Related papers: Timelike Killing Fields and Relativistic Statistic…
In the first part of this talk, I consider some exact string solutions in curved spacetimes. In curved spacetimes with a Killing vector (timelike or spacelike), the string equations of motion and constraints are reduced to the Hamilton…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the…
Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic…
Using the relativistic Fermat's principle, we establish a bridge between stationary-complete manifolds which satisfy the observer-manifold condition and pre-Randers metrics, namely, Randers metrics without any restriction on the one-form.…
We consider a free Dirac field in flat spacetime and we derive the representation of the Minkowski vacuum as an element of the Rindler-Fock space. We also compute the statistical operator obtained by tracing away the left wedge. We detail…
An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of…
We study metric solutions of Einstein-anti-Maxwell theory admitting Killing spinors. The analogue of the IWP metric which admits a space-like Killing vector is found and is expressed in terms of a complex function satisfying the wave…
We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface…
We analyse a rotating regular black hole with asymptotically Minkowski core. This Kerr-like geometry possesses the full "Killing tower" of nontrivial Killing tensor, Killing-Yano tensor, and principal tensor. The Hamilton-Jacobi equation,…
Statistical entropies of a general relativistic ideal gas obeying Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics are calculated in a general axisymmetry space-time of arbitrary dimension. This general formation can be used to…
In this manuscript we provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a background curved spacetime. Namely, using Fermi normal coordinates, we identify an inner product…
We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Second, we show that positive Bartnik mass minimizers embed…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
Motivated by supersymmetry methods in general relativity, we study four-dimensional Lorentzian space-times with a complex Dirac spinor field satisfying a Killing-spinor-like equation where the Killing constant is promoted to a complex…
Fayos and Sopuerta have recently set up a formalism for studying vacuum spacetimes with an isometry, a formalism that is centred around the bivector corresponding to the Killing vector and that adapts the tetrad to the bivector. Steele has…
We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized…
Considered is the problem of local equivalence of generic four-dimensional metrics possessing two commuting and orthogonally transitive Killing vector fields. A sufficient set of eight differential invariants is explicitly constructed,…