arXiv subjects

Erick J. Weinberg

Publications and source records attributed to Erick J. Weinberg.

46 records · Page 3Linked to original sources

arXiv1995

Static Black Hole Solutions without Rotational Symmetry

We construct static black hole solutions that have no rotational symmetry. These arise in theories, including the standard electroweak model, that include charged vector mesons with mass $m\ne 0$. In such theories, a magnetically charged Reissner-Nordstrom black hole with horizon radius less than a critical value of the order of $m^{-1}$ is classically unstable against the development of a nonzero vector meson field just outside the horizon, indicating the existence of static black hole solutions with vector meson hair. For the case of unit magnetic charge, spherically symmetric solutions of this type have previously been studied. For other values of the magnetic charge, general arguments show that any new solution with hair cannot be spherically symmetric. In this paper we develop and apply a perturbative scheme (which may have applicability in other contexts) for constructing such solutions in the case where the Reissner-Nordstrom solution is just barely unstable. For a few low values of the magnetic charge the black holes retain a rotational symmetry about a single axis, but this axial symmetry disappears for higher charges. While the vector meson fields vanish exponentially fast at distances greater than $O(m^{-1})$, the magnetic field and the metric have higher multipole components that decrease only as powers of the distance from the black hole.

gr-qc↗

arXiv1995

Magnetically Charged Black Holes with Hair

In these lectures the properties of magnetically charged black holes are described. In addition to the standard Reissner-Nördstrom solution, there are new types of static black holes that arise in theories containing electrically charged massive vector mesons. These latter solutions have nontrivial matter fields outside the horizon; i.e., they are black holes with hair. While the solutions carrying unit magnetic charge are spherically symmetric, those with more than two units of magnetic charge are not even axially symmetric. These thus provide the first example of time-independent black hole solutions that have no rotational symmetry.

gr-qc↗

arXiv1994

Instabilities of Magnetically Charged Black Holes

The stability of the magnetically charged Reissner-Nordstrom black hole solution is investigated in the context of a theory with massive charged vector mesons. By exploiting the spherical symmetry of the problem, the linear perturbations about the Reissner-Nordstrom solution can be decomposed into modes of definite angular momentum $J$. For each value of $J$, unstable modes appear if the horizon radius is less than a critical value that depends on the vector meson gyromagnetic ratio $g$ and the monopole magnetic charge $q/e$. It is shown that such a critical radius exists (except in the anomalous case $q={1\over 2}$ with $0 \le g \le 2$), provided only that the vector meson mass is not too close to the Planck mass. The value of the critical radius is determined numerically for a number of values of $J$. The instabilities found here imply the existence of stable solutions with nonzero vector fields (``hair'') outside the horizon; unless $q=1$ and $g>0$, these will not be spherically symmetric.

hep-th↗

arXiv1994

Bubble Nucleation in Theories with Symmetry Breaking by Radiative Corrections

A formalism is developed to calculate the bubble nucleation rate in theories where the symmetry breaking is by radiative corrections. Although to leading and next-to-leading order the result can be expressed in terms of the effective action of the theory, this is not true of the higher order corrections. In particular, the imaginary part of the effective potential does not explicitly enter the calculation and the problems of interpretation which it would entail are avoided. Based on a talk given at the NATO Advanced Research Workshop Electroweak Physics and the Early Universe, Sintra, Portugal, March 25, 1994

hep-ph↗

arXiv1994

Nontopological Magnetic Monopoles and New Magnetically Charged Black Holes

The existence of nonsingular classical magnetic monopole solutions is usually understood in terms of topologically nontrivial Higgs field configurations. We show that finite energy magnetic monopole solutions also exist within a class of purely Abelian gauge theories containing charged vector mesons, even though the possibility of nontrivial topology does not even arise. provided that certain relationships among the parameters of the theory are satisfied. These solutions are singular if these relationships do not hold, but even then become meaningful once the theory is coupled to gravity, for they then give rise to an interesting new class of magnetically charged black holes with hair.

hep-th↗

arXiv1994

Dynamical Solutions to the Horizon and Flatness Problems

We discuss in some detail the requirements on an early-Universe model that solves the horizon and flatness problems during the epoch of classical cosmology ($t\ge t_i\gg 10^{-43}\sec$). We show that a dynamical resolution of the horizon problem requires superluminal expansion (or very close to it) and that a truly satisfactory resolution of the flatness problem requires entropy production. This implies that a proposed class of adiabatic models in which the Planck mass varies by many orders of magnitude cannot fully resolve the flatness problem. Furthermore, we show that, subject to minimal assumptions, such models cannot solve the horizon problem either. Because superluminal expansion and entropy production are the two generic features of inflationary models, our results suggest that inflation, or something very similar, may be the only dynamical solution to the horizon and flatness problems.

astro-ph↗

arXiv1993

Radiation from a moving Scalar Source

We study classical radiation and quantum bremsstrahlung effect of a moving point scalar source. Our classical analysis provides another example of resolving a well-known apparent paradox, that of whether a constantly accelerating source radiates or not. Quantum mechanically, we show that for a scalar source with arbitrary motion, the tree level emission rate of scalar particles in the inertial frame equals the sum of emission and absorption rates of zero-energy Rindler particles in the Rindler frame. We then explicitly verify this result for a source undergoing constant proper acceleration.

hep-th↗

arXiv1993

Monopole Vector Spherical Harmonics

Eigenfunctions of total angular momentum for a charged vector field interacting with a magnetic monopole are constructed and their properties studied. In general, these eigenfunctions can be obtained by applying vector operators to the monopole spherical harmonics in a manner similar to that often used for the construction of the ordinary vector spherical harmonics. This construction fails for the harmonics with the minimum allowed angular momentum. These latter form a set of vector fields with vanishing covariant curl and covariant divergence, whose number can be determined by an index theorem.

hep-th↗

arXiv1992

Vacuum Decay in Theories with Symmetry Breaking by Radiative Corrections

The standard bounce formalism for calculating the decay rate of a metastable vacuum cannot be applied to theories in which the symmetry breaking is due to radiative corrections, because in such theories the tree-level action has no bounce solutions. In this paper I derive a modified formalism to deal with such cases. As in the usual case, the bubble nucleation rate may be written in the form $A e^{-B}$. To leading approximation, $B$ is the bounce action obtained by replacing the tree-level potential by the leading one-loop approximation to the effective potential, in agreement with the generally adopted {\it ad hoc} remedy. The next correction to $B$ (which is proportional to an inverse power of a small coupling) is given in terms of the next-to-leading term in the effective potential and the leading correction to the two-derivative term in the effective action. The corrections beyond these (which may be included in the prefactor) do not have simple expressions in terms of the effective potential and the other functions in the effective action. In particular, the scalar-loop terms which give an imaginary part to the effective potential do not explicitly appear; the corresponding effects are included in a functional determinant which gives a manifestly real result for the nucleation rate.

hep-ph↗

arXiv1991

Black Holes in Magnetic Monopoles

We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs vacuum expectation value $v$ is less than or equal to a critical value $v_{cr}$, which is of the order of the Planck mass. In the limiting case the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For $v<v_{cr}$, we find additional solutions which are singular at $r=0$, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of $v$ and of the total mass $M$ and their relation to the Reissner-Nordstrom solutions is discussed.

hep-th↗