Randall-Sundrum Braneworld Research Articles

Observable strong field effects of extra spacetime dimension in the braneworld black hole

Inspired by the string theory, the braneworld picture introduces extra dimensions beyond the four that may have observable non-trivial effects in short distance (strong field) gravity experiments. A case in point is the Randall–Sundrum braneworld picture that projects the 5d bulk Weyl tensor onto the 3d brane providing a stress tensor in the effective Einstein field equations on the brane. Dadhich, Maartens, Papadopoulos and Rezania (DMPR) derived an exact braneworld black hole solution of the brane vacuum field equations. The solution formally resembles that of Reissner–Nordström but is physically different from it since the ”tidal charge” Υ in the solution is not the electric charge but an imprint from the fifth dimension allowing both signs in the power law modification ±Υ2r2 to the Schwarzschild metric Υ=0. The corresponding black holes are designated as DMPR±. We study here the effect of Υ on strong field lensing observables and compare in the eikonal limit the ring down quasinormal mode (QNM) frequencies of DMPR− with those of DMPR＋ , the two variants of tidal charge modified Schwarzschild black hole (Υ=0). It turns out that the tidal charge can significantly modify the Schwarzschild lensing observables and QNM frequencies. In particular, we find that the Pretorius–Khurana critical exponent γ of circular null orbits in the DMPR− black hole has a lower value than that for the Schwarzschild black hole, which indicates a stronger Lyapunov instability suggesting that the accretion disks of DMPR− black holes would appear brighter. The case of the SgrA* black hole is considered for a possible constraint on Υ from the EHT observation of its shadow size.

Induced current by a cosmic string and a brane in high-dimensional AdS spacetime

In this paper we investigate the bosonic current induced by a brane and a magnetic flux running along the idealized cosmic string in a (D+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(D+1)$$\\end{document}-dimensional anti-de Sitter (AdS) background. We consider the brane is parallel to the AdS boundary and the cosmic string is orthogonal to them. Moreover, we assume that on the brane the charged bosonic field obeys the Robin boundary condition. The brane divides the space into two regions with different properties of the vacuum state. We show that the only nonzero component of the current density is along the azimuthal direction in both regions. In order to develop this analysis we calculate, for both regions, the positive frequency Wightman functions. Both functions present a part associated with the AdS in presence of a cosmic string only, and the other part induced by the brane. In this paper we consider only the contributions induced by the brane. We show that in both regions the azimuthal current densities are odd functions of the magnetic flux along the string. Different analytic and numerical analysis are performed and an application of our results is provided for the Randall-Sundrum braneworld model with a single brane.

Vacuum polarization induced by a cosmic string and a brane in AdS spacetime

In this paper we investigate the vacuum polarization effects associated to a charged quantum massive scalar field on a (D+1)-dimensional anti-de Sitter background induced by a magnetic-flux-carrying cosmic string in the braneworld model context. We consider the brane parallel to the anti-de Sitter boundary and the cosmic string orthogonal to them. Moreover, we assume that the field obeys the Robin boundary condition on the brane. Because the brane divides the space into two regions with different properties of the quantum vacuum, we calculate the vacuum expectation value (VEV) of the field squared and the energy–momentum tensor (EMT) in each region. To develop these analyses, we have constructed the positive frequency Wightman function for both regions. The latter is decomposed in a part associated with the anti-de Sitter bulk in the presence of a cosmic string only, and the other part induced by the brane. The vacuum polarization effects associated with the higher-dimensional anti-de Sitter bulk in the presence of cosmic string have been developed in the literature, and here we are mainly interested in the effects induced by the brane. We show that the VEVs of the field squared and the components of the EMT induced by the cosmic string are finite on the brane. Explicitly, we compare these observables with the corresponding ones induced by the brane only, and show that near the brane the contribution induced by the latter is larger than the one induced by the string; however, for points distant from the brane the situation is reversed. Moreover, some asymptotic expressions for the VEV of the field squared and EMT are provided for specific limiting cases of the physical parameters of the model. Also, an application of our results is given for a cosmic string in the Z_2-symmetric Randall–Sundrum braneworld model with a single brane.

Geodesics and optical properties of a rotating black hole in Randall–Sundrum brane with a cosmological constant

The presence of tidal charge and cosmological constant has considerable consequences on the spacetime geometry and its study is much more important from the observational point of view. Henceforth, we investigate their effects on particle dynamics and the shadow cast by a Randall–Sundrum braneworld black hole with a cosmological constant. On studying the circular geodesics of timelike particles, we have acquired the expressions of energy, angular momentum, effective potential and the innermost stable circular orbits on the equatorial plane. We noted that the negative values of tidal charge and cosmological constant decrease the energy of particles. In addition, the negative value of the cosmological constant leads us to stable circular orbits, whereas its positive value destabilizes the circular orbits. Our exploration shows that the cosmological constant diminishes the radius of the black hole shadow. In response to the dragging effect, black hole rotation elongates its shadow towards the rotational axis. Besides, black hole spin and positive charge distort shadow and its distortion becomes maximum as far as the black hole rotates faster. We also discussed the energy emission rate by considering different cases and compared our result with the standard Kerr black hole.

Shadows and observation intensity of black holes in the Randall–Sundrum brane world model * *Supported by the National Natural Science Fund of China (11775038, 12047564)

The shadow and observation intensity of a black hole surrounded by a thin spherical accretion in the Randall–Sundrum brane world model are investigated. The bulk metric depends on the tidal charge parameter, q, and deformation parameter, C. It reduces to the metric that possesses similar form with the Reissner–Nordström metric if . It is shown that the radius of the photon sphere of this black hole depends only on the tidal charge parameter. The radius of the photon sphere decreases with higher q. The observation intensity is mainly influenced by the tidal charge parameter, q, and the deformation parameter, C, is of secondary importance. In the optical observation, the black holes appear brighter with higher q or lower C.

Traversable wormhole on the brane with non-exotic matter: a broader view

In this article, the possibility of construction of a traversable wormhole on the Randall–Sundrum braneworld with non-exotic matter employing the Kuchowicz potential has been studied. We have obtained the solution for the shape function of the wormhole and studied its properties along with validity of null energy condition. The junction conditions at the surface of the wormhole are used to evaluate the model parameters. We also evaluate the surface density and surface pressure for the wormhole. We study the geometrical nature of the wormhole and consider the radial and tangential tidal constraints on a traveller trying to traverse the wormhole. Besides, a linearized stability analysis is performed to obtain the region of stability for the wormhole. Our analysis, besides giving an estimate for the bulk equation of state (EoS) parameter, imposes restrictions on the brane tension, which is a very essential parameter in braneworld physics, and very interestingly the restrictions imposed by our physically plausible and traversable wormhole model are in conformity with those imposed by other braneworld geometries which are not associated with a wormhole solution. Besides, it is important to study such constraints imposed by geometrical objects such as wormholes on any gravity theory operating at high-energy scales like braneworld, as wormholes are believed to have been formed from massive compact objects of high energy densities. Also, we go on to justify that the possible detection of a wormhole may well indicate that we live on a three-brane universe.

Swampland criteria in Chaplygin-braneworld warm inflation scenario

In recent times, it has been perceived that incorporation of branes in higher dimensional theories of quantum gravity is very effective to differentiate those theories which successfully satisfy the swampland criteria. Moreover, warm inflation is considered to be most appropriate single scalar field inflationary model in the framework of swampland criteria. In this regard, we study two well-known Chaplygin gas (CG) models embedded in Randall–Sundrum braneworld. It is known that the de Sitter constraint is derived by taking into account Bousso’s covariant entropy bound. We discuss the application of this result in the context of Chaplygin-brane models and find the condition on the slope of the potential. Furthermore, it is demonstrated that in view of warm inflation dynamics this condition remains essentially unchanged indicating the compatibility of the models with swampland criteria. In addition, we investigate the constraint on the warm inflation parameter imposed by the de Sitter conjecture which shows that the warm inflation is in accordance with de Sitter bound in the strong as well as in weak dissipative regime for both models of Chaplygin gas.

Dark bubbles and black holes

In this paper we study shells of matter and black holes on the expanding bubbles realizing de Sitter space, that were proposed in [4]. We construct explicit solutions for a rigid shell of matter as well as black hole like solutions. The latter of these can also be used to construct Randall-Sundrum braneworld black holes in four dimensions.

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in d-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.

Fine tuning problem of the cosmological constant in a generalized Randall-Sundrum model * *Supported by State Key Program of National Natural Science Foundation of China (11535005), the National Natural Science Foundation of China (11647087), the Natural Science Foundation of Yangzhou Polytechnic Institute (201917) and the Natural Science Foundation of Changzhou Institute of Technology (YN1509)

To solve the cosmological constant fine tuning problem, we investigate an (n+1)-dimensional generalized Randall-Sundrum brane world scenario with two -branes instead of two 3-branes. Adopting an anisotropic metric ansatz, we obtain the positive effective cosmological constant of order and only require a solution . Meanwhile, both the visible and hidden branes are stable because their tensions are positive. Therefore, the fine tuning problem can be solved quite well. Furthermore, the Hubble parameter as a function of redshift is in good agreement with the cosmic chronometers dataset. The evolution of the universe naturally shifts from deceleration to acceleration. This suggests that the evolution of the universe is intrinsically an extra-dimensional phenomenon. It can be regarded as a dynamic model of dark energy that is driven by the evolution of the extra dimensions on the brane.

Gravastar in the framework of braneworld gravity

Gravastars have been considered as a serious alternative to black holes in the past couple of decades. Stable models of gravastar have been constructed in many of the alternate gravity models besides standard General Relativity (GR). The Randall-Sundrum (RS) braneworld model has been a popular alternative to GR, specially in the cosmological and astrophysical context. Here we consider a gravastar model in RS brane gravity. The mathematical solutions in different regions have been obtained along with calculation of matching conditions. Various important physical parameters for the shell have been calculated and plotted to see their variation with radial distance. We also calculate and plot the surface redshift to check the stability of the gravastar within the purview of RS brane gravity.

Dynamical system analysis of Randall-Sundrum model with tachyon field on the brane

In this manuscript we use the dynamical system approach to study the linear dynamics of a Randall-Sundrum braneworld model with a tachyon scalar field confined to the brane. We recognize that the form of the tachyon potential plays a significant role in the evolution of the universe. For the case of an inverse square potential we find that one of our new variables, $\lambda$, is constant. We obtain critical points of the system in this situation and investigate their stability using the linear perturbation method. Then we turn to a Gaussian potential in which $\lambda$ is not constant. Using the idea of instantaneous critical points we study the behavior of the universe and its possible fates. One of the interesting results of this manuscript is that our universe will probably experience another phase transition from acceleration to deceleration in the future.

Warm brane inflation with an exponential potential: A consistent realization away from the swampland

It has very recently been realized that coupling branes to higher dimensional quantum gravity theories and considering the consistency of what lives on the branes, one is able to understand whether such theories can belong either to the swampland or to the landscape. In this regard, in the present work, we study a warm inflation model embedded in the Randall-Sundrum braneworld scenario. It is explicitly shown that this model belongs to the landscape by supporting a strong dissipative regime with an inflaton steep exponential potential. The presence of extra dimension effects from the braneworld allow achieving this strong dissipative regime, which is shown to be both theoretically and observationally consistent. In fact, such strong dissipation effects, which decrease towards the end of inflation, together with the extra dimension effect, allow the present realization to simultaneously satisfy all previous restrictions imposed on such a model and to evade the recently proposed swampland conjectures. The present implementation of this model, in terms of an exponential potential for the scalar field, makes it also a possible candidate for describing the late-time Universe in the context of a dissipative quintessential inflation model and we discuss this possibility in the Conclusions.

Gravastar model in Randall–Sundrum braneworld

In this work we derive a gravastar model in Randall–Sundrum II braneworld scenario. Gravastars (or gravitationally vacuum stars) were proposed by Mazur and Mottola as systems of gravitational collapse alternative to black holes. The external region of the gravastar is described by a Schwarzschild space-time, while its internal region is filled by dark energy. In between there is a thin shell surface with ultrarelativistic matter (sometimes referred to as stiff matter). We obtain solutions for some physical quantities of the braneworld gravastars. Those are compared to original Mazur–Mottola results as well as with some gravastar solutions in alternative gravity theories. The consequences of the braneworld setup in gravastar physics is deeply discussed.

Anisotropic evolution of 4-brane in a 6D generalized Randall-Sundrum model * * Supported by the Key Program of National Natural Science Foundation of China (11535005), the National Natural Science Foundation of China (11647087 and 11805097), the Natural Science Foundation of Yangzhou Polytechnic Institute (201917), and the Natural Science Foundation of Changzhou Institute of Technology (YN1509)

We investigate a 6D generalized Randall-Sundrum brane world scenario with a bulk cosmological constant. Each stress-energy tensor on the brane is shown to be similar to a constant vacuum energy. This is consistent with the Randall-Sundrum model, in which each 3-brane Lagrangian yielded a constant vacuum energy. By adopting an anisotropic metric ansatz, we obtain the 5D Friedmann-Robertson-Walker field equations. In a slightly later period, the expansion of the universe is proportional to the square root of time, , which is similar to the period of the radiation-dominated regime. Moreover, we investigate the case with two and two . In a large range of , we obtain the 3D effective cosmological constant , which is independent of the integral constant. Here, the scale factor is an exponential expansion, which is consistent with our present observation of the universe. Our results demonstrate that it is possible to construct a model that solves the dark energy problem, while guaranteeing a positive brane tension.

Effective Mass of Radion via GW Mechanism with a Non-Minimally Coupled Bulk Scalar Field

In the Randall-Sundrum braneworld scenario via the Goldberger-Wise mechanism, the effective mass of 4D radion, where the bulk scalar field is coupled to 5D gravity, has been investigated in two different case of the self-coupling constants, infinite and finite cases. It is shown that in the finite case, the modulus parameter should be greater than the finite coupling constants.

Spinors fields in co-dimension one braneworlds

In this work we analyze the zero mode localization and resonances of 1/2−spin fermions in co-dimension one Randall-Sundrum braneworld scenarios. We consider delta-like, domain walls and deformed domain walls membranes. Beyond the influence of the spacetime dimension D we also consider three types of couplings: (i) the standard Yukawa coupling with the scalar field and parameter η1, (ii) a Yukawa-dilaton coupling with two parameters η2 and λ and (iii) a dilaton derivative coupling with parameter h. Together with the deformation parameter s, we end up with five free parameter to be considered. For the zero mode we find that the localization is dependent of D, because the spinorial representation changes when the bulk dimensionality is odd or even and must be treated separately. For case (i) we find that in odd dimensions only one chirality can be localized and for even dimension a massless Dirac spinor is trapped over the brane. In the cases (ii) and (iii) we find that for some values of the parameters, both chiralities can be localized in odd dimensions and for even dimensions we obtain that the massless Dirac spinor is trapped over the brane. We also calculated numerically resonances for cases (ii) and (iii) by using the transfer matrix method. We find that, for deformed defects, the increasing of D induces a shift in the peaks of resonances. For a given λ with domain walls, we find that the resonances can show up by changing the spacetime dimensionality. For example, the same case in D = 5 do not induces resonances but when we consider D = 10 one peak of resonance is found. Therefore the introduction of more dimensions, diversely from the bosonic case, can change drastically the zero mode and resonances in fermion fields.

Extra Dimensions, Brane Worlds, and the Vanishing of Axion Contributions to Inflation

We examine from first principles the implications of the 5th Randall Sundrum Brane world dimension in terms of setting initial conditions for chaotic inflationary physics. Our model pre-supposes that the inflationary potential pioneered by Guth is equivalent in magnitude in its initial inflationary state to the effective potential presented in the Randall-Sundrum model. We also consider an axion contribution to chaotic inflation (which may have a temperature dependence) which partly fades out up to the point of chaotic inflation being matched to a Randall-Sundrum effective potential. If we reject an explicit axion mass drop off to infinitesimal values at high temperatures, we may use the Bogomolnyi inequality to re-scale and reset initial conditions for the chaotic inflationary potential. One of the potential systems embedded in the Randall-Sundrum brane world is a model with a phase transition bridge from a tilted washboard potential to the chaotic inflationary model pioneered by Guth which is congruent with the slow roll criteria. If, as written up earlier, the axion wall contribution is due to di-quarks, which is equivalent to tying in baryogenesis to the formation of chaotic inflation initial conditions, with the Ran-dall-Sundrum brane world effective potential delineating the end of the dominant role of di-quarks, and the beginning of inflation.

Thermodynamic geometry and phase transitions of AdS braneworld black holes

The thermodynamics and phase transitions of charged RN-AdS and rotating Kerr-AdS black holes in a generalized Randall-Sundrum braneworld are investigated in the framework of thermodynamic geometry. A detailed analysis of the thermodynamics, stability and phase structures in the canonical and the grand canonical ensembles for these AdS braneworld black holes are described. The thermodynamic curvatures for both these AdS braneworld black holes are computed and studied as a function of the thermodynamic variables. Through this analysis we illustrate an interesting dependence of the phase structures on the braneworld parameter for these black holes.

Randall-Sundrum braneworld in modified gravity

We modify Randall-Sundrum model of brane-world (with two branes) by adding the scalar curvature squared term in five dimensions. We find that it does not destabilize Randall-Sundrum solution to the hierarchy problem of the Standard Model in particle physics.