr old. This particular work led to a press release that was picked up by newspapers and popular science magazines around the world (see here).

The corresponding publication has been published in Physical Review Letters, and was highlighted as a Physics Synopsis.

Multiblocks in general-relativity with flux-conservative AMR

Christian — Sat, 20 Dec 2014 10:06:20 +0000

A z=0 slice through the simulation domain: a central Cartesian patch with AMR is surrounded by 6 “inflated cube” grid patches.

A radial shell of the spherical inflated cube patch system. On interpatch boundaries, one coordinate direction always coincides, reducing ghost-zone interpolation two 1d.

I and collaborators have successfully implemented and tested a multiblock scheme with flux-conservative adaptive mesh refinement (AMR). Multiblocks allow one to cover the simulation domain with multiple curvi-linear grid patches. This enables a greater flexibility in adapting the grid resolution to the problem symmetry. For instance, the gravitational-wave zone or the outer layers of a star exhibit approximately spherical symmetry. Hence, the most natural way of covering the simulation domain is given by a spherical coordinate system. The interior of a star, or more generally, the gravitating source may not exhibit any symmetry and is therefore best modeled with Cartesian grids. A suitable multiblock system is given by our 7-patch inflated cube system. The spherical region is covered by 6 overlapping “inflated cube” grid patches. The strong field region is covered by a central Cartesian patch with flux-conservative Berger-Oliger AMR with sub-cycling in time. The multiblock code enables studies of stellar collapse and binary neutron star mergers with unprecedented accuracy and represents state-of-the art numerical relativity technology. It can be downloaded here. The corresponding publication is available here.

A new high-order nullcone evolution scheme

Christian — Wed, 10 Dec 2014 10:05:17 +0000

I and collaborators have developed a new high-order algorithm for solving the characteristic initial boundary value problem of the Einstein equations.
In the characteristic initial boundary value problem of general relativity, the Einstein equations are recast using a particular coordinate system along outgoing nullrays (along the light (or null) cone).
The characteristic Einstein evolution system is useful for modeling the far-field region of the gravitational-wave zone, and allows one to include future null infinity on the computational grid via radial compactification.
Future null infinity is the region where gravitational waves are unambiguously defined, and is also the place where a gravitational-wave detector would be located.
Previous characteristic evolution schemes were limited to second-order accuracy. The system is peculiar to discretize since there is a hierarchy of equations that must be solved via an outward radial march.
We have devised a new high-order scheme which solves the radial and time direction via a fourth-order Runge-Kutta scheme. The angular differential operators are approximated via a pseudo-spectral collocation method.
The resulting code requires only a fraction of the computational costs of previous algorithms while offering significantly higher accuracy.
More details can be found here.

Cauchy-characteristic extraction in numerical relativity

Christian — Tue, 02 Dec 2014 10:08:09 +0000

I and collaborators have developed and applied the gravitational-wave extraction technique of Cauchy-characteristic extraction (CCE) to simulations of binary black hole mergers, stellar collapse, and binary neutron star mergers to compute the first unambiguous and gauge-invariant GW signal ever extracted for these problems, allowing me to measure, for the first time, the non-linear memory effect in binary black hole mergers. Without gauge-invariant and mathematically unambiguous gravitational-wave extraction, the computed gravitational-wave forms extracted from a numerical spacetime contain large systematic errors on the order of 10%. However, gravitational-wave detectors data analysis requires an error margin that is significantly smaller. In cauchy-characteristic extraction, the strong field region around, e.g. two orbiting black holes is modeled via standard Cauchy initial boundary value problems. Within a finite radius from the source, on a worldtube, metric data is collected during the evolution. This metric data serves as inner boundary data for a subsequent characteristic evolution. Characteristic evolutions are very efficient at modeling the gravitational-wave far-field region, and allow one to place future null infinity on the computational grid via compactification of the radial coordinate direction. Future null infinity is the region of spacetime that any light ray hits after an infinite amount of time. It is only in this region where gravitational waves can be unambiguously disentangled from the curvature of the backround spacetime.
The corresponding publications (here, here, and here) mark a breakthrough in numerical relativity computations.