Geodesic Circular Orbits Sharing the Same Orbital Frequencies in the Black String Spacetime

We consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with Ωr^, Ωφ^, and Ωω^ in a particular region of parameter space around black string spacetime geometry. We study the effect of a compact extra spatial dimension on the isofrequency pairing of geodesic orbits and show that such orbits would occur in the allowed region when particles move along the black string. We find that the presence of the compact extra dimension leads to an increase in the number of the isofrequency pairing of geodesic orbits. Interestingly we also find that isofrequency pairing of geodesic orbits in the region of parameter space cannot be realized beyond the critical value Jcr≈0.096 of the conserved quantity of the motion arising from the compact extra spatial dimension.

Inflation with a class of concave inflaton potentials in Randall–Sundrum model

We investigate inflation with a class of concave inflaton potentials of the form $$\sim \phi ^n$$∼ϕn$$(0<n<1)$$(0<n<1) in the Randall–Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ($$M_5$$M5) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology.

Relativity: An Alternative Interpretation In the Light of The Existence of An Extra Spatial Dimension – A Systematic Review

This paper represents the latest revision of a portion of the research work, still in progress, carried out by the author during the last four years. The overall aim of the study fundamentally consists in showing how, while postulating the absoluteness of time, the validity of the relativistic equations may be formally preserved. Starting from the writing of the first Friedmann – Lemaître Equation (and therefore from General Relativity), a Simple-Harmonically Oscillating Universe (flat, upper-bounded, conventionally singular at

Holographic Skyrmions

Skyrmions are topological solitons that describe baryons within a nonlinear theory of pions. In holographic QCD, baryons correspond to topological solitons in a bulk theory with an extra spatial dimension. Thus, the three-dimensional Skyrmion lifts to a four-dimensional holographic Skyrmion in the bulk. We begin this review with a description of the simplest example of this correspondence, where the holographic Skyrmion is exactly the self-dual Yang–Mills instanton in flat space. This places an old result of Atiyah and Manton within a holographic framework and reveals that the associated Skyrme model extends the nonlinear pion theory to include an infinite tower of vector mesons, with specific couplings for a BPS theory. We then describe the more complicated curved space version that arises from the string theory construction of Sakai and Sugimoto. The basic concepts remain the same but the technical difficulty increases as the holographic Skyrmion is a curved space version of the Yang–Mills instanton, so self-duality and integrability are lost. Finally, we turn to a low-dimensional analog of holographic Skyrmions, where aspects such as multi-baryons and finite baryon density are amenable to both numerical computation and an approximate analytic treatment.

TSALLIS STATISTICS AND THE ROLE OF A STABILIZED RADION IN THE SUPERNOVAE SN1987A COOLING

The radion in the two-brane Randall–Sundrum model is required to stabilize the size of the fifth (extra) spatial dimension. It can be copiously produced inside the supernova core due to electron–positron annihilation (e+e-→ϕ), plasmon–plasmon annihilation (γP+γP→ϕ) and nucleon–nucleon bremsstrahlung and can take away the energy released in SN1987A explosion. Working within the q-deformed statistics (Tsallis statistics) and using the "Raffelt criterion" on the supernovae cooling rate [Formula: see text], we find that in Case I (cooling due to e+e-→ϕ channel): for q = 1.22, as the radion mass mϕ changes from 20 GeV to 150 GeV, the lower bound 〈ϕ〉 changes from 7 TeV to ~1.5 TeV and in Case II (cooling due to γP+γP→ϕ channel): for q = 1.11, as mϕ ranges from 20 GeV to 150 GeV, the lower bound 〈ϕ〉 changes from 201 TeV to 3.3 TeV. We investigate the dependence of 〈ϕ〉 on q and found that in Case I: mϕ = 50(100) GeV , 〈ϕ〉 changes from 0.5(0.2) TeV (for q = 1.18) to 5.5(4.8) TeV (for q = 1.30) and in Case II: for mϕ = 50(100) GeV , 〈ϕ〉 changes from 0.8(~0.1) TeV (for q = 1.09) to 569(216) TeV (for q = 1.13). We also verified that the normal Fermi–Dirac and Bose–Einstein statistics get recovered from the Tsallis statistics in the q→1 limit.

EXACT SOLUTIONS OF EMBEDDING THE 4D UNIVERSE IN A 5D EINSTEIN MANIFOLD

One of the simplest ways to extend 4D cosmological models is to add another spatial dimension to make them 5D. In particular, it has been shown that the simplest of such 5D models, i.e. one in which the right-hand side of the Einstein equation is empty, induces a 4D nonempty universe. Accordingly, the origin of matter in a real 4D universe might be mathematically attributed to the existence of one (fictitious) extra spatial dimension. Here we consider the case of an empty 5D universe possessing a cosmological constant Λ and obtain exact solutions for both positive and negative values of the Λ. It is seen that such a model can naturally reduce to a power law ΛCDM model for the real universe. Further, it can be seen that the arbitrary constants and functions appearing in this model are endowed with definite physical meanings.

ACCELERATING UNIVERSE FROM EXTRA SPATIAL DIMENSION

We present a simple higher dimensional FRW-type of model where the acceleration is apparently caused by the presence of the extra dimensions. Assuming an ansatz in the form of the deceleration parameter, we get a class of solutions some of which shows the desirable feature of dimensional reduction as well as reasonably good physical properties of matter. Interestingly we do not have to invoke an extraneous scalar field or a cosmological constant to account for this acceleration. One argues that the terms containing the higher dimensional metric coefficients produces an extra negative pressure that apparently drives the inflation of the 4D space with an accelerating phase. It is further found that in line with the physical requirements our model admits of a decelerating phase in the early era along with an accelerating phase at present. Further the models asymptotically mimic a steady-state-type of universe although it starts from a big-bang-type of singularity. Correspondence to Wesson's induced matter theory is also briefly discussed and, in line with it, it is argued that the terms containing the higher dimensional metric coefficients apparently creates a negative pressure which drives the inflation of the 3-space with an accelerating phase.