Gravitational potential of a point mass in a brane world (original) (raw)

Brane world regularization of point particle classical self-energy

Physical Review D, 2011

Physical effects in brane worlds models emerge by the incorporation of field modes coming from extra dimensions with the usual four dimensional ones. Such effects can be tested with well established experiments to set bounds on the parameters of the brane models. In this work we extend a previous result which gave finite electromagnetic potentials and self energies for a source looking pointlike to an observer sitting in a 4D Minkowski subspace of a single brane of a Randall-Sundrum spacetime including compact dimensions, and along which the source stretches uniformly. We show that a scalar particle produces a nonsingular static potential, possess a finite self-energy and that technically its analysis is very similar to the electrostatic case. As for the latter, we use the deviations from the Coulomb potential to set bounds on the anti de Sitter radius of the brane model on the basis of two experiments, namely, one of the Cavendish type and other being the scattering of electrons by Helium atoms. We found these are less stringent than others previously obtained using the Lamb shift in Hydrogen.

Gravitational forces in the brane world

Physical Review D, 2005

We consider the problem of gravitational forces between point particles on the branes in a Randall-Sundrum (R-S) two brane model with S 1 /Z 2 symmetry. Matter is assumed to produce a perturbation to the R-S vacuum metric and all the 5D Einstein equations are solved to linearized order (for arbitrary matter on both branes). We show that while the gauge condition h i5 = 0, i = 0, 1, 2, 3 can always be achieved without brane bending, the condition h 55 = 0 leads to large brane bending. The static potential arising from the zero modes and the corrections due to the Kaluza-Klein (KK) modes are calculated. Gravitational forces on the Planck (y 1 = 0) brane recover Newtonian physics with small KK corrections (in accord with other work). However, forces on the TeV (y 2) brane due to particles on that brane are strongly distorted by large R-S exponentials.

On the localisation of four-dimensional brane-world black holes: II. The general case

Classical and Quantum Gravity, 2015

We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the 5-dimensional metric tensor that allows for time-dependence, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions, energy-momentum tensor, solutions that have the form of a Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge, however, the resulting profile of the mass-function along the bulk coordinate, when allowed, is not the correct one to eliminate the bulk singularities.

On the localization of four-dimensional brane-world black holes

Class.Quant.Grav. 30 (2013) 235017, 2013

In the context of brane-world models, we pursue the question of the existence of five-dimensional solutions describing regular black holes localized close to the brane. Employing a perturbed Vaidya-type line-element embedded in a warped fifth dimension, we attempt to localize the extended black-string singularity, and to restore the regularity of the AdS spacetime at a finite distance from the brane by introducing an appropriate bulk energy-momentum tensor. As a source for this bulk matter, we are considering a variety of non-ordinary fieldtheory models of scalar fields either minimally coupled to gravity, but including non-canonical kinetic terms, mixing terms, derivative interactions and ghosts, or non-minimally coupled to gravity through a general coupling to the Ricci scalar. In all models considered, even in those characterized by a high degree of flexibility, a negative result was reached. Our analysis demonstrates how difficult the analytic construction of a localized brane-world black hole may be in the context of a well-defined field-theory model. Finally, with regard to the question of the existence or not of a static classical black-hole solution on the brane, our analysis suggests that such solutions could in principle exist; however, the associated field configuration itself has to be dynamic.

2 1 3 O ct 2 00 3 Nonsingular Increasing Gravitational Potential for the Brane in 6 D

2008

We present a new (1+3)-brane solution to Einstein equations in (1+5)-space. As distinct from previous models this solution is free of singularities in the full 6-dimensional space-time. The gravitational potential transverse to the brane is an increasing (but not exponentially) function and asymptotically approaches a finite value. The solution localizes the zero modes of all kinds of matter fields and Newtonian gravity on the brane. An essential feature of the model is that different kind of matter fields have different localization radii. PACS: 11.10.Kk, 04.50.+h, 98.80.Cq The scenario where our world is associated with a brane embedded in a higher dimensional space-time with non-factorizable geometry has attracted a lot of interest since the appearance of papers [1, 2, 3]. In this model gravitons, which are allowed to propagate in the bulk, are confined on the brane because of a warped geometry. However, there are difficulties with the choice of a natural trapping mechanism for s...

The Singularity Problem in Brane Cosmology

Universe, 2017

We review results about the development and asymptotic nature of singularities in "brane-bulk" systems. These arise for warped metrics obeying the five-dimensional Einstein equations with fluid-like sources, and including a brane four-metric that is either Minkowski, de Sitter, or Anti-de Sitter. We characterize all singular Minkowski brane solutions, and look for regular solutions with nonzero curvature. We briefly comment on matching solutions, energy conditions, and finite Planck mass criteria for admissibility, and we briefly discuss the connection of these results to ambient theory.

Classical tests in brane gravity

The vacuum solutions in brane gravity differ from such solutions in a 4-dimensional world by a number of additional term and reduce to the familiar Schwarzschild metric at small distances. We study the possible roles that such terms may play by investigating the bending of light, radar retardation and the anomaly in mean motion of test bodies. Using the available data from Solar System experiments, we determine the range of the free parameters associated with the linear term in the metric. The best results come from the anomalies in the mean motion of planets. Such studies should be useful in accounting for the origin of dark energy via the solar system tests.

Gravity, stability, and energy conservation on the Randall-Sundrum brane world

Physical Review D, 2000

We carefully investigate the gravitational perturbation of the Randall-Sundrum (RS) single braneworld solution [hep-th/9906064], based on a covariant curvature tensor formalism recently developed by us. Using this curvature formalism, it is known that the 'electric' part of the 5-dimensional Weyl tensor, denoted by Eµν , gives the leading order correction to the conventional Einstein equations on the brane. We consider the general solution of the perturbation equations for the 5-dimensional Weyl tensor caused by the matter fluctuations on the brane. By analyzing its asymptotic behaviour in the direction of the 5th dimension, we find the curvature invariant diverges as we approach the Cauchy horizon. However, in the limit of asymptotic future in the vicinity of the Cauchy horizon, the curvature invariant falls off fast enough to render the divergence harmless to the brane-world. We also obtain the asymptotic behavior of Eµν on the brane at spatial infinity, assuming the matter perturbation is localized. We find it falls off sufficiently fast and will not affect the conserved quantities at spatial infinity. This indicates strongly that the usual conservation law, such as the ADM energy conservation, holds on the brane as far as asymptotically flat spacetimes are concerned.

The Power of Brane-Induced Gravity

2001

We study the role of the brane-induced graviton kinetic term in theories with large extra dimensions. In five dimensions we construct a model with a TeV-scale fundamental Planck mass and a flat extra dimension the size of which can be astronomically large. 4D gravity on the brane is mediated by a massless zero-mode, whereas the couplings of the heavy Kaluza-Klein modes to ordinary matter are suppressed. The model can manifest itself through the predicted deviations from Einstein theory in long distance precision measurements of the planetary orbits. The bulk states can be a rather exotic form of dark matter, which at sub-solar distances interact via strong 5D gravitational force. We show that the induced term changes dramatically the phenomenology of sub-millimeter extra dimensions. For instance, high-energy constraints from star cooling or cosmology can be substantially relaxed.