Killing vectors of vacuum space times and electromagnetic four potentials

A conjecture is formulated about the connection between isometries of vacuum space times and the existence of corresponding space times with electromagnetic fields for which the structure of electromagnetic four potentials is readily predicted. One example is presented showing how this conjecture works, three others are only commented.     

Inclusion complexes of proteins: Interaction of cyclodextrins with peptides containing aromatic amino acids studied by competitive spectrophotometry

The stability constants were measured of inclusion complexes formed from aromatic amino acids and their oligopeptides with - and-cyclodextrin, hydroxypropyl-cyclodextrin, and partially methylated-cyclodextrin. The method of competitive spectrophotometry withp-nitrophenol as a competing reagent was used, and measurements were made at pH 7.4-Cyclodextrin formed complexes of higher stability than the other hosts. The stability of complexes of oligopeptides containing L-phenylalanine was invariably higher than that of L-phenylalanine itself. A model for interaction of proteins with cyclodextrins is proposed, in which the most stable complexes are formed when the native functional form of proteins is unfolded and the nonpolar residues that are buried inside the structure are exposed to water. The complexation of the unfolded structure favors its formation; thus thermal denaturation of proteins is easier in the presence of cyclodextrins. On the other hand, this complexation prevents the intermolecular association of unfolded structures by noncovalent hydrophobic bonding between the exposed nonpolar residues; furthermore, the unfolded complexed forms may revert to the native functional form. This prevention of intermolecular association may explain the stabilizing effect of cyclodextrins on solutions of proteins: a return to the native form is achieved more easily from the complexed, unfolded form than from the unfolded, aggregated forms.Dedicated to Professor József Szejtli.     

On the analogy between the plane and the spherical solutions of einstein equations in the vacuum

It is shown that some simple and interesting analogy between the plane and the spherical solutions of Einstein gravitational equations in vacuum exists. This analogy is applied to the solutions of some problems of motions in the plane gravitational field.The authors thank I. Kraval for performing some calculations.     

Letter: A Cylindrically Symmetric Solution in Einstein-Maxwell-Dilaton Gravity

We consider the existence of Einstein-Maxwell-dilaton plus fluid systems for the case of stationary cylindrically symmetric spacetimes. An exact inhomogeneous -order solution is found, where the parameter parametrizes the non-minimally coupled electromagnetic field. Some its physical attributes are investigated and a connection with the already known Gödel-type solution is given. It is shown that our solution also survives in the string-inspired charged gravity framework. We find that a magnetic field has positive influence on the chronology violation unlike the dilaton influence.     

Charged perfect fluid and scalar field coupled to gravity

Charged perfect fluid with vanishing Lorentz force and massless scalar field is studied for the case of stationary cylindrically symmetric spacetime. The scalar field can depend both on radial and longitudinal coordinates. Solutions are found and classified according to scalar field gradient and magnetic field relationship. Their physical and geometrical properties are examined and discussion of particular cases, directly generalizing Gödel-type spacetimes, is presented.     

New Einstein-Maxwell fields of Levi-Civita’s type

The method based on the Horsky-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found explicitly. Some of the obtained classes are quite new. Radial geodesic motion in constructed space-times is discussed and graphically illustrated in the Appendix.     

Conservation laws in general relativity

In recent years an increased interest in General Relativity Theory (GRT) has been apparent among theoretical physicists, mathematicians, astronomers and geophysicists. At the same time, the necessity of rinding a final and generally satisfactory solution of a very important problem, namely that of conservation laws, has become topical. Surprising difficulties have been encountered in the attempt to transfer these concepts to General Relativity Theory. In the course of a few years a comprehensive literature has resulted and now the time is ripe for a thorough summary of the results attained so far.The authors would like to thank Dr. P. Burcev from the Dept of Theoretical Physics, J. E. Purkyn University in Brno, and Dr. K. Kucha from the Dept. of Theoretical Physics, Charles University in Prague, for their permanent interest in this work and for valuable discussions.     

On the Rayski formulation of the laws of conservation in general relativity

The Rayski method is used to calculate the energy of a static and spherically symmetrical gravitational system.In conclusion, the author thanks Dr. P. Burcev and Dr. K. Kucha for kindly pointing out some shortcomings which could thus be eliminated in time.     

Geometric interpretation of chronometric invariants in general theory of relativity

The geometric interpretation of Zelmanov's Chronometric invarians is given and their conection to observable quantities as well as the connection of Zelmanov's approach to the generally covariant Dehnen's method is found.The authors would like to thank Dr. J. Biák from the Dept. of Theoretical Physics, Charles University in Prague, for discussion and critical remarks.