Potential for ill-posedness in several second-order formulations of the Einstein equations

Frittelli, Simonetta

doi:10.1103/physrevd.70.044029

Cited by 2 publications

(2 citation statements)

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“…Furthermore, for a constrained system, like the equations of electromagnetism and general relativity, enlarging the system of equations by adding new fields can suppress unphysical constraint violations. The standard ADM formulation is now known to be ill-posed in the nonlinear regime [69,70]. On the other hand, many well-posed formulations have been proposed but turned out not to be an immediate panacea for unstable black hole simulations.…”

Section: Making the Problem Well Posedmentioning

confidence: 99%

“…As will be discussed later, the ADM equations by themselves proved to be unstable for many strong-field problems, including black-hole mergers. With all the difficulties encountered trying to implement the ADM equations in the 1990s, emphasis changed to developing new 3 + 1 systems and analyzing their well-posedness [60][61][62][62][63][64][65][66][67][68][69][70][71][72][73]. Informally speaking, a hyperbolic system of equations is well posed if the solution depends continuously on the initial and boundary data.…”

Section: Making the Problem Well Posedmentioning

confidence: 99%

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Numerical relativity of compact binaries in the 21st century

Duez

Zlochower²

2018

Rep. Prog. Phys.

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We review the dramatic progress in the simulations of compact objects and compact-object binaries that has taken place in the first two decades of the twenty-first century. This includes simulations of the inspirals and violent mergers of binaries containing black holes and neutron stars, as well as simulations of black-hole formation through failed supernovae and high-mass neutron star-neutron star mergers. Modeling such events requires numerical integration of the field equations of general relativity in three spatial dimensions, coupled, in the case of neutron-star containing binaries, with increasingly sophisticated treatment of fluids, electromagnetic fields, and neutrino radiation. However, it was not until 2005 that accurate long-term evolutions of binaries containing black holes were even possible (Pretorius 2005 Phys. Rev. Lett. 95 121101, Campanelli et al 2006 Phys. Rev. Lett. 96 111101, Baker et al 2006 Phys. Rev. Lett. 96 111102). Since then, there has been an explosion of new results and insights into the physics of strongly-gravitating system. Particular emphasis has been placed on understanding the gravitational wave and electromagnetic signatures from these extreme events. And with the recent dramatic discoveries of gravitational waves from merging black holes by the Laser Interferometric Gravitational Wave Observatory and Virgo, and the subsequent discovery of both electromagnetic and gravitational wave signals from a merging neutron star-neutron star binary, numerical relativity became an indispensable tool for the new field of multimessenger astronomy.

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Section: Making the Problem Well Posedmentioning

confidence: 99%