The method of adjoint operators and a symmetry operator for the Maxwell equations in type-D vacuum backgrounds

2001 ◽  
Vol 42 (1) ◽  
pp. 368-375 ◽  
Author(s):  
Gilberto Silva-Ortigoza
Keyword(s):  
Maxwell Equations ◽  
Symmetry Operator ◽  
Type D ◽  
Adjoint Operators

scholarly journals A Class of Solutions of Einstein-Maxwell Equations with the Cosmological Constant

1974 ◽  
Vol 64 ◽  
pp. 188-190
Author(s):  
J. F. Plebański
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Maxwell Equations ◽  
Type D ◽  
The Common ◽  
Image Position

Working in the signature (+ + + -) and units such that G = 1 = c, it was found a solution of Einstein-Maxwell equations with λ (without current and pseudo-current). In real coordinates xμ=(p, σ, q, τ) the solutions is: (1)(2) where (3) is pure imaginary; in (1) ‘d’ denotes the external differential]. Not all constants m0, n0, e0, g0, b, ∊, λ are physically significant: by re-scaling coordinates ∊ can be made equal to +1,0, or −1. The solution is of the type D: the double Debever-Penrose vectors (4) have the common complex expansion Z = (q + ip)-1. Among C(a)'s only C(3) given by: (5) is in general ≠0. The invariants of the electromagnetic field are: (6)

Complex recurrent space-times

1972 ◽  
Vol 327 (1569) ◽  
pp. 229-249 ◽  
Keyword(s):  
Maxwell Equations ◽  
Symmetric Spaces ◽  
Null Vector ◽  
Petrov Type ◽  
Algebraic Form ◽  
Type D ◽  
Conformally Recurrent ◽  
Petrov Type D ◽  
Arbitrary Curvature ◽  
Plane Gravitational Waves

It is shown that the complex recurrent space-times are of Petrov type D or N. The spaces of type D are non-empty and decomposable into the product of two 2-dimensional spaces of arbitrary curvature, the recurrence vector being necessarily real. It is established that the problem of determining the type N complex recurrent spaces is equivalent to that of determining the spaces of type N admitting a recurrent null vector field. A coordinate system is given in which the metric of such spaces is determined up to three arbitrary functions and a constant. The spaces fall into four invariant classes according to the permitted algebraic form of the Ricci tensor. The Einstein-Maxwell equations are solved, the solutions obtained providing examples for three of the classes. It seems that the remaining class cannot contain any physically reasonable solutions of Einstein’s equations. The general metric of the complex recurrent space of Petrov type N with recurrence vector proportional to the principal null vector of the Weyl tensor is also given and some of its properties are discussed. The space of plane gravitational waves admitting a singular electromagnetic field is the only physically significant space-time of this class. The conformally recurrent spaces and the conformal symmetric spaces are also determined.

On colliding waves that develop time–like singularities: a new class of solutions of the Einstein–Maxwell equations

1987 ◽  
Vol 410 (1839) ◽  
pp. 311-336 ◽  
Keyword(s):  
Maxwell Equations ◽  
Three Dimensional ◽  
Flat Space ◽  
Conformally Flat ◽  
Schwarzschild Solution ◽  
New Class ◽  
Type D ◽  
New Family ◽  
Static Black Hole ◽  
Petrov Type D

Solutions of the Einstein–Maxwell equations are found that provide generalizations of a solution discovered by Bell and Szekeres, which represents the collision of impulsive gravitational waves coupled with electromagnetic shock-waves in a conformally flat space-time. Starting with the Bell–Szekeres solution in a form more general than their original one (though equivalent to it) and applying to it a so-called Ehlers transformation, we obtain a new family of Petrov type-D space-times in which horizons form and subsequently two-dimensional time-like singularities develop. A second solution provides a generalization of the Bell–Szekeres solution in the same way as the axisymmetric distorted static black-hole solutions provide a generalization of the Schwarzschild solution. This second solution also forms a horizon but the time-like singularity that develops is three-dimensional. The mathematical theory that is developed seems specially adapted to the solution of these and related problems.

The Type D Construct

2014 ◽  
Vol 30 (4) ◽  
pp. 283-288 ◽  
Author(s):  
Gesine Grande ◽  
Matthias Romppel ◽  
Matthias Michal ◽  
Elmar Brähler
Keyword(s):  
Social Functioning ◽  
Negative Affectivity ◽  
Population Based ◽  
Type D Personality ◽  
Social Orientation ◽  
German Population ◽  
Social Competencies ◽  
Social And Emotional ◽  
Type D ◽  
Worse Prognosis

The interaction of negative affectivity (NA) and social inhibition (SI), known as the Type D personality, is associated with a worse prognosis in cardiac patients. Until now, causal models have been speculative, and this is partly due to a lack of clarity related to the validity of SI, its role in emotion regulation, and the postulated independence of social and emotional functioning. To examine the construct validity of the Type D personality, we analyzed associations of NA and SI with different measures of affectivity, social anxiety, and social competencies in a German population-based representative sample (n = 2,495). Both NA and SI were associated with all other measures of social functioning and negative affect (all rs > .30) and showed considerable cross-loadings (NA: a 1 = .39, a 2 = .63; SI: a1 = .73 and a2 = .34) in a two-factor solution with the factors labeled as Social Functioning and Negative Affectivity. The SI subscale did not properly differentiate between social fears and social competencies, which emerged as rather different aspects of social functioning. Further studies should examine the effect of broader dimensions of social orientation and competencies and their interaction with NA on cardiac prognosis.

Illness Perception and Its Changes During Six Months After Cardiac Rehabilitation

2019 ◽  
Vol 26 (3) ◽  
pp. 90-100
Author(s):  
Justė Lukoševičiūtė ◽  
Kastytis Šmigelskas
Keyword(s):  
New York ◽  
Social Factors ◽  
Nyha Class ◽  
Illness Perception ◽  
Heart Association ◽  
Class Iii ◽  
Cognitive Representations ◽  
Coronary Syndrome ◽  
Type D ◽  
New York Heart Association

Abstract. Illness perception is a concept that reflects patients' emotional and cognitive representations of disease. This study assessed the illness perception change during 6 months in 195 patients (33% women and 67% men) with acute coronary syndrome, taking into account the biological, psychological, and social factors. At baseline, more threatening illness perception was observed in women, persons aged 65 years or more, with poorer functional capacity (New York Heart Association [NYHA] class III or IV) and comorbidities ( p < .05). Type D personality was the only independent factor related to more threatening illness perception (βs = 0.207, p = .006). At follow-up it was found that only self-reported cardiovascular impairment plays the role in illness perception change (βs = 0.544, p < .001): patients without impairment reported decreasing threats of illness, while the ones with it had a similar perception of threat like at baseline. Other biological, psychological, and social factors were partly associated with illness perception after an acute cardiac event but not with perception change after 6 months.

Does Type D predict vital exhaustion in heart failure patients?

2006 ◽  
Author(s):  
H. J. Michielsen ◽  
O. R. F. Smith ◽  
A. A. Schiffer ◽  
J. Denollet
Keyword(s):  
Heart Failure ◽  
Heart Failure Patients ◽  
Vital Exhaustion ◽  
Type D
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