3 research outputs found
Spherically symmetric spacetimes in f(R) gravity theories
We study both analytically and numerically the gravitational fields of stars
in f(R) gravity theories. We derive the generalized Tolman-Oppenheimer-Volkov
equations for these theories and show that in metric f(R) models the
Parameterized Post-Newtonian parameter is a robust
outcome for a large class of boundary conditions set at the center of the star.
This result is also unchanged by introduction of dark matter in the Solar
System. We find also a class of solutions with in
the metric model, but these solutions turn out to be unstable
and decay in time. On the other hand, the Palatini version of the theory is
found to satisfy the Solar System constraints. We also consider compact stars
in the Palatini formalism, and show that these models are not inconsistent with
polytropic equations of state. Finally, we comment on the equivalence between
f(R) gravity and scalar-tensor theories and show that many interesting Palatini
f(R) gravity models can not be understood as a limiting case of a
Jordan-Brans-Dicke theory with .Comment: Published version, 12 pages, 7 figure
Geometry, pregeometry and beyond
This article explores the overall geometric manner in which human beings make
sense of the world around them by means of their physical theories; in
particular, in what are nowadays called pregeometric pictures of Nature. In
these, the pseudo-Riemannian manifold of general relativity is considered a
flawed description of spacetime and it is attempted to replace it by
theoretical constructs of a different character, ontologically prior to it.
However, despite its claims to the contrary, pregeometry is found to
surreptitiously and unavoidably fall prey to the very mode of description it
endeavours to evade, as evidenced in its all-pervading geometric understanding
of the world. The question remains as to the deeper reasons for this human,
geometric predilection--present, as a matter of fact, in all of physics--and as
to whether it might need to be superseded in order to achieve the goals that
frontier theoretical physics sets itself at the dawn of a new century: a
sounder comprehension of the physical meaning of empty spacetime.Comment: 41 pages, Latex. v2: Date added. v3: Main arguments refined,
secondary discussions abridged; expands on the published versio
Quantum-mechanical model of the Kerr-Newman black hole
We consider a Hamiltonian quantum theory of stationary spacetimes containing
a Kerr-Newman black hole. The physical phase space of such spacetimes is just
six-dimensional, and it is spanned by the mass , the electric charge and
angular momentum of the hole, together with the corresponding canonical
momenta. In this six-dimensional phase space we perform a canonical
transformation such that the resulting configuration variables describe the
dynamical properties of Kerr-Newman black holes in a natural manner. The
classical Hamiltonian written in terms of these variables and their conjugate
momenta is replaced by the corresponding self-adjoint Hamiltonian operator and
an eigenvalue equation for the Arnowitt-Deser-Misner (ADM) mass of the hole,
from the point of view of a distant observer at rest, is obtained. In a certain
very restricted sense, this eigenvalue equation may be viewed as a sort of
"Schr\"odinger equation of black holes". Our "Schr\"odinger equation" implies
that the ADM mass, electric charge and angular momentum spectra of black holes
are discrete, and the mass spectrum is bounded from below. Moreover, the
spectrum of the quantity , where is the angular momentum per
unit mass of the hole, is strictly positive when an appropriate self-adjoint
extension is chosen. The WKB analysis yields the result that the large
eigenvalues of , and are of the form , where is an
integer. It turns out that this result is closely related to Bekenstein's
proposal on the discrete horizon area spectrum of black holes.Comment: 30 pages, 3 figures, RevTe