Related papers: Hessian Tensor and Standard Static Space-times
Irreducible bilinear tensorial concomitants of an arbitrary complex antisymmetric valence-2 tensor are derived in four-dimensional spacetime. In addition these bilinear concomitants are symmetric (or antisymmetric), self-dual (or…
In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling…
We present in this paper a covariant quantization of the ``massive'' vector field on de Sitter (dS) space based on analyticity in the complexified pseudo-Riemanian manifold. The correspondence between unitary irreducible representations of…
We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of $\eta$-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterising them in terms of generalised Killing spinors. We propose…
In a space-time $M$ with a Killing vector field $\xi^a$ which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of $\xi^a$ gives a 3-dimension space $S$. Besides the symmetry-reduced action from that…
We discuss the pairs of quadratic integrals of motion belonging to the $n$-dimensional space of independent integrals of motion in involution, that provide integrability of the corresponding Hamiltonian equations of motion by quadratures.…
In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the…
We use a Hamiltonian version of the semiclassical Einstein equation to study classical gravity coupled to a quantum scalar field with potential in spherical symmetry. The system is defined by effective constraints where the matter terms are…
The notion of uniform and/or constant tensor fields of rank $>0$ is incompatible with general curved spacetimes. This work considers the consequences of certain tensor-valued coefficients for Lorentz violation in the Standard-Model…
We analyse a stationary, cylindrically symmetric spacetime endowed with an intrinsic helical twist, $ds^{2} = -dt^{2} + dr^{2} + r^{2} d\phi^{2} + (dz + \omega\, r\,d\phi)^{2}$. Solving the Einstein equations exactly yields an anisotropic…
We consider compact hypersurfaces in an $(n+1)$-dimensional either Riemannian or Lorentzian space $N^{n+1}$ endowed with a conformal Killing vector field. For such hypersurfaces, we establish an integral formula which, especially in the…
We discuss the physics of interacting tensor fields and particles living in $M=\mathrm{S0}(1,4)/\mathrm{S0} (1,3)\simeq\mathbb{R}\times S^{3}$ a submanifold of $\mathring{M}=(\mathbb{R}^{5},\boldsymbol{\mathring{g}})$, where…
In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on these spacetimes. Central to our analysis…
We continue a previous analysis of the covariant Hamiltonian symplectic structure of General Relativity for spatially bounded regions of spacetime. To allow for near complete generality, the Hamiltonian is formulated using any fixed…
The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the…
The components of the renormalized quantum Energy-Momentum tensor for a massive vector field coupled to the gravitational field configuration of a static Black-String are analytically evaluated using the Schwinger-DeWitt approximation. The…
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
A non-minimal photon-torsion axial coupling in the quantum electrodynamics (QED) framework is considered. The geometrical optics in Riemannian-Cartan spacetime is considering and a plane wave expansion of the electromagnetic vector…
Killing tensor fields have been thought of as describing hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Many problems in classical mechanics can be…
We characterize the $2$-Killing vector fields on a multiply twisted product manifold, with a special view towards generalized spacetimes. More precisely, we determine the nonlinear differential equations that completely describe them and…