Stated succinctly, the original version of the Campbell-Magaard theorem says that it is always possible to locally embed any solution of 4-dimensional general relativity in a 5-dimensional Ricciflat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our universe is a 4-dimensional hypersurface Σ0 within a 5-dimensional manifold, such as Space-Time-Matter (STM) theory and the Randall & Sundrum (RS) braneworld scenario. In particular, we determine whether or not arbitrary spacetimes may be embedded in such theories, and demonstrate how these seemingly disparate models are interconnected. Special attention is given to the motion of test observers in 5 dimensions, and the circumstances under which they are confined to Σ0. For each 5-dimensional scenario considered, the requirement that observers be confined to the embedded spacetime places restrictions on the 4-geometry. For example, we find that observers in the thin braneworld scenario can be localized around the brane if its total stress-energy tensor obeys the 5-dimensional strong energy condition. As a concrete example of some of our technical results, we discuss a Z2 symmetric embedding of the standard radiation-dominated cosmology in a 5-dimensional vacuum.
Using the black string between two branes as a model of a brane-world black hole, we compute the gravity wave perturbations and identify the features arising from the additional polarizations of the graviton. The standard four-dimensional gravitational wave signal acquires late-time oscillations due to massive modes of the graviton. The Fourier transform of these oscillations shows a series of spikes associated with the masses of the Kaluza-Klein modes, providing in principle a spectroscopic signature of extra dimensions.Black holes are central to our understanding of gravity, and are expected to be key sources of gravity waves that should be detected by the current and upcoming generation of experiments. Such a detection will not only confirm the indirect evidence from binary pulsars for gravity waves, but will also also allow us to probe the properties of black holes and of gravity. In particular, this will open up a new window for testing modifications to general relativity, such as those arising from quantum gravity theories. String theory for example predicts that spacetime has extra spatial dimensions, so that the gravitational field propagates in higher dimensions and has extra polarizations. Recent developments in string theory indicate that Standard Model fields may be confined to a fourdimensional 'brane', while gravity propagates in the full 'bulk' spacetime. This has spurred the development of brane-world models, such as Randall-Sundrum (RS) type models, which can be used to explore astrophysical predictions [1]. RS type models have a five-dimensional bulk with negative cosmological constant, so that the metric is warped along the extra dimension. As a result, these models provide a new approach to the hierarchy problem, dimensional reduction and holography.The nature of black holes that form by gravitational collapse on an RS brane is only partly understood [1,2], and no exact solution is known for a black hole localized on one brane. If there is a second 'shadow' brane, the black string may be used to model large black holes on the visible brane, when the horizon on the brane is much greater than the extent of the horizon into the bulk [3]. The black string reproduces the Schwarzschild metric on the visible brane but is not confined to the brane, since there is a line singularity at r = 0 into the extra dimension (see Fig. 1). The shadow brane can also introduce an infra-red cut-off to shut down the GregoryLaflamme (GL) instability of the black string at long wavelengths [4]. If the shadow brane is close enough to the visible brane for a given black hole mass M , or if M is large enough for a given brane separation d, then GM e −d/ℓ /ℓ is above a positive critical value and the GL instability is removed (see below). This is the background model that we perturb.
We report on the possibility of detecting a submillimetre-sized extra dimension by observing gravitational waves (GWs) emitted by pointlike objects orbiting a braneworld black hole. Matter in the 'visible' universe can generate a discrete spectrum of high frequency GWs with amplitudes moderately weaker than the predictions of general relativity (GR), while GW signals generated by matter on a 'shadow' brane hidden in the bulk are potentially strong enough to be detected using current technology. We know of no other astrophysical phenomena that produces GWs with a similar spectrum, which stresses the need to develop detectors capable of measuring this high-frequency signature of large extra dimensions.
We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricciflat, then there is an induced cosmological constant in the 4D sub-manifold. We derive the general form of the 5D Killing vectors and relate them to the 4D Killing vectors of the embedded spacetime. We then study the 5D null geodesic paths and show that the 4D part of the motion can be timelikethat is, massless particles in 5D can be massive in 4D. We find that if the null trajectories are affinely parameterized in 5D, then the particle is subject to an anomalous acceleration or fifth force. However, this force may be removed by reparameterization, which brings the correct definition of the proper time into question. Physical properties of the geodesics -such as rest mass variations induced by a variable cosmological "constant", constants of the motion and 5D time-dilation effects -are discussed and are shown to be open to experimental or observational investigation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.