31 research outputs found
Exterior and interior metrics with quadrupole moment
We present the Ernst potential and the line element of an exact solution of
Einstein's vacuum field equations that contains as arbitrary parameters the
total mass, the angular momentum, and the quadrupole moment of a rotating mass
distribution. We show that in the limiting case of slowly rotating and slightly
deformed configuration, there exists a coordinate transformation that relates
the exact solution with the approximate Hartle solution. It is shown that this
approximate solution can be smoothly matched with an interior perfect fluid
solution with physically reasonable properties. This opens the possibility of
considering the quadrupole moment as an additional physical degree of freedom
that could be used to search for a realistic exact solution, representing both
the interior and exterior gravitational field generated by a self-gravitating
axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio
Hadamard states from null infinity
Free field theories on a four dimensional, globally hyperbolic spacetime,
whose dynamics is ruled by a Green hyperbolic partial differential operator,
can be quantized following the algebraic approach. It consists of a two-step
procedure: In the first part one identifies the observables of the underlying
physical system collecting them in a *-algebra which encodes their relational
and structural properties. In the second step one must identify a quantum
state, that is a positive, normalized linear functional on the *-algebra out of
which one recovers the interpretation proper of quantum mechanical theories via
the so-called Gelfand-Naimark-Segal theorem. In between the plethora of
possible states, only few of them are considered physically acceptable and they
are all characterized by the so-called Hadamard condition, a constraint on the
singular structure of the associated two-point function. Goal of this paper is
to outline a construction scheme for these states which can be applied whenever
the underlying background possesses a null (conformal) boundary. We discuss in
particular the examples of a real, massless conformally coupled scalar field
and of linearized gravity on a globally hyperbolic and asymptotically flat
spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum
Mathematical Physics", held in Regensburg from the 29th of September to the
02nd of October 201
Unwrapping Closed Timelike Curves
Closed timelike curves (CTCs) appear in many solutions of the Einstein
equation, even with reasonable matter sources. These solutions appear to
violate causality and so are considered problematic. Since CTCs reflect the
global properties of a spacetime, one can attempt to change its topology,
without changing its geometry, in such a way that the former CTCs are no longer
closed in the new spacetime. This procedure is informally known as unwrapping.
However, changes in global identifications tend to lead to local effects, and
unwrapping is no exception, as it introduces a special kind of singularity,
called quasi-regular. This "unwrapping" singularity is similar to the string
singularities. We give two examples of unwrapping of essentially 2+1
dimensional spacetimes with CTCs, the Gott spacetime and the Godel universe. We
show that the unwrapped Gott spacetime, while singular, is at least devoid of
CTCs. In contrast, the unwrapped Godel spacetime still contains CTCs through
every point. A "multiple unwrapping" procedure is devised to remove the
remaining circular CTCs. We conclude that, based on the two spacetimes we
investigated, CTCs appearing in the solutions of the Einstein equation are not
simply a mathematical artifact of coordinate identifications, but are indeed a
necessary consequence of General Relativity, provided only that we demand these
solutions do not possess naked quasi-regular singularities.Comment: 29 pages, 9 figure
Derivation of fluid dynamics from kinetic theory with the 14--moment approximation
We review the traditional derivation of the fluid-dynamical equations from
kinetic theory according to Israel and Stewart. We show that their procedure to
close the fluid-dynamical equations of motion is not unique. Their approach
contains two approximations, the first being the so-called 14-moment
approximation to truncate the single-particle distribution function. The second
consists in the choice of equations of motion for the dissipative currents.
Israel and Stewart used the second moment of the Boltzmann equation, but this
is not the only possible choice. In fact, there are infinitely many moments of
the Boltzmann equation which can serve as equations of motion for the
dissipative currents. All resulting equations of motion have the same form, but
the transport coefficients are different in each case.Comment: 15 pages, 3 figures, typos fixed and discussions added; EPJA: Topical
issue on "Relativistic Hydro- and Thermodynamics
The Causal Boundary of spacetimes revisited
We present a new development of the causal boundary of spacetimes, originally
introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime
(or, more generally, a chronological set), we reconsider the GKP ideas to
construct a family of completions with a chronology and topology extending the
original ones. Many of these completions present undesirable features, like
those appeared in previous approaches by other authors. However, we show that
all these deficiencies are due to the attachment of an ``excessively big''
boundary. In fact, a notion of ``completion with minimal boundary'' is then
introduced in our family such that, when we restrict to these minimal
completions, which always exist, all previous objections disappear. The optimal
character of our construction is illustrated by a number of satisfactory
properties and examples.Comment: 37 pages, 10 figures; Definition 6.1 slightly modified; multiple
minor changes; one figure added and another replace
Deformations of quantum field theories on spacetimes with Killing vector fields
The recent construction and analysis of deformations of quantum field
theories by warped convolutions is extended to a class of curved spacetimes.
These spacetimes carry a family of wedge-like regions which share the essential
causal properties of the Poincare transforms of the Rindler wedge in Minkowski
space. In the setting of deformed quantum field theories, they play the role of
typical localization regions of quantum fields and observables. As a concrete
example of such a procedure, the deformation of the free Dirac field is
studied.Comment: 35 pages, 3 figure
Linking and causality in globally hyperbolic spacetimes
The linking number is defined if link components are zero homologous.
Our affine linking invariant generalizes to the case of linked
submanifolds with arbitrary homology classes. We apply to the study of
causality in Lorentz manifolds. Let be a spacelike Cauchy surface in a
globally hyperbolic spacetime . The spherical cotangent bundle
is identified with the space of all null geodesics in
Hence the set of null geodesics passing through a point gives an
embedded -sphere in called the sky of Low observed
that if the link is nontrivial, then are causally
related. This motivated the problem (communicated by Penrose) on the Arnold's
1998 problem list to apply link theory to the study of causality. The spheres
are isotopic to fibers of They are nonzero
homologous and is undefined when is closed, while is well defined. Moreover, if is not an
odd-dimensional rational homology sphere. We give a formula for the increment
of \alk under passages through Arnold dangerous tangencies. If is
such that takes values in and is conformal to having all
the timelike sectional curvatures nonnegative, then are causally
related if and only if . We show that in
nonrefocussing are causally unrelated iff can be deformed
to a pair of -fibers of by an isotopy through skies. Low
showed that if (\ss, g) is refocussing, then is compact. We show that the
universal cover of is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing
space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal
classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A
part of the paper (several results of sections 4,5,6,9,10) is an extension
and development of our work math.GT/0207219 in the context of Lorentzian
geometry. The results of sections 7,8,11,12 and Appendix B are ne
Approximate gravitational field of a rotating deformed mass
A new approximate solution of vacuum and stationary Einstein field equations
is obtained. This solution is constructed by means of a power series expansion
of the Ernst potential in terms of two independent and dimensionless parameters
representing the quadrupole and the angular momentum respectively. The main
feature of the solution is a suitable description of small deviations from
spherical symmetry through perturbations of the static configuration and the
massive multipole structure by using those parameters. This quality of the
solution might eventually provide relevant differences with respect to the
description provided by the Kerr solution.Comment: 16 pages. Latex. To appear in General Relativity and Gravitatio
Anisotropic Conformal Infinity
We generalize Penrose's notion of conformal infinity of spacetime, to
situations with anisotropic scaling. This is relevant not only for
Lifshitz-type anisotropic gravity models, but also in standard general
relativity and string theory, for spacetimes exhibiting a natural asymptotic
anisotropy. Examples include the Lifshitz and Schrodinger spaces (proposed as
AdS/CFT duals of nonrelativistic field theories), warped AdS_3, and the
near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears
crucial for resolving puzzles of holographic renormalization in such
spacetimes.Comment: 11 page
Einstein energy associated with the Friedmann -Robertson -Walker metric
Following Einstein's definition of Lagrangian density and gravitational field
energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A.,
Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I.
Publications, Mumbai, 1963, Trans. by G. Field), Tolman derived a general
formula for the total matter plus gravitational field energy () of an
arbitrary system (Tolman, R.C., Phys. Rev., 35(8), 875 (1930); Tolman, R.C.,
{\it Relativity, Thermodynamics & Cosmology}, Clarendon Press, Oxford, 1962));
Xulu, S.S., arXiv:hep-th/0308070 (2003)). For a static isolated system, in
quasi-Cartesian coordinates, this formula leads to the well known result , where is the
determinant of the metric tensor and is the energy momentum tensor of
the {\em matter}. Though in the literature, this is known as "Tolman Mass", it
must be realized that this is essentially "Einstein Mass" because the
underlying pseudo-tensor here is due to Einstein. In fact, Landau -Lifshitz
obtained the same expression for the "inertial mass" of a static isolated
system without using any pseudo-tensor at all and which points to physical
significance and correctness of Einstein Mass (Landau, L.D., and Lifshitz,
E.M., {\it The Classical Theory of Fields}, Pergamon Press, Oxford, 2th ed.,
1962)! For the first time we apply this general formula to find an expression
for for the Friedmann- Robertson -Walker (FRW) metric by using the same
quasi-Cartesian basis. As we analyze this new result, physically, a spatially
flat model having no cosmological constant is suggested. Eventually, it is seen
that conservation of is honoured only in the a static limit.Comment: By mistake a marginally different earlier version was loaded, now the
journal version is uploade