2,109 research outputs found

### Multiply Warped Products with Non-Smooth Metrics

In this article we study manifolds with $C^{0}$-metrics and properties of
Lorentzian multiply warped products. We represent the interior Schwarzschild
space-time as a multiply warped product space-time with warping functions and
we also investigate the curvature of a multiply warped product with
$C^0$-warping functions. We given the {\it{Ricci curvature}} in terms of $f_1$,
$f_2$ for the multiply warped products of the form $M=(0,\
2m)\times_{f_1}R^1\times_{f_2} S^2$.Comment: LaTeX, 7 page

### Taub-NUT/Bolt Black Holes in Gauss-Bonnet-Maxwell Gravity

We present a class of higher dimensional solutions to Gauss-Bonnet-Maxwell
equations in $2k+2$ dimensions with a U(1) fibration over a $2k$-dimensional
base space $\mathcal{B}$. These solutions depend on two extra parameters, other
than the mass and the NUT charge, which are the electric charge $q$ and the
electric potential at infinity $V$. We find that the form of metric is
sensitive to geometry of the base space, while the form of electromagnetic
field is independent of $\mathcal{B}$. We investigate the existence of
Taub-NUT/bolt solutions and find that in addition to the two conditions of
uncharged NUT solutions, there exist two other conditions. These two extra
conditions come from the regularity of vector potential at $r=N$ and the fact
that the horizon at $r=N$ should be the outer horizon of the black hole. We
find that for all non-extremal NUT solutions of Einstein gravity having no
curvature singularity at $r=N$, there exist NUT solutions in
Gauss-Bonnet-Maxwell gravity. Indeed, we have non-extreme NUT solutions in
$2+2k$ dimensions only when the $2k$-dimensional base space is chosen to be
$\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet-Maxwell gravity has
extremal NUT solutions whenever the base space is a product of 2-torii with at
most a 2-dimensional factor space of positive curvature, even though there a
curvature singularity exists at $r=N$. We also find that one can have bolt
solutions in Gauss-Bonnet-Maxwell gravity with any base space. The only case
for which one does not have black hole solutions is in the absence of a
cosmological term with zero curvature base space.Comment: 23 pages, 3 figures, typos fixed, a few references adde

### NUT-Charged Black Holes in Gauss-Bonnet Gravity

We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet
gravity and obtain the general form of these solutions in $d$ dimensions. We
find that for all non-extremal NUT solutions of Einstein gravity having no
curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet
gravity that contain these solutions in the limit that the Gauss-Bonnet
parameter $\alpha$ goes to zero. Furthermore there are no NUT solutions in
Gauss-Bonnet gravity that yield non-extremal NUT solutions to Einstein gravity
having a curvature singularity at $r=N$ in the limit $% \alpha \to 0$. Indeed,
we have non-extreme NUT solutions in $2+2k$ dimensions with non-trivial
fibration only when the $2k$-dimensional base space is chosen to be
$\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet gravity has extremal NUT
solutions whenever the base space is a product of 2-torii with at most a
2-dimensional factor space of positive curvature. Indeed, when the base space
has at most one positively curved two dimensional space as one of its factor
spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though
there a curvature singularity exists at $r=N$. We also find that one can have
bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces
of zero or positive constant curvature. The only case for which one does not
have bolt solutions is in the absence of a cosmological term with zero
curvature base space.Comment: 20 pages, referrence added, a few typos correcte

### The Efroimsky formalism adapted to high-frequency perturbations

The Efroimsky perturbation scheme for consistent treatment of gravitational
waves and their influence on the background is summarized and compared with
classical Isaacson's high-frequency approach. We demonstrate that the Efroimsky
method in its present form is not compatible with the Isaacson limit of
high-frequency gravitational waves, and we propose its natural generalization
to resolve this drawback.Comment: 7 pages, to appear in Class. Quantum Gra

### Self-enforcing cooperation via strategic investment

We investigate how, in a situation with two players in which noncooperation is the only equilibrium, cooperation can be achieved via costly investment. We find that in the resulting equilibria, cooperation is an all-or-nothing outcome, that is, either there is full cooperation by both players, or no cooperation at all. The cost of investment is unrelated to the degree of cooperation that is ultimately achieved, unless the cost is too high, in which case investment cannot in any degree overcome the disincentive to cooperate. Moreover, the positive externalities that players have on each other in the course of play, although they affect investment, are ultimately irrelevant to the degree of cooperation achieved. We view our model as an explanation for the formation and stable existence of business alliances, where the players are firms forming a partnership defined and sustained by contractual agreements, but which is short of a merger or acquisition

### Distributional energy momentum tensor of the extended Kerr geometry

We generalize previous work on the energy-momentum tensor-distribution of the
Kerr geometry by extending the manifold structure into the negative mass
region. Since the extension of the flat part of the Kerr-Schild decomposition
from one sheet to the double cover develops a singularity at the branch surface
we have to take its non-smoothness into account. It is however possible to find
a geometry within the generalized Kerr-Schild class that is in the
Colombeau-sense associated to the maximally analytic Kerr-metric.Comment: 12 pages, latex2e, amslatex and epsf macro

### Relativistic Acoustic Geometry

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous
isentropic flow is studied in terms of acoustic geometry. The sound wave
equation turns out to be equivalent to the equation of motion for a massless
scalar field propagating in a curved space-time geometry. The geometry is
described by the acoustic metric tensor that depends locally on the equation of
state and the four-velocity of the fluid. For a relativistic supersonic flow in
curved space-time the ergosphere and acoustic horizon may be defined in a way
analogous the non-relativistic case. A general-relativistic expression for the
acoustic analog of surface gravity has been found.Comment: 14 pages, LaTe

### Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model

To analyze linear field equations on a locally homogeneous spacetime by means
of separation of variables, it is necessary to set up appropriate harmonics
according to its symmetry group. In this paper, the harmonics are presented for
a spatially compactified Bianchi II cosmological model -- the nilgeometric
model. Based on the group structure of the Bianchi II group (also known as the
Heisenberg group) and the compactified spatial topology, the irreducible
differential regular representations and the multiplicity of each irreducible
representation, as well as the explicit form of the harmonics are all
completely determined. They are also extended to vector harmonics. It is
demonstrated that the Klein-Gordon and Maxwell equations actually reduce to
systems of ODEs, with an asymptotic solution for a special case.Comment: 28 pages, no figures, revised version to appear in JM

### The Exact Geometry of a Kerr-Taub-NUT Solution of String Theory

In this paper we study a solution of heterotic string theory corresponding to
a rotating Kerr-Taub-NUT spacetime. It has an exact CFT description as a
heterotic coset model, and a Lagrangian formulation as a gauged WZNW model. It
is a generalisation of a recently discussed stringy Taub-NUT solution, and is
interesting as another laboratory for studying the fate of closed timelike
curves and cosmological singularities in string theory. We extend the
computation of the exact metric and dilaton to this rotating case, and then
discuss some properties of the metric, with particular emphasis on the
curvature singularities.Comment: 14 pages, 3 figure

### Localizing gravity on exotic thick 3-branes

We consider localization of gravity on thick branes with a non trivial
structure. Double walls that generalize the thick Randall-Sundrum solution, and
asymmetric walls that arise from a Z_2-symmetric scalar potential, are
considered. We present a new asymmetric solution: a thick brane interpolating
between two AdS_5 spacetimes with different cosmological constants, which can
be derived from a ``fake supergravity'' superpotential, and show that it is
possible to confine gravity on such branes.Comment: Final version, minor changes, references adde

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