arXiv subjects
Publications and source records attributed to J. P. Krisch.
Generalized inheritance is used with the almost-conformal Killing equation. Examples are the flat FRW, Kasner, and deSitter metrics. The volume changes in FRW while transitioning to a stiff fluid are discussed. An inheritance current is implicit in the generalized condition
A set of cylindrical solutions to Einstein's field equations for power law densities is described. The solutions have a Bessel function contribution to the metric. For matter cylinders regular on axis, the first two solutions are the constant density Gott-Hiscock string and a cylinder with a metric Airy function. All members of this family have the Vilenkin limit to their mass per length. Some examples of Bessel shells and Bessel motion are given.
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum mechanics. In this paper we investigate the fractional versions of the stellar structure equations for non radiating spherical objects. Using incompressible fluids as a comparison, we develop models for constant density Newtonian objects with fractional mass distributions or stress conditions. To better understand the fractional effects, we discuss effective values for the density, gravitational field and equation of state. The fractional ob- jects are smaller and less massive than integer models. The fractional parameters are related to a polytropic index for the models considered.
Shear-free composite fluids are constructed from two Letelier rotated unaligned perfect fluids. The component fluid parameters necessary to construct a shear-free composite are investigated. A metric in the Stephani-Barnes solution family and a simple stationary metric are discussed.
We describe the stress energy of a fluid with two unequal stresses and heat flow in terms of two perfect fluid components. The description is in terms of the fluid velocity overlap of the components, and makes no assumptions about the equations of state of the perfect fluids. The description is applied to the metrics of a conformally flat system and a black string.
The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index α. When the fractional index is continued into the negative α region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.
We describe a spheroidal fluid shell between two Kerr vacuum regions which have opposite rotation parameters. The shell has a stiff equation of state and a heat flow vector related to the rotational Killing current. The shell description is useful in exploring the significance of counter-rotation in Kerr metric matches.
We consider an action that can generate fluids with three unequal stresses for metrics with a spacelike Killing vector. The parameters in the action are directly related to the stress anisotropies. The field equations following from the action are applied to an anisotropic cosmological expansion and an extension of the Gott-Hiscock cosmic string.
A relation between stress-energy and motion is derived for accelerated Israel layers. The relation, for layers between two Schwarzschild manifolds, generalizes the equation of state for geodesic collapse. A set of linked layers is discussed.
We discuss Israel layers collapsing inward from rest at infinity along Schwarzschild-Lemaitre geodesics. The dynamics of the collapsing layer and its equation of state are developed. There is a general equation of state which is approximately polytropic in the limit of very low pressure. The equation of state establishes a new limit on the stress-density ratio.
Energy transport mechanisms can be generated by imposing relations between null tetrad Ricci components. Several kinds of mass and density transport generated by these relations are studied for the generalized Vaidya system.
We present a method for constructing stationary, asymptotically flat, rotating solutions of Einstein's field equations. One of the spun-up solutions has quasilocal mass but no global mass. It has an ergosphere but no event horizon. The angular momentum is constant everywhere beyond the ergosphere. The energy-momentum content of this solution can be interpreted as a rotating string-fluid.
The static Kottler metric is the Schwarzschild vacuum metric extended to include a cosmological constant. Angular momentum is added to the Kottler metric by using Newman and Janis' complexifying algorithm. The new metric is the Lambda generalization of the Kerr spacetime. It is stationary, axially symmetric, Petrov type II, and has Kerr-Schild form.
We present an exact solution of Einstein's field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter spacetime. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of the cosmological constant.
We present a solution generating technique for anisotropic fluids which preserves specific Killing symmetries. Anisotropic matter distributions that can be used with the one parameter Ehlers-Geroch transform are discussed. Example spacetimes that support the appropriate anisotropic stress-energy are found and the transformation applied. The 3+1 black string solution is one of the spacetimes with the appropriate matter distribution. Use of the transform with a black string seed is discussed.
Dimensional scales are examined in an extended 3+1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.
Regarding the spin-up of Schwarzschild-Kerr and Banados-Teitelboim-Zanelli systems as a symmetry breaking phase transition, critical exponents are evaluated and compared with classical Landau predictions. We suggest a definition of isothermal compressibity which is independent of spin direction. We find identical exponents for both systems, and possible universality in the phase transitions of these systems.
Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.