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Register a new userHigher Dimensional Metrics of Colliding Gravitational Plane Waves
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We give a higher even dimensional extension of vacuum colliding gravitational plane waves with the combinations of collinear and non-collinear polarized four-dimensional metric. The singularity structure of space-time depends on the parameters of the solution.
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We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves and, for generic initial data, produce a spacetime singularity at the focusing hypersurface. There is, in addition, an infinite family of regular solutions and an intriguing static geometry supported by scalar fields. Upon dimensional reduction, the theory can be viewed as an exactly solvable two-dimensional gravity model. This provides a new viewpoint on the gravitational dynamics. Finally, we comment on a simple mechanism by which short-distance corrections in the two-dimensional model can remove the singularity.
The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The role of twist in the relation of the Rosen coordinates adapted to a null congruence with the fundamental Brinkmann coordinates is explained and a generalised form of the Rosen metric describing a gravitational plane wave is derived. The Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are described in both Brinkmann and twisted Rosen form and used to demonstrate the coset space structure of HPWs. The van Vleck-Morette determinant for twisted congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted null congruences of the Ozsvath-Schucking,`anti-Mach plane wave are investigated in detail. These developments provide the necessary geometric toolkit for future investigations of the role of twist in loop effects in quantum field theory in curved spacetime, where gravitational plane waves arise generically as Penrose limits; in string theory, where they are important as string backgrounds; and potentially in the detection of gravitational waves in astronomy.
Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on the junction surface vanishes. So a spherical vacuum shell, containing no matter, arises as a boundary between two regions of the space-time. A general analysis is given of solutions that can be constructed by this method of geometric surgery. Such solutions are a generalized kind of spherically symmetric empty space solutions, described by metric functions of the class $C^0$. New global structures arise with surprising features. In particular, we show that vacuum spherically symmetric wormholes do exist in this theory. These can be regarded as gravitational solitons, which connect two asymptotically (Anti) de-Sitter spaces with different masses and/or different effective cosmological constants. We prove the existence of both static and dynamical solutions and discuss their (in)stability under perturbations that preserve the symmetry. This leads us to discuss a new type of instability that arises in five-dimensional Lovelock theory of gravity for certain values of the coupling of the Gauss-Bonnet term. The issues of existence and uniqueness of solutions and determinism in the dynamical evolution are also discussed.
Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGOs detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with $D>4$ dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in $D>4$. Here, we develop a numerical implementation of the formalism by Godazgar and Reall (Ref.[1]) -- based on projections of the Weyl tensor analogous to the Newman-Penrose scalars -- that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in $D=6$ spacetime dimensions and find that a fraction $(8.19pm 0.05)times 10^{-4}$ of the Arnowitt-Deser-Misner mass is radiated away from the system, in excellent agreement with literature results based on the Kodama-Ishibashi perturbation technique. The method presented here complements the perturbative approach by automatically including contributions from all multipoles rather than computing the energy content of individual multipoles.
The low-energy dynamics of any system admitting a continuum of static configurations is approximated by slow motion in moduli (configuration) space. Here, following Ferrell and Eardley, this moduli space approximation is utilized to study collisions of two maximally charged Reissner--Nordstr{o}m black holes of arbitrary masses, and to compute analytically the gravitational radiation generated by their scattering or coalescence. The motion remains slow even though the fields are strong, and the leading radiation is quadrupolar. A simple expression for the gravitational waveform is derived and compared at early and late times to expectations.
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