Modern Physics Letters A

We review the results of arXiv:hep-th/0703190, on brane induced gravity (BIG) in 6D. Among a large diversity of regulated codimension-2 branes, we find that for near-critical tension branes live inside very deep throats which efficiently compactify the angular dimension. In there, 4D gravity first changes to 5D, and only later to 6D. The crossover from 4D to 5D is independent of the tension, but the crossover from 5D to 6D is not. This shows how the vacuum energy problem manifests in BIG: instead of tuning vacuum energy to adjust the 4D curvature, generically one must tune it to get the desired crossover scales and the hierarchy between the scales governing the 4D → 5D → 6D transitions. In the near-critical limit, linearized perturbation theory remains under control below the crossover scale, and we find that linearized gravity around the vacuum looks like a scalar–tensor theory.

The Einstein–Hilbert Lagrangian R is expressed in terms of the chronometrically invariant quantities introduced by Zel'manov for an arbitrary four-dimensional metric g_ij. The chronometrically invariant three-space is the physical space γ_αβ = -g_αβ+e^2ϕ γ_αγ_β, where e^2ϕ = g₀₀ and γ_α = g_0α/g₀₀, and whose determinant is h. The momentum canonically conjugate to γ_αβ is , where and ∂_t≡e^-ϕ∂₀ is the chronometrically invariant derivative with respect to time. The Wheeler–DeWitt equation for the wave function Ψ is derived. For a stationary space-time, such as the Kerr metric, π^αβ vanishes, implying that there is then no dynamics. The most symmetric, chronometrically-invariant space, obtained after setting ϕ = γ_α = 0, is , where δ_αβ is constant and has curvature k. From the Friedmann and Raychaudhuri equations, we find that λ is constant only if k=1 and the source is a perfect fluid of energy-density ρ and pressure p=(γ-1)ρ, with adiabatic index γ=2/3, which is the value for a random ensemble of strings, thus yielding a three-dimensional de Sitter space embedded in four-dimensional space-time. Furthermore, Ψ is only invariant under the time-reversal operator if γ=2/(2n-1), where n is a positive integer, the first two values n=1,2 defining the high-temperature and low-temperature limits ρ ~ T^±2, respectively, of the heterotic superstring theory, which are thus dual to one another in the sense T↔1/2π²α′T.

In the Hamiltonian approach to the gauge models, the constraints on the one hand and the Hamiltonian and constraints on the other hand have to form closed algebras with respect to the Poisson brackets. We investigate the consequences of this requirement when the dynamical system is invariant under gauge transformations with higher order time derivatives of the gauge parameter. It is demonstrated that the required algebraic structure leads to rigid relations in the constraint algebra.

It is proved that plane symmetric Lorentzian manifolds representing a sourceless electromagnetic field admit only a four-dimensional maximal symmetry group and consist of only the McVittie⁵ spacetime and its non-static analogue.⁴

Improving the beginning steps of a previous work, we settle the dual embedding method (DEM) as an alternative and efficient method for obtaining dual equivalent actions also in D = 3. We show that we can obtain dual equivalent actions which were previously obtained in the literature using the gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the DEM is more profound since it can reveal a whole family of dual equivalent actions. The result confirms the one obtained previously which is important since it has the same structure that appears in the Abelian Higgs model with an anomalous magnetic interaction.

Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein–Hawking entropy of a black hole. In this paper, we calculate the correction value of thermodynamic quantities of the Achucarro–Oritz black hole motivated by utilizing the generalized uncertainty principle. We obtain the Cardy–Verlinde formula after considering the correction.