Related papers: Holography, Dimensional Reduction and the Bekenste…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
We emphasized the importance of underlying noncommutative geometry or Lorenz-covariant quantized space-time towards ultimate theory of quantum gravity and Planck scale physics. We focused there our attention on the statistical and…
Spacetimes obtained by dimensional reduction along lattices containing a lightlike direction can admit semigroup extensions of their isometry groups. We show by concrete examples that such a semigroup can exhibit a natural order, which in…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing…
During the last century, two independent theories using the concept of dimensional reduction have been developed independently. The first, known as F\"oppl-von K\`arm\`an theory, uses Riemannian geometry and continuum mechanics to study the…
We investigate how deviations from the Bekenstein-Hawking entropy modify black-hole spacetimes through the recently proposed entropy-geometry correspondence. For four representative modified entropies, namely Barrow, R\'enyi, Kaniadakis,…
We study a modified version of Lerman-Whitehouse Menger-like curvature defined for m+2 points in an n-dimensional Euclidean space. For 1 <= l <= m+2 and an m-dimensional subset S of R^n we also introduce global versions of this discrete…
In the old spirit of Kaluza-Klein, we consider a spacetime of the form $P = M_4 \times K$, where $K$ is the Lie group $\mathrm{SU}(3)$ equipped with a left-invariant metric that is not fully right-invariant. This metric has a ${\rm U}(1)…
In this paper, the generation of topological energy in models with large extra dimensions is investigated. The origin of this energy is attributed to a topological deformation of the standard Minkowski vacuum due to compactification of…
We analyze the validity of the generalized covariant entropy bound near the apparent horizon of isotropic expanding cosmological models. We encounter violations of the bound for cosmic times smaller than a threshold. By introducing an…
The holographic bound in Brans-Dicke $k=1$ matter dominated Cosmology is discussed. In this talk, both the apparent horizon and the particle horizon are taken for the holographic bound. The covariant entropy conjecture proposed by Bousso is…
We greatly simplify the light-cone gauge description of a relativistic membrane moving in Minkowski space by performing a field-dependent change of variables which allows the explicit solution of all constraints and a Hamiltonian reduction…
We study generic types of holographic matter residing in Lifshitz invariant defect field theory as modeled by adding probe D-branes in the bulk black hole spacetime characterized by dynamical exponent $z$ and with hyperscaling violation…
On a manifold with boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a (local) Killing horizon, a natural set of…
We employ a Kaluza-Klein dimensional reduction process on the action of the antisymmetric tensor field in five-dimensional space-time. The result is a joint field theory of four-dimensional antisymmetric and vector fields. We write the…
It is shown that holographic cosmology implies an evolving Hubble radius $c^{-1}\dot{R}_H = -1 + 3\Omega_m$ in the presence of a dimensionless matter density $\Omega_m$ scaled to the closure density $3H^2/8\pi G$, where $c$ denotes the…
We provide general arguments regarding the connection between low-energy theories (gravity and quantum field theory) and a hypothetical fundamental theory of quantum gravity, under the assumptions of (i) validity of the holographic bound…
We discuss the entropy change due to fragmentation for black hole solutions in various dimensions. We find three different types of behavior. The entropy may decrease, increase or have a mixed behavior, characterized by the presence of a…
We study tight-binding models in the crossover from hyperbolic to Euclidean lattices, realized through the successive insertion of Euclidean defects into hyperbolic lattices. We analyze how the holographic two-point boundary correlation…