Being Good Lawyers: A Relational Approach to Law Practice

In response to past generations of debates regarding whether law is a business or profession, we advance an alternative approach that rejects the dichotomies of business and profession, or hired gun and wise counselor. Instead, we propose a relational account of law practice. Unlike frameworks grounded in assumptions of atomistic individualism or communitarianism, a relational perspective recognizes that all actors, whether individuals or organizations, have separate identities yet are intrinsically inter-connected and cannot maximize their own good in isolation. Through the lens of relational self-interest, maximizing the good of the individual or business requires consideration of the good of the neighbor, the employee or customer, and of the public. Accordingly, relational lawyers advise and assist clients, colleagues, and themselves to take into account the well-being of others when contemplating and pursuing their own interests. A relational approach to law practice does not require a choice between labeling law a business or a profession, and indeed is consistent with both perspectives. Lawyers can access relational perspectives from a wide range of understandings of the lawyer’s role, with the exception of the particular hired gun ideology that views lawyers as amoral mouthpieces for clients who act as Holmesian bad men and women aggressively pursuing their self-interest with no regard to others. The relational framework offers all lawyers, whether they see themselves as professionals or business persons, a framework for understanding that they can continue to serve as society’s civic teachers in their capacity as intermediaries between the people and the law, integrating relational self-interest into their representation of clients and their community service. By doing so, lawyers as professionals, individuals, and community members will more effectively represent clients, as well as enhance their contribution to the public good and to the quality of their own professional and private lives. They will also surmount the generation-long malaise resulting from the crisis of professionalism

First Law of Black Rings Thermodynamics in Higher Dimensional Dilaton Gravity with p + 1 Strength Forms

We derive the first law of black rings thermodynamics in n-dimensional Einstein dilaton gravity with additional (p+1)-form field strength being the simplest generalization of five-dimensional theory containing a stationary black ring solution with dipole charge. It was done by means of choosing any cross section of the event horizon to the future of the bifurcation surface.Comment: 6 pages, to be published in Phys.Rev.D1

Trapped surfaces in prolate collapse in the Gibbons-Penrose construction

We investigate existence and properties of trapped surfaces in two models of collapsing null dust shells within the Gibbons-Penrose construction. In the first model, the shell is initially a prolate spheroid, and the resulting singularity forms at the ends first (relative to a natural time slicing by flat hyperplanes), in analogy with behavior found in certain prolate collapse examples considered by Shapiro and Teukolsky. We give an explicit example in which trapped surfaces are present on the shell, but none exist prior to the last flat slice, thereby explicitly showing that the absence of trapped surfaces on a particular, natural slicing does not imply an absence of trapped surfaces in the spacetime. We then examine a model considered by Barrabes, Israel and Letelier (BIL) of a cylindrical shell of mass M and length L, with hemispherical endcaps of mass m. We obtain a "phase diagram" for the presence of trapped surfaces on the shell with respect to essential parameters $\lambda \equiv M/L$ and $\mu \equiv m/M$. It is found that no trapped surfaces are present on the shell when $\lambda$ or $\mu$ are sufficiently small. (We are able only to search for trapped surfaces lying on the shell itself.) In the limit $\lambda \to 0$, the existence or nonexistence of trapped surfaces lying within the shell is seen to be in remarkably good accord with the hoop conjecture.Comment: 22 pages, 6 figure

A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories

We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the gauge and solving the linearized gravitational field equations to eliminate the metric perturbation variable in terms of the matter variables. In a wide class of cases--which include f(R) gravity, the Einstein-aether theory of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining perturbation equations for the matter fields are second order in time. We show how the symplectic current arising from the original Lagrangian gives rise to a symmetric bilinear form on the variables of the reduced theory. If this bilinear form is positive definite, it provides an inner product that puts the equations of motion of the reduced theory into a self-adjoint form. A variational principle can then be written down immediately, from which stability can be tested readily. We illustrate our method in the case of Einstein's equation with perfect fluid matter, thereby re-deriving, in a systematic manner, Chandrasekhar's variational principle for radial oscillations of spherically symmetric stars. In a subsequent paper, we will apply our analysis to f(R) gravity, the Einstein-aether theory, and Bekenstein's TeVeS theory.Comment: 13 pages; submitted to Phys. Rev. D. v2: changed formatting, added conclusion, corrected sign convention

On leading order gravitational backreactions in de Sitter spacetime

Backreactions are considered in a de Sitter spacetime whose cosmological constant is generated by the potential of scalar field. The leading order gravitational effect of nonlinear matter fluctuations is analyzed and it is found that the initial value problem for the perturbed Einstein equations possesses linearization instabilities. We show that these linearization instabilities can be avoided by assuming strict de Sitter invariance of the quantum states of the linearized fluctuations. We furthermore show that quantum anomalies do not block the invariance requirement. This invariance constraint applies to the entire spectrum of states, from the vacuum to the excited states (should they exist), and is in that sense much stronger than the usual Poincare invariance requirement of the Minkowski vacuum alone. Thus to leading order in their effect on the gravitational field, the quantum states of the matter and metric fluctuations must be de Sitter invariant.Comment: 12 pages, no figures, typos corrected and some clarifying comments added, version accepted by Phys. Rev.

Isolated Horizon, Killing Horizon and Event Horizon

We consider space-times which in addition to admitting an isolated horizon also admit Killing horizons with or without an event horizon. We show that an isolated horizon is a Killing horizon provided either (1) it admits a stationary neighbourhood or (2) it admits a neighbourhood with two independent, commuting Killing vectors. A Killing horizon is always an isolated horizon. For the case when an event horizon is definable, all conceivable relative locations of isolated horizon and event horizons are possible. Corresponding conditions are given.Comment: 14 pages, Latex, no figures. Some arguments tightened. To appear in Class. Quant. Gra

On Cosmological Implication of the Trace Anomaly

We establish a connection between the trace anomaly and a thermal radiation in the context of the standard cosmology. This is done by solving the covariant conservation equation of the stress tensor associated with a conformally invariant quantum scalar field. The solution corresponds to a thermal radiation with a temperature which is given in terms of a cut-off time excluding the spacetime regions very close to the initial singularity. We discuss the interrelation between this result and the result obtained in a two-dimensional schwarzschild spacetime.Comment: 8 pages, no figure

Quantum Hamiltonian for gravitational collapse

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion operators presented in an earlier work, form a framework for studying gravitational collapse in quantum gravity. We describe a setting for its numerical implementation, and discuss some conceptual issues associated with quantum dynamics in a partial gauge fixing.Comment: 17 pages, published version (minor changes