TY - JOUR

T1 - Black hole formation from the collision of plane-fronted gravitational waves

AU - Pretorius, Frans

AU - East, William E.

N1 - Funding Information:
We thank Herbert Balasin and Peter Aichelburg for useful comments regarding an earlier version of this manuscript. F. P. acknowledges support from NSF Grant No. PHY-1607449, the Simons Foundation, and the Canadian Institute For Advanced Research (CIFAR). This research was further supported in part by the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science, and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science. Computational resources were provided by The Extreme Science and Engineering Discovery Environment (XSEDE) under Grant No. TG-PHY100053 and the Perseus cluster at Princeton University.

PY - 2018/10/15

Y1 - 2018/10/15

N2 - This paper introduces a new effort to study the collision of plane-fronted gravitational waves in four-dimensional, asymptotically flat spacetime, using numerical solutions of the Einstein equations. The pure vacuum problem requires singular, Aichelburg-Sexl-type sources to achieve finite energy solutions, which are problematic to treat both mathematically and numerically. Instead then, we use null (massless) particles to source nontrivial geometry within the initial wave fronts. The main purposes of this paper are to (a) motivate the problem, (b) introduce methods for numerically solving the Einstein equations coupled to distributions of collisionless massless or massive particles, and (c) present a first result on the formation of black holes in the head-on collision of axisymmetric distributions of null particles. Regarding the last-named, initial conditions are chosen so that a black hole forms promptly, with essentially no matter escaping the collision. This can be interpreted as approaching the ultrarelativistic collision problem from within an infinite boost limit, but where the matter distribution is spread out, and thus nonsingular. We find results that are consistent with earlier perturbative calculations of the collision of Aichelburg-Sexl singularities, as well as numerical studies of the high-speed collision of boson stars, black holes, and fluid stars: a black hole is formed containing most of the energy of the spacetime, with the remaining 15±1% of the initial energy radiated away as gravitational waves. The methods developed here could be relevant for other problems in strong-field gravity and cosmology that involve particle distributions of matter.

AB - This paper introduces a new effort to study the collision of plane-fronted gravitational waves in four-dimensional, asymptotically flat spacetime, using numerical solutions of the Einstein equations. The pure vacuum problem requires singular, Aichelburg-Sexl-type sources to achieve finite energy solutions, which are problematic to treat both mathematically and numerically. Instead then, we use null (massless) particles to source nontrivial geometry within the initial wave fronts. The main purposes of this paper are to (a) motivate the problem, (b) introduce methods for numerically solving the Einstein equations coupled to distributions of collisionless massless or massive particles, and (c) present a first result on the formation of black holes in the head-on collision of axisymmetric distributions of null particles. Regarding the last-named, initial conditions are chosen so that a black hole forms promptly, with essentially no matter escaping the collision. This can be interpreted as approaching the ultrarelativistic collision problem from within an infinite boost limit, but where the matter distribution is spread out, and thus nonsingular. We find results that are consistent with earlier perturbative calculations of the collision of Aichelburg-Sexl singularities, as well as numerical studies of the high-speed collision of boson stars, black holes, and fluid stars: a black hole is formed containing most of the energy of the spacetime, with the remaining 15±1% of the initial energy radiated away as gravitational waves. The methods developed here could be relevant for other problems in strong-field gravity and cosmology that involve particle distributions of matter.

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U2 - 10.1103/PhysRevD.98.084053

DO - 10.1103/PhysRevD.98.084053

M3 - Article

AN - SCOPUS:85056191511

VL - 98

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 8

M1 - 084053

ER -