Interpreting doubly special relativity as a modified theory of measurement

In this article we develop a physical interpretation for the deformed (doubly) special relativity theories (DSRs), based on a modification of the theory of measurement in special relativity. We suggest that it is useful to regard the DSRs as reflecting the manner in which quantum gravity effects induce Planck-suppressed distortions in the measurement of the "true" energy and momentum. This interpretation provides a framework for the DSRs that is manifestly consistent, non-trivial, and in principle falsifiable. However, it does so at the cost of demoting such theories from the level of "fundamental" physics to the level of phenomenological models -- models that should in principle be derivable from whatever theory of quantum gravity one ultimately chooses to adopt.Comment: 18 pages, plain LaTeX2

Growing Perfect Decagonal Quasicrystals by Local Rules

A local growth algorithm for a decagonal quasicrystal is presented. We show that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to form on the upper layer, successive 2D PPT layers can be added on top resulting in a perfect decagonal quasicrystalline structure in bulk with a point defect only on the bottom surface layer. Our growth rule shows that an ideal quasicrystal structure can be constructed by a local growth algorithm in 3D, contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure

Entropy of gravitationally collapsing matter in FRW universe models

We look at a gas of dust and investigate how its entropy evolves with time under a spherically symmetric gravitational collapse. We treat the problem perturbatively and find that the classical thermodynamic entropy does actually increase to first order when one allows for gravitational potential energy to be transferred to thermal energy during the collapse. Thus, in this situation there is no need to resort to the introduction of an intrinsic gravitational entropy in order to satisfy the second law of thermodynamics.Comment: 9 pages, 4 figures. Major changes from previous version. We consider only thermodynamic entropy in this version. Published in PR

The inequality between mass and angular momentum for axially symmetric black holes

In this essay I first discuss the physical relevance of the inequality $m\geq \sqrt{|J|}$ for axially symmetric (non-stationary) black holes, where m is the mass and J the angular momentum of the spacetime. Then, I present a proof of this inequality for the case of one spinning black hole. The proof involves a remarkable characterization of the extreme Kerr black hole as an absolute minimum of the total mass. Finally, I conjecture on the physical implications of this characterization for the non linear stability problem for black holes.Comment: 8 pages, Honorable Mention in the Gravity Research Foundation Essay Competition 200

Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case

We have studied spacetime structures of static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\Lambda$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $\alpha$ is non-negative and $4{\tilde \alpha}/\ell^2\leq 1$ in order to define the relevant vacuum state. Solutions have the $(n-2)$-dimensional Euclidean sub-manifold whose curvature is $k=1,~0$, or -1. In Gauss-Bonnet gravity, solutions are classified into plus and minus branches. In the plus branch all solutions have the same asymptotic structure as those in general relativity with a negative cosmological constant. The charge affects a central region of the spacetime. A branch singularity appears at the finite radius $r=r_b>0$ for any mass parameter. There the Kretschmann invariant behaves as $O((r-r_b)^{-3})$, which is much milder than divergent behavior of the central singularity in general relativity $O(r^{-4(n-2)})$. Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although there is a maximum mass for black hole solutions in the plus branch for $k=-1$ in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with $k=-1$ and $n\geq6$ have an "inner" black hole, and inner and the "outer" black hole horizons. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.Comment: 20 pages, 10 figure

Energy Estimates and Gravitational Collapse

We study the cancelations in the energy estimates for Einstein vacuum equations in order to prove the formation of black holes along evolutions. The novelty of the paper is that, we completely avoid using rotation vector fields to establish the global existence theorem of the solution. More precisely, we use only canonical null directions as commutators to derive energy estimates at the level of one derivatives of null curvature components.Comment: 2 figures, 40 page

On the exact evaluation of spin networks

We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs