1,499 research outputs found
Towards a general description of the interior structure of rotating black holes
The purpose of this paper is to present a number of proposals about the
interior structure of a rotating black hole that is accreting slowly, but in an
arbitrary time- and space-dependent fashion. The proposals could potentially be
tested with numerical simulations. Outgoing and ingoing particles free-falling
in the parent Kerr geometry become highly focused along the principal outgoing
and ingoing null directions as they approach the inner horizon, triggering the
mass inflation instability. The original arguments of Barrabes, Israel &
Poisson (1990) regarding inflation in rotating black holes are reviewed, and
shown to be based on Raychauduri's equation applied along the outgoing and
ingoing null directions. It is argued that gravitational waves should behave in
the geometric optics limit, and consequently that the spacetime should be
almost shear-free. A full set of shear-free equations is derived. A specific
line-element is proposed, which is argued should provide a satisfactory
approximation during early inflation. Finally, it is argued that
super-Planckian collisions between outgoing and ingoing particles will lead to
entropy production, bringing inflation to an end, and precipitating collapse.Comment: 15 page
Bi-gravity with a single graviton
We analyze a bi-gravity model based on the first order formalism, having as
fundamental variables two tetrads but only one Lorentz connection. We show that
on a large class of backgrounds its linearization agrees with general
relativity. At the non-linear level, additional degrees of freedom appear, and
we reveal the mechanism hiding them around the special backgrounds. We further
argue that they do not contain a massive graviton, nor the Boulware-Deser
ghost. The model thus propagates only one graviton, whereas the nature of the
additional degrees of freedom remains to be investigated. We also present a
foliation-preserving deformation of the model, which keeps all symmetries
except time diffeomorphisms and has three degrees of freedom.Comment: 29 page
Chiral description of ghost-free massive gravity
We propose and study a new first order version of the ghost-free massive
gravity. Instead of metrics or tetrads, it uses a connection together with
Plebanski's chiral 2-forms as fundamental variables, rendering the phase space
structure similar to that of SU(2) gauge theories. The chiral description
simplifies computations of the constraint algebra, and allows us to perform the
complete canonical analysis of the system. In particular, we explicitly compute
the secondary constraint and carry out the stabilization procedure, thus
proving that in general the theory propagates 7 degrees of freedom,
consistently with previous claims. Finally, we point out that the description
in terms of 2-forms opens the door to an infinite class of ghost-free massive
bi-gravity actions. Our results apply directly to Euclidean signature. The
reality conditions to be imposed in the Lorentzian signature appear to be more
complicated than in the usual gravity case and are left as an open issue.Comment: 26 pages; extended discussion of reality conditions, added reference
On the energy of homogeneous cosmologies
An energy for the homogeneous cosmological models is presented. More
specifically, using an appropriate natural prescription, we find the energy
within any region with any gravitational source for a large class of gravity
theories--namely those with a tetrad description--for all 9 Bianchi types. Our
energy is given by the value of the Hamiltonian with homogeneous boundary
conditions; this value vanishes for all regions in all Bianchi class A models,
and it does not vanish for any class B model. This is so not only for
Einstein's general relativity but, moreover, for the whole 3-parameter class of
tetrad-teleparallel theories. For the physically favored one parameter
subclass, which includes the teleparallel equivalent of Einstein's theory as an
important special case, the energy for all class B models is, contrary to
expectation, negative.Comment: 11 pages, reformated with minor change
Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
Teleparallel gravity and its popular generalization gravity can be
formulated as fully invariant (under both coordinate transformations and local
Lorentz transformations) theories of gravity. Several misconceptions about
teleparallel gravity and its generalizations can be found in the literature,
especially regarding their local Lorentz invariance. We describe how these
misunderstandings may have arisen and attempt to clarify the situation. In
particular, the central point of confusion in the literature appears to be
related to the inertial spin connection in teleparallel gravity models. While
inertial spin connections are commonplace in special relativity, and not
something inherent to teleparallel gravity, the role of the inertial spin
connection in removing the spurious inertial effects within a given frame of
reference is emphasized here. The careful consideration of the inertial spin
connection leads to the construction of a fully invariant theory of
teleparallel gravity and its generalizations. Indeed, it is the nature of the
spin connection that differentiates the relationship between what have been
called good tetrads and bad tetrads and clearly shows that, in principle, any
tetrad can be utilized. The field equations for the fully invariant formulation
of teleparallel gravity and its generalizations are presented and a number of
examples using different assumptions on the frame and spin connection are
displayed to illustrate the covariant procedure. Various modified teleparallel
gravity models are also briefly reviewed.Comment: v2: 72 pages, revised version, references added, matches published
versio
Covariance properties and regularization of conserved currents in tetrad gravity
We discuss the properties of the gravitational energy-momentum 3-form within
the tetrad formulation of general relativity theory. We derive the covariance
properties of the quantities describing the energy-momentum content under
Lorentz transformations of the tetrad. As an application, we consider the
computation of the total energy (mass) of some exact solutions of Einstein's
general relativity theory which describe compact sources with asymptotically
flat spacetime geometry. As it is known, depending on the choice of tetrad
frame, the formal total integral for such configurations may diverge. We
propose a natural regularization method which yields finite values for the
total energy-momentum of the system and demonstrate how it works on a number of
explicit examples.Comment: 36 pages, Revtex, no figures; small changes, published versio
Lorentz Connections and Gravitation
The different roles played by Lorentz connections in general relativity and
in teleparallel gravity are reviewed. Some of the consequences of this
difference are discussed.Comment: Lecture presented at the Sixth International School on Field Theory
and Gravity, Petropolis, Brazil, 201
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