http://cds.cern.ch/record/465856/files/0009077.pdf

The Bardeen model as a nonlinear magnetic monopole

New regular black hole solution from nonlinear electrodynamics

In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge theory massive but preserves gauge invariance. The Stueckelberg mechanism is the introduction of new fields to reveal a symmetry of a gauge--fixed theory. We first review the Stueckelberg mechanism in the massive Abelian gauge theory. We then extend this idea to the standard model, stueckelberging the hypercharge U(1) and thus giving a mass to the physical photon. This introduces an infrared regulator for the photon in the standard electroweak theory, along with a modification of the weak mixing angle accompanied by a plethora of new effects. Notably, neutrinos couple to the photon and charged leptons have also a pseudo-vector coupling. Finally, we review the historical influence of Stueckelberg's 1938 idea, which led to applications in many areas not anticipated by the author, such as strings. We describe the numerous proposals to generalize the Stueckelberg trick to the non-Abelian case with the aim to find alternatives to the standard model. Nevertheless, the Higgs mechanism in spontaneous symmetry breaking remains the only presently known way to give masses to non-Abelian vector fields in a renormalizable and unitary theory.

The Stueckelberg Field

For the example of the infinite well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the momentum and the Hamiltonian operators in different settings. Additional physical requirements such as parity, time reversal, and positivity are used to restrict the large class of self-adjoint extensions of the Hamiltonian.

Self-adjoint extensions of operators and the teaching of quantum mechanics

We present a general procedure for constructing exact black hole solutions with electric or magnetic charges in general relativity coupled to a nonlinear electrodynamics. We obtain a variety of two-parameter family spherically symmetric black hole solutions. In particular, the singularity at the center of the space-time can be canceled in the parameter space and the black hole solutions become regular everywhere in space-time. We study the global properties of the solutions and derive the first law of thermodynamics. We also generalize the procedure to include a cosmological constant and construct regular black hole solutions that are asymptotic to anti--de Sitter space-time.

Construction of Regular Black Holes in General Relativity

Physical arguments related with the existence of black hole solutions having a non-trapping interior are discussed. Massive scalar fields interacting with gravity are considered. Interior asymptotic solutions showing a scalar field approaching a constant value at the horizon are given. It is argued that the coupled Einstein–Klein–Gordon equations can be satisfied in the sense of the generalized functions after removing a particular regularization designed for matching the interior solution with an external Schwarzschild space–time. The scalar field appears as just avoiding the appearance of closed trapped surfaces while coming from the exterior region. It also follows that the usual space integral over $T_0^0$ in the internal region just gives the total proper mass associated to the external Schwarzschild solution, as it should be expected.

About black holes with nontrapping interior

It is shown for a wide class of systems in the framework of the total Hamiltonian procedure that all first-class constraints generate canonical transformations connecting physically equivalent states. It occurs whenever the constraints arising in the Dirac algorithm are effective when considered in the functional form as they appear in the consistency conditions. The property of hereditary separation between first- and second-class constraints also follows from the above condition. General Poisson-brackets relations among constraints in the representation used here are also obtained. The sources of anomalies in the hereditary property reported in the literature are identified.

On Dirac's conjecture for Hamiltonian systems with first- and second-class constraints

We reconsider the quantum mechanics of scale-invariant potentials in two dimensions. The breaking of scale invariance by quantum effects is analyzed by the explicit evaluation of the phase shift and the self-adjoint extension method. We argue that the breaking of scale invariance reported in the literature for the δ(r) potential is an example of explicit symmetry breaking and not an anomaly or quantum mechanical symmetry breaking.

https://cds.cern.ch/record/320935/files/9702042.pdf

On scale invariance and anomalies in quantum mechanics

Physical arguments related with the existence of black hole solutions having a non trapping interior are discussed. Massive scalar fields interacting with gravity are considered. Interior asymptotic solutions showing a scalar field approaching a constant value at the horizon are given. It is argued that the coupled Einstein-Klein-Gordon equations can be satisfied in the sense of the generalized functions after removing a particular regularization designed for matching the interior solution with an external Scwartzschild spacetime. The scalar field appears as just avoiding the appearance of closed trapped surfaces while coming from the exterior region. It also follows that the usual space integral over the temporal- temporal components of energy-momnetum tensor in the internal region just gives the total proper mass associated to the external Schwartzschild solution, as it should be expected.

Alejandro Cabo

Papers

About black holes with nontrapping interior

On Dirac's conjecture for Hamiltonian systems with first- and second-class constraints

On scale invariance and anomalies in quantum mechanics

About Black Holes Without Trapping Interior

Finite temperature gluonic gas in a magnetic field