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Jemal Guven

Publications and source records attributed to Jemal Guven.

64 records · Page 4Linked to original sources
arXiv1997

Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data

We establish necessary conditions for the appearance of both apparent horizons and singularities in the initial data of spherically symmetric general relativity when spacetime is foliated extrinsically. When the dominant energy condition is satisfied these conditions assume a particularly simple form. Let $ρ_{Max}$ be the maximum value of the energy density and $\ell$ the radial measure of its support. If $ρ_{Max}\ell^2$ is bounded from above by some numerical constant, the initial data cannot possess an apparent horizon. This constant does not depend sensitively on the gauge. An analogous inequality is obtained for singularities with some larger constant. The derivation exploits Poincaré type inequalities to bound integrals over certain spatial scalars. A novel approach to the construction of analogous necessary conditions for general initial data is suggested.

gr-qc↗
arXiv1995

Geometry of Deformations of Relativistic Membranes

A kinematical description of infinitesimal deformations of the worldsheet spanned in spacetime by a relativistic membrane is presented. This provides a framework for obtaining both the classical equations of motion and the equations describing infinitesimal deformations about solutions of these equations when the action describing the dynamics of this membrane is constructed using {\it any} local geometrical worldsheet scalars. As examples, we consider a Nambu membrane, and an action quadratic in the extrinsic curvature of the worldsheet.

gr-qc↗
arXiv1995

Large Deformations of Relativistic Membranes: A Generalization of the Raychaudhuri Equations

A coupled system of non-linear partial differential equations is presented which describes non-perturbatively the evolution of deformations of a relativistic membrane of arbitrary dimension, $D$, in an arbitrary background spacetime. These equations can be considered from a formal point of view as higher dimensional analogs of the Raychaudhuri equations for point particles to which they are shown to reduce when $D=1$. For $D=1$ or $D=2$ (a string), there are no constraints on the initial data. If $D>2$, however, there will be constraints with a corresponding complication of the evolution problem. The consistent evolution of the constraints is guaranteed by an integrability condition which is satisfied when the equations of motion are satisfied. Explicit calculations are performed for membranes described by the Nambu action.

gr-qc↗
arXiv1995

The Constraints in Spherically Symmetric General Relativity I --- Optical Scalars, Foliations, Bounds on the Configuration Space Variables and the Positivity of the Quasi-Local Mass

We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter variables, there exist two linear combinations of the Hamiltonian and momentum constraints which are related by time reversal. We introduce a one-parameter family of linear extrinsic time foliations of spacetime. The values of the parameter yielding globally valid gauges correspond to the vanishing of a timelike vector in the superspace of spherically symmetric geometries. We define a quasi-local mass on spheres of fixed proper radius which we prove is positive when the constraints are satisfied. Underpinning the proof are various local bounds on the configuration variables. We prove that a reasonable definition of the gravitational binding energy is always negative. Finally, we provide a tentative characterization of the configuration space of the theory in terms of closed bounded trajectories on the parameter space of the optical scalars.

gr-qc↗
arXiv1995

The Constraints in Spherically Symmetric General Relativity II --- Identifying the Configuration Space: A Moment of Time Symmetry

We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations satisfy both the positive quasi-local mass (QLM) theorem and its converse. We derive an analytical expression for the spatial metric in the neighborhood of a generic singularity. The corresponding curvature singularity shows up in the traceless component of the Ricci tensor. We show that if the energy density of matter is monotonically decreasing, the geometry cannot be singular. A supermetric on the configuration space which distinguishes between singular geometries and non-singular ones is constructed explicitly. Global necessary and sufficient criteria for the formation of trapped surfaces and singularities are framed in terms of inequalities which relate appropriate measures of the material energy content on a given support to a measure of its volume. The strength of these inequalities is gauged by exploiting the exactly solvable piece-wise constant density star as a template.

gr-qc↗
arXiv1995

The Constraints in Spherically Symmetric General Relativity III --- Identifying the Configuration Space: $J\ne 0$

We continue our examination of the constraints in spherically symmetric general relativity begun in I (gr-qc/9411009) and II (gr-qc/9411010). We extend to general configurations with $J\ne 0$ the analysis of II which treated a moment of time symmetry. We exploit the one parameter family of foliations introduced in I which are linear and homogeneous in the extrinsic curvature to characterize apparent horizons and spatial singularities in the initial data. In particular, we demonstrate that these characterizations do not depend sensitively on the foliation.

gr-qc↗
arXiv1994

Super-Minisuperspace and New Variables

We consider the specialization to spatially homogenous solutions of the Jacobson formulation of N=1 canonical supergravity in terms of Ashtekar's new variables. We find that the classical Poisson algebra of the supersymmetry constraints is preserved by this specialization only for Bianchi type A models. The quantization of supersymmetric Bianchi type A models is carried out in the triad representation. We find the physical states of this quantum theory. Since we are missing a suitable inner product on these physical states, our results are only formal.

gr-qc↗
arXiv1993

Covariant perturbations of domain walls in curved spacetime

A manifestly covariant equation is derived to describe the perturbations in a domain wall on a given background spacetime. This generalizes recent work on domain walls in Minkowski space and introduces a framework for examining the stability of relativistic bubbles in curved spacetimes.

gr-qc↗