On the Penrose inequality

The purpose of this Letter is to point out an argument which may ultimately lead to a rigorous proof of the Penrose inequality in the general case. The argument is a variation of Geroch's original proposal for a proof of the positive-energy theorem which was later adapted by Jang and Wald to apply to initial data sets containing apparent horizons. The new input is to dispense with the a priori restriction to an initial data set and to use the four-dimensional structure of spacetime in an essential way.     

On the Penrose inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the Arnowitt-Deser-Misner mass and the area of an outermost apparent horizon, if the data are suitably restricted. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Leaving smoothness issues aside, we also show that our restrictions on the data can be locally fulfilled by a suitable choice of the initial surface in a given spacetime.     

Fermions and spherically symmetric monopoles

The interaction of fermions with monopoles is analyzed for general spherically symmetric monopoles of arbitrary strength and massless fermions in arbitrary representations of the gauge group. The results are based on a solution to the Dirac equation in the field of the monopole, valid in the point limit and in all partial waves. The partial waves in which non-conservation of global charges may occur are identified. A two-dimensional lagrangian is derived, which includes the Coulomb interactions generated by the complete abelian subgroup of the unbroken gauge group. The fermions are represented by a set of doublets with a boundary condition that reflects the structure of the core. We derive a simple formula for the conservation laws of this model which determine all scattering processes completely. The results have a consistent interpretation in terms of anomalies and field configurations with non-trivial winding number. We give an explicit construction of the zero modes for all helicity-violating multi-fermion condensates. The formalism is applied to several higher strength monopoles in SO(10) based models.     

On the spherically symmetric gauge fields

The spherically symmetric gauge fields with a compact gauge group over 4-dimensional Minkowski space are determined completely. Expressions for the gauge potentials of these fields are obtained.     

Geometric inequalities in spherically symmetric spacetimes

In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner–Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.     

Relativistic fluids in spherically symmetric space

Some of McVittie and Wiltshire's (1977) solutions of Walker's (1935) isotropy conditions for relativistic perfect-fluid spheres are generalized. Solutions are spherically symmetric and conformally flat.     

Escape factors in spherically symmetric plasmas

In this paper we present explicit formulas for the escape factors of strong spectral lines in spherical-symmetric plasmas. The plasma does not necessarily have a homogeneous density. The calculations include two new elements: the first incorporates an accurate calculation of the angle-averaged areal density of ions from any internal point to the edge of the sphere. The second is the use of a saddle point method to carry out the integration over the line profile. Approximate expressions for the asymptotic behavior of the escape factor are given for Gaussian, Lorentzian and Holtsmarkian line shapes.     

Static spherically symmetric fields in the scalar-tetradic theoryA

The scalar-tetradic TheoryA has been recently formulated. In this paper it is proved that, for a suitable tetrad field and any given value of the coupling constantW of the theory, there is a unique static spherically symmetric solution of the field equations describing the outer field of a standard perfect fluid sphere (such as the sun); the explicit form of this solution in terms of the radial isotropic coordinater appears to be different in the three cases: (1)W <0 orW > 2, (2) 0 <W < 2, and (3)W =2. On account of the Birkhoff theorem the quoted solution appears to have considerable physical interest.     

Self-consistent spherically symmetric solutions of the Yang-Mills-Dirac-equations

TheSU(2) Yang-Mills equations coupled self-consistently to an isospin 1/2-Dirac equation are studied. Static spherically symmetric exact analytic solutions are given. They all share the property of infinite energy.     

On spherically symmetric fields in gauge theories

Gauge fields admitting spherical symmetry are listed. Spherically symmetric solutions of Yang-Mills equations and spherically symmetric magnetic monopoles are studied. A simple exact solution of the Yang-Mills and Einstein equations is found.     

Static spherically symmetric star in Gauss-Bonnet gravity

We explore static spherically symmetric stars in Gauss-Bonnet gravity without a cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of the Gauss-Bonnet term with a positive coupling constant completely changes thermal and gravitational energies, and the upper bound of the red shift of spectral lines from the surface of stars. Unlike in general relativity, the upper bound of the red shift is dependent on the density of stars in our case. Moreover, we have proven that two theorems for judging the stability of equilibrium of stars in general relativity can hold in Gauss-Bonnet gravity.     

Viscous fluid in static spherically symmetric space-time

The paper presents a static spherically symmetric viscous fluid solution of Einstein field equation, assuming an equation of statep=(γ?1)ρ. Though static, the solution has expansion, shear, and acceleration and can explain cosmological red shift. Also it has a particle horizon. The singularity at the origin and larger viscosity make it unfit to represent a real universe.     

Conformal symmetries in static spherically symmetric spacetimes

We obtain the conformal symmetry vector in static, spherically symmetric spacetimes, in terms of functions subject to a number of integrability conditions that also place restrictions on the metric. Some conformal symmetries found previously are regained as special cases.