Modified dispersion relations and black hole physics

A modified formulation of energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such modification will give corrections to both the temperature and the entropy of black holes. In particular this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaching the Planck scale. It can prevent black holes from total evaporation, as a result providing a plausible mechanism to treat the remnant of black holes as a candidate for dark matter.Comment: 4 pages, Revtex. Final version to appear in PR

Equilibrium configurations of two charged masses in General Relativity

An asymptotically flat static solution of Einstein-Maxwell equations which describes the field of two non-extreme Reissner - Nordstr\"om sources in equilibrium is presented. It is expressed in terms of physical parameters of the sources (their masses, charges and separating distance). Very simple analytical forms were found for the solution as well as for the equilibrium condition which guarantees the absence of any struts on the symmetry axis. This condition shows that the equilibrium is not possible for two black holes or for two naked singularities. However, in the case when one of the sources is a black hole and another one is a naked singularity, the equilibrium is possible at some distance separating the sources. It is interesting that for appropriately chosen parameters even a Schwarzschild black hole together with a naked singularity can be "suspended" freely in the superposition of their fields.Comment: 4 pages; accepted for publication in Phys. Rev.

Energy dissipation in wave propagation in general relativistic plasma

Based on a recent communication by the present authors the question of energy dissipation in magneto hydrodynamical waves in an inflating background in general relativity is examined. It is found that the expanding background introduces a sort of dragging force on the propagating wave such that unlike the Newtonnian case energy gets dissipated as it progresses. This loss in energy having no special relativistic analogue is, however, not mechanical in nature as in elastic wave. It is also found that the energy loss is model dependent and also depends on the number of dimensions.Comment: 12 page

The structure of black hole magnetospheres. I. Schwarzschild black holes

We introduce a multipolar scheme for describing the structure of stationary, axisymmetric, force-free black-hole magnetospheres in the ``3+1'' formalism. We focus here on Schwarzschild spacetime, giving a complete classification of the separable solutions of the stream equation. We show a transparent term-by-term analogy of our solutions with the familiar multipoles of flat-space electrodynamics. We discuss electrodynamic processes around disk-fed black holes in which our solutions find natural applications: (a) ``interior'' solutions in studies of the Blandford-Znajek process of extracting the hole's rotational energy, and of the formation of relativistic jets in active galactic nuclei and ``microquasars'', and, (b) ``exterior'' solutions in studies of accretion disk dynamos, disk-driven winds and jets. On the strength of existing numerical studies, we argue that the poloidal field structures found here are also expected to hold with good accuracy for rotating black holes, except for maximum possible rotation rates. We show that the closed-loop exterior solutions found here are not in contradiction with the Macdonald-Thorne theorem, since these solutions, which diverge logarithmically on the hole's horizon $\cal H$, apply only to those regions which exclude $\cal H$.Comment: 6 figures. Accepted for publication by MNRA

Local C-Reactive Protein Expression in Obliterative Lesions and the Bronchial Wall in Posttransplant Obliterative Bronchiolitis

The local immunoreactivity of C-reactive protein (CRP) was studied in a heterotopic porcine model of posttranplant obliterative bronchiolitis (OB). Bronchial allografts and control autografts were examined serially 2–28 days after subcutaneous transplantation. The autografts stayed patent. In the allografts, proliferation of inflammatory cells (P < .0001) and fibroblasts (P = .02) resulted in occlusion of the bronchial lumens (P < .01). Influx of CD4+ (P < .001) and CD8+ (P < .0001) cells demonstrated allograft immune response. CRP positivity simultaneously increased in the bronchial walls (P < .01), in macrophages, myofibroblasts, and endothelial cells. Local CRP was predictive of features characteristic of OB (R = 0.456–0.879, P < .05−P < .0001). Early obliterative lesions also showed CRP positivity, but not mature, collagen-rich obliterative plugs (P < .05). During OB development, CRP is localized in inflammatory cells, myofibroblasts and endothelial cells probably as a part of the local inflammatory response

Black holes in which the electrostatic or scalar equation is solvable in closed form

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerated horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordstrom black holes in higher dimensions.Comment: 20 pages, no figur

An Action for Black Hole Membranes

The membrane paradigm is the remarkable view that, to an external observer, a black hole appears to behave exactly like a dynamical fluid membrane, obeying such pre-relativistic equations as Ohm's law and the Navier-Stokes equation. It has traditionally been derived by manipulating the equations of motion. Here we provide an action formulation of this picture, clarifying what underlies the paradigm, and simplifying the derivations. Within this framework, we derive previous membrane results, and extend them to dyonic black hole solutions. We discuss how it is that an action can produce dissipative equations. Using a Euclidean path integral, we show that familiar semi-classical thermodynamic properties of black holes also emerge from the membrane action. Finally, in a Hamiltonian description, we establish the validity of a minimum entropy production principle for black holes.Comment: LaTeX, 30 Pages, minor editorial change

Thermal Control of Spin Excitations in the Coupled Ising-Chain Material RbCoCl₃

We have used neutron spectroscopy to investigate the spin dynamics of the quantum (S = 1/2) antiferromagnetic Ising chains in RbCoCl3. The structure and magnetic interactions in this material conspire to produce two magnetic phase transitions at low temperatures, presenting an ideal opportunity for thermal control of the chain environment. The high-resolution spectra we measure of two-domain-wall excitations therefore characterize precisely both the continuum response of isolated chains and the "Zeeman-ladder" bound states of chains in three different effective staggered fields in one and the same material. We apply an extended Matsubara formalism to obtain a quantitative description of the entire dataset, Monte Carlo simulations to interpret the magnetic order, and finite-temperature density-matrix renormalization-group calculations to fit the spectral features of all three phases

Region of magnetic dominance near a rotating black hole

This is a brief contribution in which a simplified criterion of the relevance of the test-particle approximation describing motion of material near a magnetized black hole is discussed. Application to processes of the dissipative collimation of astronomical jets (as proposed by de Felice and Curir, 1992) is mentioned.Comment: 11 pages, to appear in General Relativity and Gravitation, also available (with additional illustrations) at http://otokar.troja.mff.cuni.cz/user/karas/au_www/karas/papers.ht