Martin Scholtz

On asymptotically flat solutions of Einstein's equations periodic in time: II. Spacetimes with scalar-field sources

We extend the work in our earlier paper (Biˇ´ ak J et al 2010 Class. Quantum Grav. 27 055007 ) to show that time-periodic, asymptotically flat solutions of the Einstein equations analytic at I, whose source is one of a range of scalarfield models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptotically flat solutions analytic at I, the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.

On asymptotically flat solutions of Einstein's equations periodic in time: I. Vacuum and electrovacuum solutions

By an argument similar to that of Gibbons and Stewart (1984 Absence of asymptotically flat solutions of Einsteins equations which are periodic and empty near infinity Classical General Relativity (London, 1983) ed W Bonnor, J N Islam and M A H Callum (Cambridge: Cambridge University Press) pp 77–94), but in a different coordinate system and less restrictive gauge, we show that any weakly asymptotically simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary.

Numerical investigation of scaling regimes in a model of an anisotropically advected vector field

Influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field theoretic renormalization group. Turbulent fluctuations of the velocity field are taken to have the Gaussian statistics with zero mean and defined noise with finite correlations in time. It is shown that stability of the inertial-range scaling regimes in the three-dimensional case is not destroyed by anisotropy, but the corresponding stability of the two-dimensional system can be corrupted by the presence of anisotropy. A borderline dimension dc below which the stability of the scaling regime is not present is calculated as a function of anisotropy parameters.

Kerr-Newman black hole in the formalism of isolated horizons

The near horizon geometry of general black holes in equilibrium can be conveniently characterized in the formalism of weakly isolated horizons in the form of the Bondi-like expansions (Krishnan B, Class.\ Quantum Grav.\ 29, 205006, 2012). While the intrinsic geometry of the Kerr-Newman black hole has been extensively investigated in the weakly isolated horizon framework, the off-horizon description in the Bondi-like system employed by Krishnan has not been studied. We extend Krishnans work by explicit, non-perturbative construction of the Bondi-like tetrad in the full Kerr-Newman spacetime. Namely, we construct the Bondi-like tetrad which is parallelly propagated along a nontwisting null geodesic congruence transversal to the horizon and provide all Newman-Penrose scalars associated with this tetrad. This work completes the description of the Kerr-Newman spacetime in the formalism of weakly isolated horizons and is a starting point for the investigation of deformed black holes.

COMBINED EFFECTS OF SMALL SCALE ANISOTROPY AND COMPRESSIBILITY ON ANOMALOUS SCALING OF A PASSIVE SCALAR

Model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance

Meissner effect for weakly isolated horizons

\propto \delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}

On the implications of the Bekenstein bound for black hole evaporation

is studied by using the field theoretic renormalization group and the operator product expansion. The inertial-range stability of the corresponding scaling regime is established. The anomalous scaling of the single-time structure functions is studied and the corresponding anomalous exponents are calculated. Their dependence on the compressibility parameter and anisotropy parameters is analyzed. It is shown that, as in the isotropic case, the presence of compressibility leads to the decreasing of the critical dimensions of the important composite operators, i.e., the anomalous scaling is more pronounced in the compressible systems. All calculations are done to the first order in

On the Bondi mass of Maxwell–Klein–Gordon spacetimes

\epsilon

Quasiparticle picture from the Bekenstein bound

.

A gravitational energy–momentum and the thermodynamic description of gravity

Black holes are important astrophysical objects describing an end state of stellar evolution, which are observed frequently. There are theoretical predictions that Kerr black holes with high spins expel magnetic �elds. However, Kerr black holes are pure vacuum solutions, which do not include accretion disks, and additionally previous investigations are mainly limited to weak magnetic �elds. We prove for the �rst time in full general relativity that generic rapidly spinning black holes including those deformed by accretion disks still expel even strong magnetic �elds. Analogously to a similar property of superconductors, this is called Meissner e�ect.