Whether a string has rotation and shear can be investigated by an anology with a congruence of point particles. Rotation and shear involve first covariant spacetime derivatives of a vector field and, because the metric stress tensor for both the point particle and the string have no such derivatives, the best vector fields can be identified by requiring the conservation of metric stress. It is ...

General relativity (GR) is a covariant theory of gravity on curved spacetime (general covariance) which, however, denies a covariant Hamiltonian. Most alternative works of gravity on flat spacetime present non-covariant Lagrangians which treat time t as a parameter entirely distinct from the spatial coordinates. A covariant formulation would require that space and time be considered as entirely...

For there is always a wrong sign in the mass of graviton in the so-called perturbation expansion approximation of both Minkowski and de Sitter spacetimes, the existence of gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. We try another way to start from the assumption that the gravitational wave equation should be both general covariant and conformal invariant...

A closed bosonic string in a curved affine--metric spacetime is considered as an example of dissipative quantum field theory. The eonformal anomaly of the trace of the energy--momentum tensor for the string on the affine--metrie manifold is investigated. The two-loop metric beta function for the two-dimensional nonlinear dissipative sigma model is calculated. Examples of nonflat manifolds that ...

In conventional Maxwell–Lorentz electrodynamics, the propagation of light is influenced by the metric, not, however, by the possible presence of a torsion T . Still the light can feel torsion if the latter is coupled nonminimally to the electromagnetic field F by means of a supplementary Lagrangian of the type ∼ l2T 2 F 2 (l = coupling constant). Recently Preuss suggested a specific nonminimal ...

Kruskal’s extension solves the problem of the arrow of time of the “Schwarzschild solution” through combining two Hilbert manifolds by a singular coordinate transformation. We discuss the implications for the singularity problem and the definition of the mass point. The analogy set by Rindler between the Kruskal metric and the Minkowski spacetime is investigated anew. The question is answered, ...

We present a detailed examination of the variational principle for metric general relativity as applied to a " quasilocal " spacetime region M (that is, a region that is both spatially and temporally bounded). Our analysis relies on the Hamiltonian formulation of general relativity, and thereby assumes a foliation of M into spacelike hypersurfaces Σ. We allow for near complete generality in the...

In abstract Yang–Mills theory the standard instanton construction relies on the Hodge star having real eigenvalues which makes it inapplicable in the Lorentzian case. We show that for the affine connection an instanton-type construction can be carried out in the Lorentzian setting. The Lorentzian analogue of an instanton is a spacetime whose connection is metric compatible and Riemann curvature...

For a black hole’s spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the...