58 research outputs found

### Extended Palatini action for general relativity and the natural emergence of the cosmological constant

In the Palatini action of general relativity the connection and the metric
are treated as independent dynamical variables. Instead of assuming a relation
between these quantities, the desired relation between them is derived through
the Euler-Lagrange equations of the Palatini action. In this manuscript we
construct an extended Palatini action, where we do not assume any a priori
relationship between the connection, the covariant metric tensor, and the
contravariant metric tensor. Instead we treat these three quantities as
independent dynamical variables. We show that this action reproduces the
standard Einstein field equations depending on a single metric tensor. We
further show that in this formulation the cosmological constant has an
additional theoretical significance. Normally the cosmological constant is
added to the Einstein field equations for the purpose of having general
relativity be consistent with cosmological observations. In the formulation
presented here, the nonvanishing cosmological constant also ensures the
self-consistency of the theory.Comment: in the revised version the original scalar matter action is replaced
with a general matter actio

### Regularization of the second-order gravitational perturbations produced by a compact object

The equations for the second-order gravitational perturbations produced by a
compact-object have highly singular source terms at the point particle limit.
At this limit the standard retarded solutions to these equations are
ill-defined. Here we construct well-defined and physically meaningful solutions
to these equations. These solutions are important for practical calculations:
the planned gravitational-wave detector LISA requires preparation of waveform
templates for the potential gravitational-waves. Construction of templates with
desired accuracy for extreme mass ratio binaries, in which a compact-object
inspirals towards a supermassive black-hole, requires calculation of the
second-order gravitational perturbations produced by the compact-object.Comment: 12 pages, discussion expanded, to be published in Phys. Rev. D Rapid
Communicatio

### Construction of the second-order gravitational perturbations produced by a compact object

Accurate calculation of the gradual inspiral motion in an extreme mass-ratio
binary system, in which a compact-object inspirals towards a supermassive
black-hole requires calculation of the interaction between the compact-object
and the gravitational perturbations that it induces. These metric perturbations
satisfy linear partial differential equations on a curved background spacetime
induced by the supermassive black-hole. At the point particle limit the
second-order perturbations equations have source terms that diverge as
$r^{-4}$, where $r$ is the distance from the particle. This singular behavior
renders the standard retarded solutions of these equations ill-defined. Here we
resolve this problem and construct well-defined and physically meaningful
solutions to these equations. We recently presented an outline of this
resolution [E. Rosenthal, Phys. Rev. D 72, 121503 (2005)]. Here we provide the
full details of this analysis. These second-order solutions are important for
practical calculations: the planned gravitational-wave detector LISA requires
preparation of waveform templates for the expected gravitational-waves.
Construction of templates with desired accuracy for extreme mass-ratio binaries
requires accurate calculation of the inspiral motion including the interaction
with the second-order gravitational perturbations.Comment: 30 page

### Regularization of second-order scalar perturbation produced by a point-particle with a nonlinear coupling

Accurate calculation of the motion of a compact object in a background
spacetime induced by a supermassive black hole is required for the future
detection of such binary systems by the gravitational-wave detector LISA.
Reaching the desired accuracy requires calculation of the second-order
gravitational perturbations produced by the compact object. At the point
particle limit the second-order gravitational perturbation equations turn out
to have highly singular source terms, for which the standard retarded solutions
diverge. Here we study a simplified scalar toy-model in which a point particle
induces a nonlinear scalar field in a given curved spacetime. The corresponding
second-order scalar perturbation equation in this model is found to have a
similar singular source term, and therefore its standard retarded solutions
diverge. We develop a regularization method for constructing well-defined
causal solutions for this equation. Notably these solutions differ from the
standard retarded solutions, which are ill-defined in this case.Comment: 14 page

### Universal Self Force from an Extended-Object Approach

We present a consistent extended-object approach for determining the self
force acting on an accelerating charged particle. In this approach one
considers an extended charged object of finite size $\epsilon$, and calculates
the overall contribution of the mutual electromagnetic forces. Previous
implementations of this approach yielded divergent terms $\propto 1/\epsilon$
that could not be cured by mass-renormalization. Here we explain the origin of
this problem and fix it. We obtain a consistent, universal, expression for the
extended-object self force, which conforms with Dirac's well known formula.Comment: Latex, one postscript figure, 4 page

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