Frans Pretorius - US grants

This award will support a research program at Princeton University, which is focused on understanding the strong-field regime of Einstein's theory of general relativity. Projects that will be pursued include modeling sources of gravitational waves in the universe (in particular collisions of compact objects such as black holes and neutron stars), high-speed black hole collisions, gravitational collapse, the interior structure of black holes, and the nature of gravity in a universe with extra dimensions. An integral part of the research program will also be to provide a vehicle to efficiently educate students in the methodology and process of performing fundamental scientific
research via computer simulation. This will be achieved through development of a series of self-contained computational physics projects with interactive web-based interfaces; undergraduate or beginning graduate students will be able to work through the projects to write and use fully functional simulation codes of simplified model problems, while high-school level students will be able to use the web interface to explore working versions of the simulations.
The research could have broader impact in several areas. First, knowledge of the structure of the gravitational waves radiated in compact object collisions will form an integral part of identifying and understanding such events, should they occur in the universe and be seen by a new generation of gravitational wave observatories.
Second, studies of solutions of the equations of general relativity in the dynamical strong field regime should provide much insight into the nature of this enigmatic theory in extreme conditions.
Furthermore, if the universe happens to contain extra dimensions, black holes might be produced in high energy particle accelerators or in cosmic ray collisions with the earth's atmosphere, and knowledge of general relativity in extreme conditions could help in identifyng and understanding such events.
Finally, the importance of computer simulation in fundamental and applied scientific research will continue to grow in coming years, and the educational tools that this research program will produce should be of significant benefit in training the next generation of scientists and engineers.

Gravitational collapse is a central problem in General Relativity intimately tied, mathematically, to the issue of the long time behavior of general solutions to the Einstein field equations. The problem can be neatly captured in the so called final state conjecture (FSC): generic asymptotically flat initial data sets have maximal future developments, namely solutions of the Einstein vacuum equations, which look, asymptotically, in any finite region of space, as a Kerr black hole solution. The focused research effort described in this proposal identifies four related problems whose solution will greatly advance our understanding of the FSC. The first three, 1) Uniqueness and 2) Stability of the Kerr solutions and 3) Formation of black holes, are at the heart of the theory of black holes. The last one, 4) Bounded L2 curvature conjecture and break-down criterions (the problem of evolution for very rough initial conditions and optimal sufficient conditions which insure regularity of the space-time), is a topic loosely connected with the celebrated cosmic censorship conjecture, which is itself a necessary ingredient, and a formidable intellectual obstacle, for resolving the FSC.

Each of the four related problems identified above are, in themselves, very difficult and deep challenges in general relativity which have witnessed a lot of progress in recent years based on new analytical and geometric ideas. Furthermore, recent advances in numerical relativity have allowed new classes of solutions to the field equations to be obtained in highly non-trivial situations. Advances toward solving the FSC will require continued development within individual methodologies, though we plan to accelerate progress via a closer interaction amongst the different approaches. Cooperation between mathematical and numerical relativity can substantially help the former by endowing it with a powerful experimental tool and also help the latter to formulate key questions connected with the development of new numerical codes. To be successful, this will require training a new class of researcher, proficient in both the relevant formal mathematics and high performance scientific computing. We will engage graduate students and postdoctoral scholars in this effort, giving them the skills necessary to have a strong impact in their future careers, whether in academia or the broader work force. The research carried out will strengthen the foundations of general relativity and our understanding of black holes, which is of significant import to the broader nascent scientific field of gravitational wave astronomy.

Proposal #: 12-29573
PI(s): Hillegas, Curtis W.
Carter, Emily A.; Pretorius, Frans; Spitkovsky, Anatoly; Wood, Eric F.
Institution: Princeton University
Title: MRI/Acq.: Shared Parallel High Performance Storage System to Enable Computational Science and Engineering
Project Proposed:
This project, acquiring a High Performance Computing (HPC) storage system, aims to provide storage and I/O bandwidth required to enable advancement of research to new, previously unattainable areas. Specifically, in astrophysics the storage will allow an increase in dimensionality to perform full 3D modeling of shock formation; in civil and environmental engineering, it will enable the analysis of higher resolution water condition data in both time and space; in mechanical and aerospace engineering, the instrument will facilitate rigorous physical modeling of rate constants for biofuel combustion and fundamental understanding of molecular adsorptions; and in physics it will enable the modeling of gravitational waves and compact object mergers considering a broader range of physics. More generally, the system will enable projects across many disciplines in computational science and engineering.
Since data storage and access have become a bottleneck hampering researchers in the TIGRESS systems, the proposed system should contribute to remove the bottleneck. Understanding that data growth will continue, a modular storage system design has been chosen that will allow the system to grow in capacity and performance as the data deluge continuous to mount. Planned is the purchase of a 1.5 PB storage system based on hardware from NetApp, integrated with servers from SGI by Comnetco. The system will run IBMs General Parallel File System (GPFS) and provide 12 GB/s parallel performance across the institution?s TIGRESS HPC systems.
Broader Impacts:
The instrument will facilitate collaboration by making it easy for researchers to share data within the institution; furthermore, it will foster collaboration nationally and internationally through the included web server facility by allowing researchers to broadly share their data. As a research tool available to postdocs, graduate students, and advanced undergraduate students, including many researchers underrepresented minority groups, the instrument will serve as a training platform, teaching data layout, management and performance optimization.

The research goals of the project are focused on understanding the strong-field regime of Einstein's theory of general relativity. This encompasses both astrophysical and theoretical aspects of general relativity. On the astrophysical side, the main effort is an ongoing study of sources of gravitational waves in our universe, in particular binary black hole, black hole-neutron star and binary neutron star collisions. When neutron stars are involved in the collision, further questions involving potentially observable electromagnetic counterpart emission and production of r-process elements in ejected material will be pursued. The theoretical work includes studies of gravitational collapse and corresponding critical phenomena, the ultrarelativistic regime of particle collisions where gravity dominates the interaction, and the nature of gravity in higher dimensional spacetimes. Of particular interest for the latter subject are asymptotically Anti de-Sitter (AdS) spacetimes, where the gravitational dynamics can be related to the physics of strongly coupled conformal field theories (CFTs) via the AdS/CFT correspondence of string theory.

This research will contribute crucial information to our understanding of sources of gravitational waves in the universe and so form an integral part of the burgeoning field of gravitational wave astronomy. It will further provide a deeper understanding of the dynamical strong-field regime of general relativity, and help expand our knowledge of the interrelations between general relativity, high energy physics, and quantum gravity. The pursuit of these projects will involve graduate students, undergraduates and postdoctoral fellows. They will thus be trained to do leading scientific research, become knowledgeable in corresponding areas of physics, and adept in high-performance computing and numerical methods. These skills are invaluable to many professions, and would thus also benefit and further the development of those students and postdocs that subsequently wish to pursue careers outside academia.