Braneworld models, extra dimensions, and solutions
On the uplift of 4D wormholes in Braneworld models and their 5D structure
Dec 27, 2024Thomas D. Pappas and Theodoros Nakas
Recent developments in the consistent embedding of general 4D static and spherically-symmetric spacetimes in arbitrary single-brane braneworld models [Phys.Rev.D 109 (2024) 4, L041501] initiated the program of studying the bulk structure of braneworld wormholes. In this article, adopting a completely generic approach, we derive the general conditions that the metric functions of any braneworld spacetime must satisfy to describe a wormhole structure in the bulk. Particular emphasis is placed on clarifying the proper uplift of 4D wormholes, expressed in terms of various radial coordinates on the brane, and we demonstrate the important role of the circumferential radius metric function for the embedding. Additionally, the flare-out conditions for braneworld wormholes are presented for the first time and are found to differ from the case of flat extra dimensions. To illustrate the method, we first perform the uplift into the Randall-Sundrum II braneworld model for three well-known 4D wormhole spacetimes; the effective braneworld wormhole solutions of Casadio-Fabbri-Mazzacurati and Bronnikov-Kim, and the Simpson-Visser spacetime. Subsequently, we study their bulk features by means of curvature invariants, flare-out conditions, energy conditions and embedding diagrams. Our analysis reveals that the assumption of a warped extra dimension has non-trivial implications for the structure of 5D wormholes.arXiv-pdf DOI cite
Bridging dimensions: General embedding algorithm and field-theory reconstruction in 5D braneworld models
Sep 2, 2023Theodoros Nakas, Thomas D. Pappas, and Zdeněk Stuchlík
We develop a general algorithm that enables the consistent embedding of any four-dimensional static and spherically symmetric geometry into any five-dimensional single-brane braneworld model, characterized by an injective and nonsingular warp factor. Furthermore, we supplement the algorithm by introducing a method that allows one to, in principle, reconstruct 5D field theories that support the aforementioned geometries. This approach is based on a conformal transformation of the metric with the conformal factor being identified with the warp factor of the bulk geometry. The reconstructed theories depend solely on the induced brane geometry, since the warp factor is model-independently represented by a scalar field in the Lagrangian density. As a first application of our reconstruction method, we present for the first time a complete theory that supports the five-dimensional brane-localized extension of the Schwarzschild black hole, for any warp factor. The same method is subsequently utilized to illustrate the process of coherently embedding a de Sitter brane in braneworld models.arXiv-pdf DOI cite
Analytic and exponentially localized brane-world Reissner-Nordström-AdS solution: a top-down approach
May 14, 2021Theodoros Nakas and Panagiota Kanti
In this work, we construct a five-dimensional spherically-symmetric, charged and asymptotically Anti-de Sitter black hole with its singularity being point-like and strictly localised on our brane. In addition, the induced brane geometry is described by a Reissner-Nordström-(A)dS line-element. We perform a careful classification of the horizons, and demonstrate that all of them are exponentially localised close to the brane thus exhibiting a pancake shape. The bulk gravitational background is everywhere regular, and reduces to an AdS5 spacetime right outside the black-hole event horizon. This geometry is supported by an anisotropic fluid with only two independent components, the energy density \(\rho_E\) and tangential pressure \(p_2\). All energy conditions are respected close to and on our brane, but a local violation takes place within the event horizon regime in the bulk. A tensor-vector-scalar field-theory model is built in an attempt to realise the necessary bulk matter, however, in order to do so, both gauge and scalar degrees of freedom need to turn phantom-like at the bulk boundary. The study of the junction conditions reveals that no additional matter needs to be introduced on the brane for its consistent embedding in the bulk geometry apart from its constant, positive tension. We finally compute the effective gravitational equations on the brane, and demonstrate that the Reissner-Nordström-(A)dS geometry on our brane is caused by the combined effect of the five-dimensional geometry and bulk matter with its charge being in fact a tidal charge.arXiv-pdf DOI cite
Localized brane-world black hole analytically connected to an AdS\(_5\) boundary
Dec 16, 2020Theodoros Nakas and Panagiota Kanti
We construct from first principles the geometry of an analytic, exponentially localized five-dimensional brane-world black hole. The black-hole singularity lies entirely on the 3-brane, while the event horizon is shown to have a pancake shape. The induced line-element on the brane assumes the form of the Schwarzschild solution while the bulk geometry is effectively AdS\(_5\) outside the horizon. The derived geometry is supported by an anisotropic fluid in the bulk described only by two independent components, the energy density and tangential pressure, whereas no matter needs to be introduced on the brane for its consistent embedding in the bulk.arXiv-pdf DOI cite
Fermions and baryons as open-string states from brane junctions
Sep 30, 2020Theodoros Nakas and Konstantinos Rigatos
There has been recent progress towards understanding the dynamics of world-volume fermions that arise as open-string modes from brane intersections in the probe limit (\(N_f/N_c\rightarrow 0\)). In this work we consider all possible BPS brane junctions in Type IIA/B supergravity theories. We study in detail the dynamics of these states by deriving their equations of motion. We show the expected degeneracy of the bosonic and fermionic fluctuations as is expected due to the preserved supersymmetry. We also give some supporting evidence and refine the notion that these states can effectively describe baryon operators in a certain regime of the field theory's parameter space. Our piece of evidence is the demonstration of the expected scaling of the mass in the large-\(N_c\) limit of the theory for these fermionic states; \(M^2\sim N^2_c\). Finally, we explain analytically the avoided level crossing that was observed in a previous work after the inclusion of higher dimension operators in the field theory.arXiv-pdf DOI cite
Incorporating Physical Constraints in Braneworld Black-String Solutions for a Minkowski Brane in Scalar-Tensor Gravity
Jan 20, 2020Theodoros Nakas, Panagiota Kanti, and Nikolaos Pappas
In the framework of a general scalar-tensor theory, where the scalar field is non-minimally coupled to the five-dimensional Ricci scalar curvature, we investigate the emergence of complete brane-world solutions. By assuming a variety of forms for the coupling function, we solve the field equations in the bulk, and determine in an analytic way the form of the gravitational background and scalar field in each case. The solutions are always characterized by a regular scalar field, a finite energy-momentum tensor, and an exponentially decaying warp factor even in the absence of a negative bulk cosmological constant. The space-time on the brane is described by the Schwarzschild solution leading to either a non-homogeneous black-string solution in the bulk, when the mass parameter \(M\) is non-zero, or a regular anti-de Sitter space-time, when \(M=0\). We construct physically-acceptable solutions by demanding in addition a positive effective gravitational constant on our brane, a positive total energy-density for our brane and the validity of the weak energy condition in the bulk. We find that, although the theory does not allow for all three conditions to be simultaneously satisfied, a plethora of solutions emerge which satisfy the first two, and most fundamental, conditions.arXiv-pdf DOI cite
New Black-String Solutions for an Anti-de Sitter Brane in Scalar-Tensor Gravity
Mar 30, 2019Theodoros Nakas, Nikolaos Pappas, and Panagiota Kanti
We consider a five-dimensional theory with a scalar field non-minimally-coupled to gravity, and we look for novel black-string solutions in the bulk. By appropriately choosing the non-minimal coupling function of the scalar field, we analytically solve the gravitational and scalar-field equations in the bulk to produce black-string solutions that describe a Schwarzschild-Anti-de Sitter space-time on the brane. We produce two complete such solutions that are both characterised by a regular scalar field, a localised-close-to-our brane energy-momentum tensor and a negative-definite, non-trivial bulk potential that may support by itself the warping of the space-time even in the absence of the traditional, negative, bulk cosmological constant. Despite the infinitely-long string singularity in the bulk, the four-dimensional effective theory on the brane is robust with the effective gravity scale being related to the fundamental one and the warping scale. It is worth noting that if we set the mass of the black hole on the brane equal to zero, the black string disappears leaving behind a regular brane-world model with only a true singularity at the boundary of the fifth dimension.arXiv-pdf DOI cite
Anti-Gravitating Brane-World Solutions for a de Sitter Brane in Scalar-Tensor Gravity
Jul 18, 2018Theodoros Nakas and Panagiota Kanti
In the context of a five-dimensional theory with a scalar field non-minimally-coupled to gravity, we look for solutions that describe novel black-string or maximally-symmetric solutions in the bulk. The brane line-element is found to describe a Schwarzschild-(Anti)-de Sitter spacetime, and, here, we choose to study solutions with a positive four-dimensional cosmological constant. We consider two different forms of the coupling function of the scalar field to the bulk scalar curvature, a linear and a quadratic one. In the linear case, we find solutions where the theory, close to our brane, mimics an ordinary gravitational theory with a minimally-coupled scalar field giving rise to an exponentially decreasing warp factor in the absence of a negative bulk cosmological constant. The solution is characterised by the presence of a normal gravity regime around our brane and an anti-gravitating regime away from it. In the quadratic case, there is no normal-gravity regime at all, however, scalar field and energy-momentum tensor components are well-defined and an exponentially decreasing warp factor emerges again. We demonstrate that, in the context of this theory, the emergence of a positive cosmological constant on our brane is always accompanied by an anti-gravitating regime in the five-dimensional bulk.arXiv-pdf DOI cite