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Register a new userThe consistency of codimension-2 braneworlds and their cosmology
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Added by
Antonios Papazoglou
Publication date
2009
fields
Physics
and research's language is
English
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We study axially symmetric codimension-2 cosmology for a distributional braneworld fueled by a localised 4D perfect fluid, in a 6D Lovelock theory. We argue that only the matching conditions (dubbed topological) where the extrinsic curvature on the brane has no jump describe a pure codimension-2 brane. If there is discontinuity in the extrinsic curvature on the brane, this induces inevitably codimension-1 distributional terms. We study these topological matching conditions, together with constraints from the bulk equations evaluated at the brane position, for two cases of regularisation of the codimension-2 defect. First, for an arbitrary smooth regularisation of the defect and second for a ring regularisation which has a cusp in the angular part of the metric. For a cosmological ansatz, we see that in the first case the coupled system is not closed and requires input from the bulk equations away from the brane. The relevant bulk function, which is a time-dependent angular deficit, describes the energy exchange between the brane and the 6D bulk. On the other hand, for the ring regularisation case, the system is closed and there is no leakage of energy in the bulk. We demonstrate that the full set of matching conditions and field equations evaluated at the brane position are consistent, correcting some previous claim in the literature which used rather restrictive assumptions for the form of geometrical quantities close to the codimension-2 brane. We analyse the modified Friedmann equation and we see that there are certain corrections coming from the non-zero extrinsic curvature on the brane. We establish the presence of geometric self-acceleration and a possible curvature domination wedged in between the period of matter and self-acceleration eras as signatures of codimension-2 cosmology.
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We consider four-dimensional de Sitter, flat and anti de Sitter branes embedded in a six-dimensional bulk spacetime whose dynamics is dictated by Lovelock theory. We find, applying a generalised version of Birkhoffs theorem, that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of Lovelock theory. These are warped solitonic spaces, where the horizons of the black hole geometries correspond to the possible positions of codimension-2 branes. The horizon temperature is related via conical singularities to the tension or vacuum energy of the branes. We classify the braneworld solutions for certain combinations of bulk parameters, according to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. The bulk Lovelock theory gives an induced gravity term on the brane, which, we argue, generates four-dimensional gravity up to some distance scale. As a result, some simple solutions, such as the Lovelock corrected Schwarzschild black hole in six dimensions, are shown to give rise to self-accelerating braneworlds. We also find that several other solutions have self-tuning properties. Finally, we present regular gravitational instantons of Lovelock gravity and comment on their significance.
We consider five-dimensional gravity with a Gauss-Bonnet term in the bulk and an induced gravity term on a 2-brane of codimension-2. We show that this system admits BTZ-like black holes on the 2-brane which are extended into the bulk with regular horizons.
We consider maximally symmetric 3-branes embedded in a six-dimensional bulk spacetime with Lovelock dynamics. We study the properties of the solutions with respect to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. Some simple solutions are shown to give rise to self-accelerating braneworlds, whereas several others solutions have self-tuning properties. For the case of geometric self-acceleration we argue that the cross-over scale in between four-dimensional and higher-dimensional gravity and the scale of late-time geometric acceleration, fixed by the present horizon size, are related via the conical deficit angle of the six-dimensional bulk solution, which is a free parameter.
Cylindrical braneworlds have been used in the literature as a convenient way to resolve co-dimension-two branes. They are prevented from collapsing by a massless worldvolume field with non-trivial winding, but here we discuss another way of preventing collapse, which is to rotate the brane. We use a simple microscopic field theory model of a domain wall with a condensate for which rotation is a necessity, not just a nice added extra. This is due to a splitting instability, whereby the effective potential trapping the condensate is not strong enough to hold it on the defect in the presence of winding without charge. We use analytic defect solutions in the field theory (kinky vortons) to construct a thin-wall braneworld model by including gravitational dynamics, and we allow for the rotation required by the microscopic theory. We then discuss the impact rotation has on the bulk and brane geometry, thereby providing an anchor for further cosmological investigations. Our setup naturally leads to worldvolume fields living at slightly different radii, and we speculate on the consequences of this in regard to the fermion mass-hierarchy.
We study the absorption probability and Hawking radiation of the scalar field in the rotating black holes on codimension-2 branes. We find that finite brane tension modifies the standard results in Hawking radiation if compared with the case when brane tension is completely negligible. We observe that the rotation of the black hole brings richer physics. Nonzero angular momentum triggers the super-radiance which becomes stronger when the angular momentum increases. We also find that rotations along different angles influence the result in absorption probability and Hawking radiation. Compared with the black hole rotating orthogonal to the brane, in the background that black hole spins on the brane, its angular momentum brings less super-radiance effect and the brane tension increases the range of frequency to accommodate super-radiance. These information can help us know more about the rotating codimension-2 black holes.
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