55 research outputs found
Twisted Lorentzian manifolds, a characterization with torse-forming time-like unit vectors
Robertson-Walker and Generalized Robertson-Walker spacetimes may be
characterized by the existence of a time-like unit torse-forming vector field,
with other constrains. We show that Twisted manifolds may still be
characterized by the existence of such (unique) vector field, with no other
constrain. Twisted manifolds generalize RW and GRW spacetimes by admitting a
scale function that depends both on time and space. We obtain the Ricci tensor,
corresponding to the stress-energy tensor of an imperfect fluid.Comment: 6 pages, marginal errors corrected, reference update
Simple conformally recurrent space-times are conformally recurrent PP-waves
We show that in dimension n>3 the class of simple conformally recurrent
space-times coincides with the class of conformally recurrent pp-waves.Comment: Dedicated to the memory of professor Witold Rote
Extended Derdzinski-Shen theorem for the Riemann tensor
We extend a classical result by Derdzinski and Shen, on the restrictions
imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor.
The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms)
as well as tensors with gauged Codazzi condition (i.e. "recurrent 1-forms"),
typical of some well known differential structures.Comment: 5 page
Cosmological perfect-fluids in f(R) gravity
We show that an n-dimensional generalized Robertson-Walker (GRW) space-time
with divergence-free conformal curvature tensor exhibits a perfect fluid
stress-energy tensor for any f(R) gravity model. Furthermore we prove that a
conformally flat GRW space-time is still a perfect fluid in both f(R) and
quadratic gravity where other curvature invariants are considered.Comment: 13 pages, final versio
A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time
A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity
vector field, 2) null divergence of the Weyl tensor, is a generalised
Robertson-Walker space-time with Einstein fiber. Condition 1) is verified
whenever pressure and energy density are related by an equation of state. The
contraction of the Weyl tensor with the velocity vector field is zero.
Conversely, a generalized Robertson-Walker space-time with null divergence of
the Weyl tensor is a perfect-fluid space-time.Comment: 7 pages. Misprint corrected in Sect II
A second-order identity for the Riemann tensor and applications
A second-order differential identity for the Riemann tensor is obtained, on a
manifold with symmetric connection. Several old and some new differential
identities for the Riemann and Ricci tensors descend from it. Applications to
manifolds with Recurrent or Symmetric structures are discussed. The new
structure of K-recurrency naturally emerges from an invariance property of an
old identity by Lovelock.Comment: 16 page
Correction to: A simple property of the Weyl tensor for a shear, vorticity and acceleration-free velocity field
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The covariant approach to static spacetimes in Einstein and extended gravity theories
We present a covariant study of static space-times, as such and as solutions
of gravity theories. By expressing the relevant tensors through the velocity
and the acceleration vectors that characterise static space-times, the field
equations provide a natural non-redundant set of scalar equations. The same
vectors suggest the form of a Faraday tensor, that is studied in itself and in
(non)-linear electrodynamics. In spherical symmetry, we evaluate the explicit
expressions of the Ricci, the Weyl, the Cotton and the Bach tensors. Simple
restrictions on the coefficients yield well known and new solutions in
Einstein, f(R), Cotton and Conformal gravity, with or without charges, in vacuo
or with fluid source.Comment: 25 page
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