Some higher-dimensional vacuum solutions

Gurses, M
Karasu, Atalay
We study an even-dimensional manifold with a pseudo-Riemannian metric with arbitrary signature and arbitrary dimensions. We consider the Ricci flat equations and present a procedure to construct solutions to some higher(even-) dimensional Ricci flat field equations from the four-dimensional Ricci flat metrics. When the four-dimensional Ricci flat geometry corresponds to a colliding gravitational vacuum spacetime our approach provides an exact solution to the vacuum Einstein field equations for colliding gravitational plane waves in an (arbitrary) even-dimensional spacetime. We give explicitly higher-dimensional Szekeres metrics and study their singularity behaviour.


Some splitting theorems for stably causal spacetime
Garcia-Rio, E; Kupeli, DN (Springer Science and Business Media LLC, 1998-01-01)
We prove a splitting theorem for stably causal spacetimes and another splitting theorem for finitely compact spacetimes admitting a proper time synchronizable reference frame.
DERELI, T; MUKHERJEE, M; TUCKER, RW (IOP Publishing, 1988-01-01)
A set of symmetric, traceless, divergence-free differential forms, Weyl covariant under a conformal scaling of a (pseudo-)Riemannian metric, is constructed in 4n-1 dimensions.
Closed timelike curves and geodesics of Godel-type metrics
Gleiser, RJ; Gurses, M; Karasu, Atalay; Sarıoğlu, Bahtiyar Özgür (IOP Publishing, 2006-04-07)
it is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower-dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed.
Massive, topologically massive, models
Deser, S; Tekin, Bayram (IOP Publishing, 2002-06-07)
In three dimensions, there are two distinct mass-generating mechanisms for gauge fields: adding the usual Proca/Pauli-Fierz, or the more esoteric Chern-Simons (CS), terms. Here, we analyse the three-term models where both types are present and their-various limits. Surprisingly, in the tensor case, these seemingly innocuous systems are physically unacceptable. If the sign of the Einstein term is 'wrong', as is in fact required in the CS theory, then the excitation masses are always complex; with the usual s...
Accelerated Levi-Civita-Bertotti-Robinson metric in D dimensions
Gurses, M; Sarıoğlu, Bahtiyar Özgür (Springer Science and Business Media LLC, 2005-12-01)
A conformally flat accelerated charge metric is found in an arbitrary dimension D. It is a solution of the Einstein-Maxwell-null fluid equations with a cosmological constant in D >= 4 dimensions. When the acceleration is zero, our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that the charge loses its energy, for all dimensions, due to the acceleration.
Citation Formats
M. Gurses and A. Karasu, “Some higher-dimensional vacuum solutions,” CLASSICAL AND QUANTUM GRAVITY, pp. 509–516, 2001, Accessed: 00, 2020. [Online]. Available: