Thermodynamics, entropy, and stability of thin shells in 2+1 flat spacetimes

The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional flat spacetime is analyzed. Inside the ring the spacetime is flat, whereas outside it is conical flat. The first law of thermodynamics applied to the thin shell leads to a shell's entropy which is a function of its mass alone. Two simple forms for this mass function are given leading to two different expressions for the entropy. The equations of thermodynamic stability are analyzed resulting in certain allowed regions for the free parameters. Contrary to the usual (3+1)-dimensional case this shell's entropy is purely classic, as the only fundamental constant that enters into the problem is the (2+1)-dimensional gravitational constant $G_3$, which has units of inverse mass.Comment: 4 page

Procinura, P. aemula

Number of Pages: 4Integrative BiologyGeological Science

Spontaneously broken symmetry restoration of quantum fields in the vicinity of neutral and electrically charged black holes

We consider the restoration of a spontaneously broken symmetry of an interacting quantum scalar field around neutral, i.e., Schwarzschild, and electrically charged, i.e., Reissner-Nordstr\"om, black holes in four dimensions. This is done through a semiclassical self-consistent procedure, by solving the system of non-linear coupled equations describing the dynamics of the background field and the vacuum polarization. The black hole at its own horizon generates an indefinitely high temperature which decreases to the Hawking temperature at infinity. Due to the high temperature in its vicinity, there forms a bubble around the black hole in which the scalar field can only assume a value equal to zero, a minimum of energy. Thus, in this region the symmetry of the energy and the field is preserved. At the bubble radius, there is a phase transition in the value of the scalar field due to a spontaneous symmetry breaking mechanism. Indeed, outside the bubble radius the temperature is low enough such that the scalar field settles with a nonzero value in a new energy minimum, indicating a breaking of the symmetry in this outer region. Conversely, there is symmetry restoration from the outer region to the inner bubble close to the horizon. Specific properties that emerge from different black hole electric charges are also noteworthy. It is found that colder black holes, i.e., more charged ones, have a smaller bubble length of restored symmetry. In the extremal case the bubble has zero length, i.e., there is no bubble. Additionally, for colder black holes, it becomes harder to excite the quantum field modes, so the vacuum polarization has smaller values. In the extremal case, the black hole temperature is zero and the vacuum polarization is never excited.Comment: 16 pages, 4 figure

Development of subminiature multi-sensor hot-wire probes

Limitations on the spatial resolution of multisensor hot wire probes have precluded accurate measurements of Reynolds stresses very near solid surfaces in wind tunnels and in many practical aerodynamic flows. The fabrication, calibration and qualification testing of very small single horizontal and X-array hot-wire probes which are intended to be used near solid boundaries in turbulent flows where length scales are particularly small, is described. Details of the sensor fabrication procedure are reported, along with information needed to successfully operate the probes. As compared with conventional probes, manufacture of the subminiature probes is more complex, requiring special equipment and careful handling. The subminiature probes tested were more fragile and shorter lived than conventional probes; they obeyed the same calibration laws but with slightly larger experimental uncertainty. In spite of these disadvantages, measurements of mean statistical quantities and spectra demonstrate the ability of the subminiature sensors to provide the measurements in the near wall region of turbulent boundary layers that are more accurate than conventional sized probes

Litigating State Interests: Attorneys General as Amici

An important strain of federalism scholarship locates the primary value of federalism in how it carves up the political landscape, allowing groups that are out of power at the national level to flourish—and, significantly, to govern—in the states. On that account, partisanship, rather than a commitment to state authority as such, motivates state actors to act as checks on federal power. Our study examines partisan motivation in one area where state actors can, and do, advocate on behalf of state power: the Supreme Court. We compiled data on state amicus filings in Supreme Court cases from the 1979–2013 Terms and linked it up with data on the partisanship of state attorneys general (AGs). Focusing only on merits-stage briefs, we looked at each AG’s partisan affiliation and the partisanship of the AGs who either joined, or explicitly opposed, her briefs. If partisanship drives amicus activity, then we should see a strong negative relationship between the partisanship of AGs opposing each other and a strong positive relationship between those who cosign briefs. What we found was somewhat surprising. States agreed far more often than they disagreed, and—until recently—most multistate briefs represented bipartisan, not partisan, coalitions of AGs. Indeed, for the first twenty years of our study, the cosigners of these briefs were generally indistinguishable from a random sampling of AGs then in office. The picture changes after 2000, when the coalitions of cosigners become decidedly more partisan, particularly among Republican AGs. The partisanship picture is also different for the 6% of cases in which different states square off in opposing briefs. In those cases, AGs do tend to join together in partisan clusters. Here, too, the appearance of partisanship becomes stronger after the mid-1990s

BLACK HOLES IN THREE-DIMENSIONAL DILATON GRAVITY THEORIES

Three dimensional black holes in a generalized dilaton gravity action theory are analysed. The theory is specified by two fields, the dilaton and the graviton, and two parameters, the cosmological constant and the Brans-Dicke parameter. It contains seven different cases, of which one distinguishes as special cases, string theory, general relativity and a theory equivalent to four dimensional general relativity with one Killing vector. We study the causal structure and geodesic motion of null and timelike particles in the black hole geometries and find the ADM masses of the different solutions.Comment: 19 pages, latex, 4 figures as uuencoded postscript file