Papers by Pantelis Apostolopoulos
Spatially inhomogeneous and irrotational geometries admitting intrinsic conformal symmetries
Physical Review D, 2016
On the Existence of self-similar tilted Perfect Fluid Bianchi Class A Cosmological Models
It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Perco... more It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Percoco, U. "Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors" (2000) Gen. Rel. Grav. 32, 285-294] concerning the Ricci Collineations in spherically symmetric space-times with non-degenerate and diagonal Ricci tensor do not cover all possible cases. Furthermore the complete algebra of Ricci Collineations of certain Robertson-Walker metrics of vanishing spatial curvature are given.
Physical Review D Particles and Fields, Sep 3, 2007
We extend the covariant analysis of the brane cosmological evolution in order to take into accoun... more We extend the covariant analysis of the brane cosmological evolution in order to take into account, apart from a general matter content and an induced-gravity term on the brane, a Gauss-Bonnet term in the bulk. The gravitational effect of the bulk matter on the brane evolution can be described in terms of the total bulk mass as measured by a bulk observer at the location of the brane. This mass appears in the effective Friedmann equation through a term characterized as generalized dark radiation that induces mirage effects in the evolution. We discuss the normal and self-accelerating branches of the combined system. We also derive the Raychaudhuri equation that can be used in order to determine if the cosmological evolution is accelerating.
General Relativity and Gravitation, Sep 30, 2003
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting ... more We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes, (2003) Gen. Rel. Grav. 35, 97-109.] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
Gen Relativ Gravit, 2002
It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Perco... more It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Percoco, U. Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors . Gen. Rel. Grav. 32, 285-294] concerning the Ricci Collineations in spherically symmetric spacetimes with non-degenerate and diagonal Ricci tensor do not cover all possible cases. Furthermore the complete algebra of Ricci Collineations of certain Robertson-Walker metrics of vanishing spatial curvature are given.
General Relativity and Gravitation, 2003
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting ... more We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. {Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes}, 2003 Gen. Relativ. Grav. vol. 35, 97-109] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
We derive the equations of cosmological evolution from an AdS Schwarzschild black hole via hologr... more We derive the equations of cosmological evolution from an AdS Schwarzschild black hole via holographic renormalization with appropriate boundary conditions.
It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models t... more It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admit a four dimensional group of homotheties is given.
A generalisation of a known theorem concerning the computation of the conformal algebra in 1+(n-1... more A generalisation of a known theorem concerning the computation of the conformal algebra in 1+(n-1) decomposable spaces is presented. It is shown that the general form of Conformal Vector Fields (CVF) is the sum of a gradient CVF and a Killing or Homothetic (n-1)-vector. A simple criterion is established which enables one to check if a 1+(n-1) decomposable spacetime admits proper CVF. As an example, the complete conformal algebra of a G\"odel-type spacetime is computed. Comment: 10 pages, Latex. Matches version to appear in Tensor N. S
It is well known that every Killing vector is a Ricci and Matter collineation. Therefore the metr... more It is well known that every Killing vector is a Ricci and Matter collineation. Therefore the metric, the Ricci tensor and the energy-momentum tensor are all members of a large family of second order symmetric tensors which are invariant under a common group of symmetries. This family is described by a generic metric which is defined from the symmetry group of the space-time metric. The proper Ricci and Matter (inheritance) collineations are the (conformal) Killing vectors of the generic metric which are not (conformal) Killing vectors of the space-time metric. Using this observation we compute the Ricci and Matter inheritance collineations of the Robertson-Walker space-times and we determine the Ricci and Matter collineations without any further calculations. It is shown that these higher order symmetries can be used as supplementary conditions to produce an equation of state which is compatible with the Geometry and the Physics of the Robertson-Walker space-times.
We expand the study of generalized brane cosmologies by allowing for an $f(\tilde{\cal R})$ gravi... more We expand the study of generalized brane cosmologies by allowing for an $f(\tilde{\cal R})$ gravity term on the brane, with $\tilde{\cal R}$ the curvature scalar derived from the induced metric. We also include arbitrary matter components on the brane and in the five-dimensional bulk. At low energies, the effect of the bulk on the brane evolution can be described through a mirage component, termed generalized dark radiation, in the effective four-dimensional field equations. Using the covariant formalism, we derive the exact form of these equations. We also derive an effective conservation equation involving the brane matter and the generalized dark radiation. At low energies the coupled brane-bulk system has a purely four-dimensional description. The applications of the formalism include generalizations of the Starobinsky model and the Dvali-Gabadadze-Porrati cosmology.
We present two counter examples to the paper by Carot et al. in Gen. Rel. Grav. (1997). 29 1223 a... more We present two counter examples to the paper by Carot et al. in Gen. Rel. Grav. (1997). 29 1223 and show that the results obtained are correct but not general.
General Relativity and Gravitation, 2002
It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Perco... more It is shown that the results of the paper by Contreras et al. [Contreras, G., Nunez, L. A., Percoco, U. Ricci Collineations for Non-degenerate, Diagonal and Spherically Symmetric Ricci Tensors . Gen. Rel. Grav. 32, 285-294] concerning the Ricci Collineations in spherically symmetric spacetimes with non-degenerate and diagonal Ricci tensor do not cover all possible cases. Furthermore the complete algebra of Ricci Collineations of certain Robertson-Walker metrics of vanishing spatial curvature are given.
General Relativity and Gravitation, 2003
It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models t... more It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admit a four dimensional group of homotheties is given.
General Relativity and Gravitation, 2003
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting ... more We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes, (2003) Gen. Relativ. Grav. 35 97-109] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is nondegenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2005
Using a fully covariant treatment for the description of the bulk geometry, we study the brane co... more Using a fully covariant treatment for the description of the bulk geometry, we study the brane cosmological evolution in the presence of a smooth bulk matter distribution. We focus on the case of a Friedmann-Robertson-Walker (FRW) brane, invariantly characterized by the existence of a six-dimensional group of isometries acting on 3D spacelike orbits. With a FRW brane, the bulk geometry can be regarded as the 5D generalization of the inhomogeneous orthogonal family of Locally Rotationally Symmetric (LRS) spacetimes. We show that, for any bulk matter configuration, the expansion rate on the brane depends only on the covariantly defined comoving mass M of the bulk fluid within a radius equal to the average length scale of the 3D spacelike hypersurfaces of constant curvature. This unique contribution incorporates the effects of the 5D Weyl tensor and the projected tensor related to the bulk matter, and gives a transparent physical picture that includes an effective conservation equation between the brane and the bulk matter.
On the Existence of self-similar tilted Perfect Fluid Bianchi Class A Cosmological Models
Physical Review Letters, 2009
We derive the equations of cosmological evolution from an AdS Schwarzschild black hole via hologr... more We derive the equations of cosmological evolution from an AdS Schwarzschild black hole via holographic renormalization with appropriate boundary conditions.
Physical Review D, 2005
We discuss features of the brane cosmological evolution that arise through the presence of matter... more We discuss features of the brane cosmological evolution that arise through the presence of matter in the bulk. As these deviations from the conventional evolution are not associated with some observable matter component on the brane, we characterize them as mirage effects. We review an example of expansion that can be attributed to mirage non-relativistic matter (mirage cold dark matter) on the brane. The real source of the evolution is an anisotropic bulk fluid with negative pressure along the extra dimension. We also study the general problem of exchange of real non-relativistic matter between the brane and the bulk, and discuss the related mirage effects. Finally, we derive the brane cosmological evolution within a bulk that contains a global monopole (hedgehog) configuration. This background induces a mirage curvature term in the effective Friedmann equation, which can cause a brane Universe with positive spatial curvature to expand forever.
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Papers by Pantelis Apostolopoulos