Complex lapse, complex action and path integrals

Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action which generates both the usual Lorentzian theory and its Riemannian analogue, and in particular allows a change of signature between the two. The action and variational equations are manifestly well defined in the Hamiltonian representation, with the momentum fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provides a unified basis for a path-integral quantum theory of gravity involving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunnelling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunnelling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.Comment: 12 pages, Te

M{\o}ller Energy for the Kerr-Newman metric

The energy distribution in the Kerr-Newman space-time is computed using the M{\o}ller energy-momentum complex. This agrees with the Komar mass for this space-time obtained by Cohen and de Felice. These results support the Cooperstock hypothesis.Comment: 8 pages, 1 eps figure, RevTex, accepted for publication in Mod. Phys. Lett.

The Magnetization of Cu_2(C_5H_{12}N_2)_2Cl_4 : A Heisenberg Spin Ladder System

We study the magnetization of a Heisenberg spin ladder using exact diagonalization techniques, finding three distinct magnetic phases. We consider the results in relation to the experimental behaviour of the new copper compound Cu_2(C_5H_{12}N_2)_2Cl_4 and deduce that the compound is well described by such a model with a ratio of `chain' to `rung' bond strengths (J/J^\prime) of the order of 0.2, consistent with results from the magnetic susceptibility. The effects of temperature, spin impurities and additional diagonal bonds are presented and we give evidence that these diagonal bonds are indeed of a ferromagnetic nature.Comment: Latex file (4 pages), related figures (encapsulated postscript) appende

The suppression of superconductivity in MgCNi3 by Ni-site doping

The effects of partial substitution of Cu and Co for Ni in the intermetallic perovskite superconductor MgCNi3 are reported. Calculation of the expected electronic density of states suggests that electron (Cu) and hole (Co) doping should have different effects. For MgCNi3-xCux, solubility of Cu is limited to approximately 3% (x = 0.1), and Tc decreases systematically from 7K to 6K. For MgCNi3-xCox, solubility of Co is much more extensive, but bulk superconductivity disappears for Co doping of 1% (x = 0.03). No signature of long range magnetic ordering is observed in the magnetic susceptibility of the Co doped material.Comment: submitted, Solid State Communication

Energy distribution in a BTZ black hole spacetime

We evaluate the energy distribution associated with the (2+1)-dimensional rotating BTZ black hole. The energy-momentum complexes of Landau-Lifshitz and Weinberg are employed for this computation. Both prescriptions give exactly the same form of energy distribution. Therefore, these results provide evidence in support of the claim that, for a given gravitational background, different energy-momentum complexes can give identical results in three dimensions, as it is the case in four dimensions.Comment: 16 pages, LaTeX; v2: comments, clarifications and references added, version to appear in Int.J.Mod.Phys.

Kerr black holes in horizon-generating form

New coordinates are given which describe non-degenerate Kerr black holes in dual-null foliations based on the outer (or inner) horizons, generalizing the Kruskal form for Schwarzschild black holes. The construction involves an area radius for the transverse surfaces and a generalization of the Regge-Wheeler radial function, both functions of the original radial coordinate only.Comment: 4 revtex4 page

Periodic Solutions of the Einstein Equations for Binary Systems

This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with outgoing waves. A variational principle is found which has the power to provide an accurate estimate of the relationship between the mass and angular momentum of the system, the masses and angular momenta of the components, the rotational frequency of the frame of reference in which the system is periodic, the frequency of the periodicity of the system, and the amplitude and phase of each multipole component of gravitational radiation. Examination of the boundary terms of the variational principle leads to definitions of the effective mass and effective angular momentum of a periodic geometry which capture the concepts of mass and angular momentum of the source alone with no contribution from the gravitational radiation. These effective quantities are surface integrals in the weak-field zone which are independent of the surface over which they are evaluated, through second order in the deviations of the metric from flat space.Comment: 18 pages, RevTeX 3.0, UF-RAP-93-1

Construction and enlargement of traversable wormholes from Schwarzschild black holes

Analytic solutions are presented which describe the construction of a traversable wormhole from a Schwarzschild black hole, and the enlargement of such a wormhole, in Einstein gravity. The matter model is pure radiation which may have negative energy density (phantom or ghost radiation) and the idealization of impulsive radiation (infinitesimally thin null shells) is employed.Comment: 22 pages, 7 figure

Energy Associated with Schwarzschild Black Hole in a Magnetic Universe

In this paper we obtain the energy distribution associated with the Ernst space-time (geometry describing Schwarzschild black hole in Melvin's magnetic universe) in Einstein's prescription. The first term is the rest-mass energy of the Schwarzschild black hole, the second term is the classical value for the energy of the uniform magnetic field and the remaining terms in the expression are due to the general relativistic effect. The presence of the magnetic field is found to increase the energy of the system.Comment: RevTex, 8 pages, no figures, a few points are clarified, to appear in Int. J. Mod. Phys. A. This paper is dedicated to Professor G. F. R. Ellis on the occasion of his 60th birthda