An Alternative to Matter Localization in the" Brane World": An Early Proposal and its Later Improvements (original) (raw)
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Einstein's gravity from a first order lagrangian in an embedding space
Physics Letters A, 1986
We formulate a first order action principle in a higher dimensional space MN in which we embed spacetime. The action I is essentially an “area” of a four-dimensional spacetime V4 weighted with a matter density ω in MN. For a suitably chosen ω we obtain on V4 a set of worldlines. It is shown that these worldlines are geodesics of V4, provided that V4 is a solution to our variational procedure. Then it follows that our spacetime satisfies the Einstein equations for dust - apart from an additional term with zero covariant divergence. (This extra term was shown in a previous paper to be exactly zero at least in the case of the cosmological dust model.) Thus we establish a remarkable connection of the extrinsic spacetime theory with the intrinsic general relativity. This step appears to be important for quantum gravity.
Journal of High Energy Physics, 2007
The Arnowitt-Deser-Misner canonical formulation of general relativity is extended to the covariant brane-world theory in arbitrary dimensions. The exclusive probing of the extra dimensions makes a substantial difference, allowing for the construction of a non-constrained canonical theory. The quantum states of the brane-world geometry are defined by the Tomonaga-Schwinger equation, whose integrability conditions are determined by the classical perturbations of submanifolds contained in the Nash's differentiable embedding theorem. In principle, quantum brane-world theory can be tested by current experiments in astrophysics and by near future laboratory experiments at Tev energy. The implications to the black-hole information loss problem, to the accelerating cosmology, and to a quantum mathematical theory of four-sub manifolds are briefly commented.
On the quantisation of gravity by embedding spacetime in a higher dimensional space
Classical and Quantum Gravity 2 (1985) 869, 1985
Certain difficulties of quantum gravity can be avoided if we embed the spacetime V 4 into a higher dimensional space V N ; then our spacetime is merely a 4-surface in V N . What remains is conceptually not so difficult: just to quantise this 4-surface. Our formal procedure generalises our version of Stueckelberg's proper time method of worldline quantisation. We write the equations of V 4 in the covariant canonical form starting from a model Lagrangian which contains the classical Einstein gravity as a particular case. Then we perform quantisation in the Schrödinger picture by using the concepts of a phase functional and wave functional. As a result we obtain the uncertainty relations which imply that an observer is 'aware' either of a particular spacetime surface and has no information about other spacetime surfaces (which represent alternative histories); or conversely, he loses information about a particular V 4 whilst he obtains some information about other spacetimes (and histories). Equivalently, one cannot measure to an arbitrary precision both the metric on V 4 and matter distribution on various alternative spacetime surfaces. We show how this special case in the 'coordinate' representations can be generalised to an arbitrary vector in an abstract Hilbert space. † Note: This old paper was published in Classical and Quantum Gravity 2 (1985) 869-889; DOI: 10.1088/0264-9381/2/6/012. The body of the posted version is identical to the published one, except for corrections of few misprints.
Universal aspects of gravity localized on thick branes
Nuclear Physics B, 2000
We study gravity in backgrounds that are smooth generalizations of the Randall-Sundrum model, with and without scalar fields. These generalizations include three-branes in higher dimensional spaces which are not necessarily Anti-de Sitter far from the branes, intersecting brane configurations and configurations involving negative tension branes. We show that under certain mild assumptions there is a universal equation for the gravitational fluctuations. We study both the graviton ground state and the continuum of Kaluza-Klein modes and we find that the four-dimensional gravitational mode is localized precisely when the effects of the continuum modes decouple at distances larger than the fundamental Planck scale. The decoupling is contingent only on the long-range behaviour of the metric from the brane and we find a universal form for the corrections to Newton's Law. We also comment on the possible contribution of resonant modes. Given this, we find general classes of metrics which maintain localized four-dimensional gravity. We find that three-brane metrics in five dimensions can arise from a single scalar field source, and we rederive the BPS type conditions without any a priori assumptions regarding the form of the scalar potential. We also show that a single scalar field cannot produce conformally-flat locally intersecting brane configurations or a p-brane in greater than (p + 2)-dimensions.
Classical and quantum aspects of brane-world cosmology
AIP Conference Proceedings, 2011
We give a brief overview of several models in brane-world cosmology. In particular, we focus on the asymmetric DGP and Regge-Teiltelboim models. We present the associated equations of motion governing the dynamics of the brane and their corresponding Friedmann-like equations. In order to develop the quantum Regge-Teiltelboim type cosmology we construct its Ostrogradski Hamiltonian formalism which naturally leads to the corresponding Wheeler-DeWitt equation. In addition, we comment on possible generalizations for these models including second order derivative geometrical terms.
Quantum Gravity:the axiomatic approach, a possible interpretation
Twenty years ago, by extending the Wightman axiom framework, it has been found possible to quantize only a conformal factor of the gravitational field. Gravitons being excluded from this quantum scalar field theory, numerous attempts were done to give a valuable description of what could be quantum gravity. In this talk we present a familly of Lorentz manifolds which can be foliated by isotropic hypersurfaces and pose severe restrictions on the form of the energy-momentum tensor in Einstein's equations. They can be associated to gravitational waves "without gravitons" in a vacuum described by two cosmological functions, but not to a massless particle flow. From this cross-checking with the previous remark, a "very" primordial quantum cosmological scenario is proposed.
Brane world generation by matter and gravity
Journal of High Energy Physics, 2005
We present a non-compact 4 + 1 dimensional model with a local strong fourfermion interaction supplementing it with gravity. In the strong coupling regime it reveals the spontaneous translational symmetry breaking which eventually leads to the formation of domain walls, or thick 3-branes, embedded in the AdS 5 manifold. To describe this phenomenon we construct the appropriate low-energy effective Action and find kink-like vacuum solutions in the quasi-flat Riemannian metric. We discuss the generation of ultralow-energy 3 + 1 dimensional physics and we establish the relation among the bulk five dimensional gravitational constant, the brane Newton's constants and the curvature of AdS 5 space-time. The plausible relation between the compositeness scale of the scalar matter and the symmetry breaking scale is shown to support the essential decoupling of branons, the scalar fluctuations of the brane, from the Standard Model matter, supporting their possible role in the dark matter saturation. The induced cosmological constant on the brane does vanish due to exact cancellation of matter and gravity contributions.
Hamiltonian Theory of Brane-World Gravity
The Eleventh Marcel Grossmann Meeting, 2008
A brane-world universe consists of a 4-dimensional brane embedded into a 5-dimensional space-time (bulk). We apply the Arnowitt-Deser-Misner decomposition to the braneworld, which results in a 3+1+1 break-up of the bulk. We present the canonical theory of brane cosmology based on this decomposition. The Hamiltonian equations allow for the study of any physical phenomena in brane gravity. This method gives new prospects for studying the initial value problem, stability analysis, brane black holes, cosmological perturbation theory and canonical quantization in brane-worlds.
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.