String or branelike solutions in four-dimensional Einstein gravity in the presence of cosmological constant

Abstract

We investigate string or branelike solutions for four-dimensional vacuum Einstein equations in the presence of cosmological constant. For the case of negative cosmological constant, the Banados-Teitelboim-Zanelli black string is the only warped stringlike solution. The general solutions for nonwarped branelike configurations are found and they are characterized by the Arnowitt-Deser-Misner mass density and two tensions. Interestingly, the sum of these tensions is equal to the minus of the mass density. Other than the well-known black string and soliton spacetimes, all the static solutions possess naked singularities. The time-dependent solutions can be regarded as the anti-de Sitter extension of the well-known Kasner solutions. The speciality of those static regular solutions and the implication of singular solutions are also discussed in the context of cylindrical matter collapse. For the case of positive cosmological constant, the Kasner-de Sitter spacetime appears as time-dependent solutions and all static solutions are found to be naked singular.

17 pages, 6 figures, several references added, minor corrections in wordings and typos

References in corpus (11)

• Predictions from an anisotropic inflationary era
• Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
• On the stability of AdS black strings
• String-Like BTZ on Codimension-2 Braneworlds in the Thin Brane Limit
• Black String Solutions with arbitrary Tension
• Extraordinary vacuum black string solutions
• An analytic approach to perturbations from an initially anisotropic universe
• Geometrical properties of the trans-spherical solutions in higher dimensions
• Thermodynamics and Stability of Flat Anti-de Sitter Black Strings
• Symmetry Breaking Phase Transitions in ABJM Theory with a Finite U(1) Chemical Potential
• Classification of Hypercylindrical Spacetimes with Momentum Flow

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