Apparent horizons in simplicial Brill wave initial data

Abstract

Abstract. We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

“…Nontrivial results include e.g. Kasner universe, Brill waves, binary black holes, FLRW universe [27,[31][32][33][34]. A key observation in the convergence results is that the deviation of Regge calculus from general relativity is the non-commutativity of rotations in the discrete theory, while the error from the non-commutativity is of higher order in edge lengths [36].…”

Symmetry Without Symmetry: Numerical Simulation of Axisymmetric Systems Using Cartesian Grids

“…[48], we take as initial data a pure gravitational wave data set, based on the axisymmetric ansatz of Brill [49], and later studied by Eppley [45,50,51] and others [52,53]. The metric takes the form…”

Gravitational Holography and Trapped Surfaces

“…It is accepted in the literature that no gravitational wave (GW) (Misner et al, 1973;Thorne, 1980a,b) passes a spacetime region without leaving its fingerprints in this region (Brill and Lindquist, 1963;Eppley, 1977;Tipler, 1980;Urtsever, 1988a,b;Beig and Murchadha, 1991;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). As emphasized in Urtsever (1988a,b) each GW is characterized by its own intrinsic spacetime the geometry of which is imprinted upon the passed region in the sense that its geometry assume the same form as that of the GW.…”

“…As emphasized in Urtsever (1988a,b) each GW is characterized by its own intrinsic spacetime the geometry of which is imprinted upon the passed region in the sense that its geometry assume the same form as that of the GW. The imprinted geometry may be either stable for a long time if the relevant GW is strong or transient if it is weak (Eppley, 1977;Beig and Murchadha, 1991;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). This geometry is, theoretically, traced and located in the related trapped surface (Brill and Lindquist, 1963;Eppley, 1977;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981).…”

“…The imprinted geometry may be either stable for a long time if the relevant GW is strong or transient if it is weak (Eppley, 1977;Beig and Murchadha, 1991;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). This geometry is, theoretically, traced and located in the related trapped surface (Brill and Lindquist, 1963;Eppley, 1977;Abrahams and Evans, 1992;Alcubierre et al, 2000;Gentle et al, 1998;Gentle, 1999;Miyama, 1981). Among the different kinds of these surfaces one may find either the singular trapped ones (Eppley, 1977;Tipler, 1980;Urtsever, 1988a,b;Abrahams and Evans, 1992) or the nonsingular ones (Beig and Murchadha, 1991) which are related to the regular and asymptotically flat initial data (Misner et al, 1973;Eppley, 1977;Brill, 1959Brill, , 1964Brill and Hartle, 1964;Arnowitt et al, 1962;Nakamura, 1984) in vacuum.…”