Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part II: BCEA Theory

The BTZ black hole solution for (2+1)-spacetime is considered as a solution of a triad-affine theory (BCEA) in which topological matter is introduced to replace the cosmological constant in the model. Conserved quantities and entropy are calculated via Noether theorem, reproducing in a geometrical and global framework earlier results found in the literature using local formalisms. Ambiguities in global definitions of conserved quantities are considered in detail. A dual and covariant Legendre transformation is performed to re-formulate BCEA theory as a purely metric (natural) theory (BCG) coupled to topological matter. No ambiguities in the definition of mass and angular momentum arise in BCG theory. Moreover, gravitational and matter contributions to conserved quantities and entropy are isolated. Finally, a comparison of BCEA and BCG theories is carried out by relying on the results obtained in both theories.Comment: PlainTEX, 20 page

The Universality of Einstein Equations

It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as independent variables, leads to ``universal'' equations. If the dimension $n$ of space--time is greater than two these universal equations are Einstein equations for a generic Lagrangian and are suitably replaced by other universal equations at bifurcation points. We show that bifurcations take place in particular for conformally invariant Lagrangians $L=R^{n/2} \sqrt g$ and prove that their solutions are conformally equivalent to solutions of Einstein equations. For 2--dimensional space--time we find instead that the universal equation is always the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the Levi--Civita connection of the metric and an additional vectorfield ensuing from conformal invariance. As an example, we investigate in detail some polynomial Lagrangians and discuss their bifurcations.Comment: 15 pages, LaTeX, (Extended Version), TO-JLL-P1/9

The Right to Protest for Right : Reaffirming the First Amendment Principle That Limits the Tort Liability of Protest Organizers

On December 16, 2019, the U.S. Court of Appeals for the Fifth Circuit held in Doe v. Mckesson that a court could hold DeRay Mckesson liable for damages to a police officer whom an unidentified assailant injured at a 2016 Black Lives Matter protest that Mckesson helped organize. Mckesson did not cause the officer’s injuries, and he did not order, encourage, or incite the protestors at the demonstration to act violently. The Fifth Circuit held that Mckesson could be liable only because he played a role in organizing the demonstration. In 1982, the U.S. Supreme Court set forth an important principle in NAACP v. Claiborne Hardware Co. that limited the extent to which a court could hold protest organizers engaged in protected First Amendment activity liable for the violent acts of third parties. Many First Amendment scholars considered the Fifth Circuit’s decision in Doe v. Mckesson a direct affront to the principle set out in Claiborne Hardware. Indeed, Mckesson engaged in core protected speech activity when he protested police misconduct and thus should have fallen under the protection of the stringent standard. In November of 2020, in Doe v. Mckesson, the Supreme Court reversed and remanded the Fifth Circuit’s decision, but it did so in a per curiam opinion based only on issues concerning Louisiana tort law theories, leaving the First Amendment implications unanswered. This Note argues that the limited liability principle set forth in Claiborne Hardware is an essential protection for organizers and for democracy, such that the Supreme Court should look for opportunities to reaffirm it in the wake of the Fifth Circuit’s latest attack

The Expansive Scope of the Ministerial Exception After \u3cem\u3eOur Lady of Guadalupe School v. Morrissey-Berru\u3c/em\u3e

On July 8th, 2020, the United States Supreme Court held in Our Lady of Guadalupe School v. Morrissey-Berru that two parochial school teachers, Kristen Biel and Agnes-Morrissey-Berru, were ministers for purposes of the First Amendment’s ministerial exception. This meant that the First Amendment barred their respective employment discrimination actions notwithstanding the merit of their claims. When the Court first recognized the ministerial exception in 2012, in Hosanna-Tabor Evangelical Lutheran Church & School v. Equal Employment Opportunity Commission, it determined that an employee qualified as a minister through a multi-factor, totality of the circumstances analysis. Yet, in reaching its conclusion in Our Lady of Guadalupe School, the Court focused predominantly on one factor—whether the employees performed religious functions. This Comment argues that the Court’s sole focus on religious function has significantly expanded the scope of the ministerial exception, such that more employees of more religious institutions are likely to qualify as ministers and thus lose their federal antidiscrimination employment protections. Given the policy interests at stake, courts applying the ministerial exception after Our Lady of Guadalupe School should recognize that a broad reading invites exploitation and interpret the opinion in its narrowest form

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting

The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription by Wald et al. we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.Comment: PlainTEX, 16 pages. Revised version 1.

Palatini Variational Principle for NN-Dimensional Dilaton Gravity

We consider a Palatini variation on a general $N$-Dimensional second order, torsion-free dilaton gravity action and determine the resulting equations of motion. Consistency is checked by considering the restraint imposed due to invariance of the matter action under simple coordinate transformations, and the special case of N=2 is examined. We also examine a sub-class of theories whereby a Palatini variation dynamically coincides with that of the "ordinary" Hilbert variational principle; in particular we examine a generalized Brans-Dicke theory and the associated role of conformal transformations.Comment: 16 pages, LaTe

The Effects of Chemical Composition on Soft Magnetic Materials Behaviour

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The effect of particle size on the core losses of soft magnetic composites

In the field of electrical machines, the actual research activities mainly focus on improving the energetic aspects; for this reason, new magnetic materials are currently investigated and proposed, supporting the design and production of magnetic cores. The innovative aspects are related to both hard and soft magnetic materials. In the case of permanent magnets, the use of NdFeB bonded magnets represents a good solution in place of ferrites. For what concerns the soft magnetic materials, the adoption of Soft Magnetic Composites (SMCs) cores permits significant advantages compared to the laminated sheets, such as complex geometries and reduced eddy currents losses. SMC materials are ferromagnetic grains covered with an insulating layer that can be of an organic or inorganic type. The proposed study focuses on the impact of the particle size and distribution on the final material properties. The original powder was cut into three different fractions, and different combinations have been prepared, varying the fractions percentages. The magnetic and energetic properties have been evaluated in different frequency ranges, thus ranking the best combinations. The best specimens were then tested to evaluate the mechanical performances. The preliminary results are promising, but deeper analysis and tests are required to refine the selection and evaluate the improvements against the original composition taken as a reference.In the field of electrical machines, the actual research activities mainly focus on improving the energetic aspects; for this reason, new magnetic materials are currently investigated and proposed, supporting the design and production of magnetic cores. The innovative aspects are related to both hard and soft magnetic materials. In the case of permanent magnets, the use of NdFeB bonded magnets represents a good solution in place of ferrites. For what concerns the soft magnetic materials, the adoption of Soft Magnetic Composites (SMCs) cores permits significant advantages compared to the laminated sheets, such as complex geometries and reduced eddy currents losses. SMC materials are ferromagnetic grains covered with an insulating layer that can be of an organic or inorganic type. The proposed study focuses on the impact of the particle size and distribution on the final material properties. The original powder was cut into three different fractions, and different combinations have been prepared, varying th..

Gauge Formalism for General Relativity and Fermionic Matter

A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and spinors. An appropriate gauge structure is also given to General Relativity, replacing the metric field with spin frames. Finally, conserved quantities and superpotentials are calculated under a general covariant form.Comment: 18 pages, Plain TEX, revision, explicit expression for superpotential has been adde

Two-spinor Formulation of First Order Gravity coupled to Dirac Fields

Two-spinor formalism for Einstein Lagrangian is developed. The gravitational field is regarded as a composite object derived from soldering forms. Our formalism is geometrically and globally well-defined and may be used in virtually any 4m-dimensional manifold with arbitrary signature as well as without any stringent topological requirement on space-time, such as parallelizability. Interactions and feedbacks between gravity and spinor fields are considered. As is well known, the Hilbert-Einstein Lagrangian is second order also when expressed in terms of soldering forms. A covariant splitting is then analysed leading to a first order Lagrangian which is recognized to play a fundamental role in the theory of conserved quantities. The splitting and thence the first order Lagrangian depend on a reference spin connection which is physically interpreted as setting the zero level for conserved quantities. A complete and detailed treatment of conserved quantities is then presented.Comment: 16 pages, Plain TE