A Note on the Integral Formulation of Einstein's Equations Induced on a Braneworld

We revisit the integral formulation (or Green's function approach) of Einstein's equations in the context of braneworlds. The integral formulation has been proposed independently by several authors in the past, based on the assumption that it is possible to give a reinterpretation of the local metric field in curved spacetimes as an integral expression involving sources and boundary conditions. This allows one to separate source-generated and source-free contributions to the metric field. As a consequence, an exact meaning to Mach's Principle can be achieved in the sense that only source-generated (matter fields) contributions to the metric are allowed for; universes which do not obey this condition would be non-Machian. In this paper, we revisit this idea concentrating on a Randall-Sundrum-type model with a non-trivial cosmology on the brane. We argue that the role of the surface term (the source-free contribution) in the braneworld scenario may be quite subtler than in the 4D formulation. This may pose, for instance, an interesting issue to the cosmological constant problem.Comment: 10 pages, no figures, accepted for publication in the General Relativity and Gravitation Journa

Cosmological equations and Thermodynamics on Apparent Horizon in Thick Braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the Friedmann equation in some limits and demonstrate that they can be rewritten as the first law of thermodynamics on the apparent horizon of thick braneworld.Comment: 25 pages, no figure, a definition corrected, several references added, more motivation and discussio

Accelerating Universe from an Evolving Lambda in Higher Dimension

We find exact solutions in five dimensional inhomogeneous matter dominated model with a varying cosmological constant. Adjusting arbitrary constants of integration one can also achieve acceleration in our model. Aside from an initial singularity our spacetime is regular everywhere including the centre of the inhomogeneous distribution. We also study the analogous homogeneous universe in (4+d) dimensions. Here an initially decelerating model is found to give late acceleration in conformity with the current observational demands. We also find that both anisotropy and number of dimensions have a role to play in determining the time of flip, in fact the flip is delayed in multidimensional models. Some astrophysical parameters like the age, luminosity distance etc are also calculated and the influence of extra dimensions is briefly discussed. Interestingly our model yields a larger age of the universe compared to many other quintessential models.Comment: 18 pages, 9 figure

Holographic principle in the BDL brane cosmology

We study the holographic principle in the brane cosmology. Especially we describe how to accommodate the 5D anti de Sitter Schwarzschild (AdSS$_5$) black hole in the Binetruy-Deffayet-Langlois (BDL) approach of brane cosmology. It is easy to make a connection between a mass $M$ of the AdSS$_5$ black hole and a conformal field theory (CFT)-radiation dominated universe on the brane in the moving domain wall approach. But this is not established in the BDL approach. In this case we use two parameters $C_1, C_2$ in the Friedmann equation. These arise from integration and are really related to the choice of initial bulk matter. If one chooses a bulk energy density $\rho_B$ to account for a mass $M$ of the AdSS$_5$ black hole and the static fifth dimension, a CFT-radiation term with $\rho_{CFT} \sim M/a^{4}$ comes out from the bulk matter without introducing a localized matter distribution on the brane. This means that the holographic principle can be established in the BDL brane cosmology.Comment: 9 pages, a version to appear in PR

Massive scalar states localized on a de Sitter brane

We consider a brane scenario with a massive scalar field in the five-dimensional bulk. We study the scalar states that are localized on the brane, which is assumed to be de Sitter. These localized scalar modes are massive in general, their effective four-dimensional mass depending on the mass of the five-dimensional scalar field, on the Hubble parameter in the brane and on the coupling between the brane tension and the bulk scalar field. We then introduce a purely four-dimensional approach based on an effective potential for the projection of the scalar field in the brane, and discuss its regime of validity. Finally, we explore the quasi-localized scalar states, which have a non-zero width that quantifies their probability of tunneling from the brane into the bulk.Comment: 14 pages; 5 figure

Static black holes with a negative cosmological constant: Deformed horizon and anti-de Sitter boundaries

Using perturbative techniques, we investigate the existence and properties of a new static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild-anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces--i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon one for the deformed black hole, and according to the Ashtekar-Magnon definition, we construct the thermodynamic first law of the deformed black hole. The first law has a correction term which can be interpreted as the work term that is necessary for the deformation of the boundary surfaces. Because the work term is negative, the horizon area of the deformed black hole becomes larger than that of the Schwarzschild-anti-de Sitter black hole, if compared under the same mass, indicating that the quasistatic deformation of the Schwarzschild-anti-de Sitter black hole may be compatible with the thermodynamic second law (i.e., the area theorem).Comment: 31 pages, 5 figures, one reference added, to be published in PR

U(1) Gauge Field of the Kaluza-Klein Theory in the Presence of Branes

We investigate the zero mode dimensional reduction of the Kaluza-Klein unifications in the presence of a single brane in the infinite extra dimension. We treat the brane as fixed, not a dynamical object, and do not require the orbifold symmetry. It seems that, contrary to the standard Kaluza-Klein models, the 4D effective action is no longer invariant under the U(1) gauge transformations due to the explicit breaking of isometries in the extra dimension by the brane. Surprisingly, however, the linearized perturbation analysis around the RS vacuum shows that the Kaluza-Klein gauge field does possess the U(1) gauge symmetry at the linear level. In addition, the graviscalar also behaves differently from the 4D point of view. Some physical implications of our results are also discussed.Comment: 10 pages, revtex, no figure, version to appear in Phys. Rev. D, possible caveats of our results due to the zero mode ansatz we used are explained in more detai

Recent Advances in Modeling Stellar Interiors

Advances in stellar interior modeling are being driven by new data from large-scale surveys and high-precision photometric and spectroscopic observations. Here we focus on single stars in normal evolutionary phases; we will not discuss the many advances in modeling star formation, interacting binaries, supernovae, or neutron stars. We review briefly: 1) updates to input physics of stellar models; 2) progress in two and three-dimensional evolution and hydrodynamic models; 3) insights from oscillation data used to infer stellar interior structure and validate model predictions (asteroseismology). We close by highlighting a few outstanding problems, e.g., the driving mechanisms for hybrid gamma Dor/delta Sct star pulsations, the cause of giant eruptions seen in luminous blue variables such as eta Car and P Cyg, and the solar abundance problem.Comment: Proceedings for invited talk at conference High Energy Density Laboratory Astrophysics 2010, Caltech, March 2010, submitted for special issue of Astrophysics and Space Science; 7 pages; 5 figure

Brane Universes with Gauss-Bonnet-Induced-Gravity

The DGP brane world model allows us to get the observed late time acceleration via modified gravity, without the need for a ``dark energy'' field. This can then be generalised by the inclusion of high energy terms, in the form of a Gauss-Bonnet bulk. This is the basis of the Gauss-Bonnet-Induced-Gravity (GBIG) model explored here with both early and late time modifications to the cosmological evolution. Recently the simplest GBIG models (Minkowski bulk and no brane tension) have been analysed. Two of the three possible branches in these models start with a finite density ``Big-Bang'' and with late time acceleration. Here we present a comprehensive analysis of more general models where we include a bulk cosmological constant and brane tension. We show that by including these factors it is possible to have late time phantom behaviour.Comment: 12 pages, 19 figures. Minor modifications to text, comments on phantom behaviour added. References added. As submitted to JCA

Conformally Invariant Gauge Theory of 3-Branes in 6D and the Cosmological Constant

It is shown that the gauge theory of relativistic 3-Branes can be formulated in a conformally invariant way if the embedding space is six-dimensional. The implementation of conformal invariance requires the use of a modified measure, independent of the metric in the action. Brane-world scenarios without the need of a cosmological constant in 6D are constructed. Thus, no ``old'' cosmological constant problem appears at this level.Comment: 12 pages, Latex, no figures; final version accepted for publication in Phys.Rev. D; Sect.II expande