47 research outputs found
Canonical Structure of Higher Derivative Gravity in 3D
We give an explicitly gauge invariant canonical analysis of linearized
quadratic gravity theories in three dimensions for both flat and de-Sitter
backgrounds. In flat backgrounds, we also study the effects of gravitational
Chern-Simons term, and include the sources, compute the weak field limit as
well as scattering between spinning massive particles.Comment: 14 pages, references added, version to appear in PR
Born-Infeld Gravity with a Unique Vacuum and a Massless Graviton
We construct an n-dimensional Born-Infeld type gravity theory that has the
same properties as Einstein's gravity in terms of the vacuum and particle
content: Namely, the theory has a unique viable vacuum (maximally symmetric
solution) and a single massless unitary spin-2 graviton about this vacuum. The
BI gravity, in some sense, is the most natural, minimal generalization of
Einstein's gravity with a better UV behavior, and hence, is a potentially
viable proposal for low energy quantum gravity. The Gauss-Bonnet combination
plays a non-trivial role in the construction of the theory. As an extreme
example, we consider the infinite dimensional limit where an interesting
exponential gravity arises.Comment: 27 pages, 2 figures. v2: Added discussion
Born-Infeld-Horava gravity
We define various Born-Infeld gravity theories in 3+1 dimensions which reduce
to Horava's model at the quadratic level in small curvature expansion. In their
exact forms, our actions provide z->(infinity) extensions of Horava's gravity,
but when small curvature expansion is used, they reproduce finite z models,
including some half-integer ones.Comment: 7 pages, typo corrected, matches the published versio
Spin-Spin Interactions in Massive Gravity and Higher Derivative Gravity Theories
We show that, in the weak field limit, at large separations, in sharp
contrast to General Relativity (GR), all massive gravity theories predict
distance-dependent spin alignments for spinning objects. For all separations GR
requires anti-parallel spin orientations with spins pointing along the line
joining the sources. Hence total spin is minimized in GR. On the other hand,
while massive gravity at small separations () gives the same
result as GR, for large separations () the spins become parallel to
each other and perpendicular to the line joining the objects. Namely, the
potential energy is minimized when the total spin is maximized in massive
gravity for large separations. We also compute the spin-spin interactions in
quadratic gravity theories and find that while at large separations GR result
is intact, at small separations, spins become perpendicular to the line joining
sources and anti-parallel to each other.Comment: 7 pages, title has changed, derivations of the results incorporated
to the Appendix. Matches the published version in Physics Letters
Massive Higher Derivative Gravity in D-dimensional Anti-de Sitter Spacetimes
We find the propagator and calculate the tree level scattering amplitude
between two covariantly conserved sources in an Anti-de Sitter background for
the most general D-dimensional quadratic, four-derivative, gravity with a
Pauli-Fierz mass. We also calculate the Newtonian potential for various limits
of the theory in flat space. We show how the recently introduced three
dimensional New Massive Gravity is uniquely singled out among higher derivative
models as a (tree level) unitary model and that its Newtonian limit is
equivalent to that of the usual massive gravity in flat space.Comment: 9 pages, references added, to appear in PR
Born-Infeld Gravity with a Massless Graviton in Four Dimensions
We construct Born-Infeld (BI) type gravity theories which describe tree-level
unitary (non-ghost and non-tachyonic) massless spin-2 modes around their
maximally symmetric vacua in four dimensions. Building unitary BI actions
around flat vacuum is straightforward; but, this is a complicated task around
(anti)-de Sitter backgrounds. In this work, we solve the issue and give details
of constructing perturbatively viable determinantal BI theories. It is
interesting that the Gauss-Bonnet combination, which is a total derivative in
four dimensions, plays an important role in the construction of viable BI
theories.Comment: 46 pages, references adde
AdS Waves as Exact Solutions to Quadratic Gravity
We give an exact solution of the quadratic gravity in D dimensions. The
solution is a plane fronted wave metric with a cosmological constant. This
metric solves not only the full quadratic gravity field equations but also the
linearized ones which include the linearized equations of the recently found
critical gravity. A subset of the solutions change the asymptotic structure of
the anti-de Sitter space due to their logarithmic behavior.Comment: 11 pages, references added, version to appear in Phys. Rev.
All unitary cubic curvature gravities in D dimensions
We construct all the unitary cubic curvature gravity theories built on the
contractions of the Riemann tensor in D -dimensional (anti)-de Sitter
spacetimes. Our construction is based on finding the equivalent quadratic
action for the general cubic curvature theory and imposing ghost and tachyon
freedom, which greatly simplifies the highly complicated problem of finding the
propagator of cubic curvature theories in constant curvature backgrounds. To
carry out the procedure we have also classified all the unitary quadratic
models. We use our general results to study the recently found cubic curvature
theories using different techniques and the string generated cubic curvature
gravity model. We also study the scattering in critical gravity and give its
cubic curvature extensions.Comment: 24 pages, 1 figure, v2: A subsection on cubic curvature extensions of
critical gravity is added, v3: The part regarding critical gravity is
revised. Version to appear in Class. Quant. Gra
Application of artificial neural networks to height transformation
Dvije su osnovne komponente vertikalnog pozicioniranja: visina i odgovarajuća referentna površina. Definicija visine se mijenja u skladu s odabranom referentnom površinom. Satelitski sustavi globalne navigacije (Global Navigation Satellite Systems - GNSS) daju elipsoidne visine razmjerne površini geodetski referentnog elipsoida. Međutim, mnoge aplikacije zahtijevaju visine koje su povezane s fizikalno značajnom površinom kao što je geoid. Takve visine su u obliku ortometrijskih (ili normalnih) visina. Veza između elipsoidnih i ortometrijskih visina je visina geoida iznad referentnog elipsoida, obično nazivana valovitim kretanjem geoida. Dva su osnovna pristupa kod pretvaranja elipsoidnih u ortometrijske visine: gravimetrijski model geoida i interpolacija između geometrijski deriviranih valovitih kretanja geoida gdje su GNSS mjerenja locirana uz nivelacijske točke. U ovom se radu istražuje korisnost umjetnih neuronskih mreža s unatražnim rasprostiranjem kao alternativni alat za transformaciju visine.The vertical positioning has two indispensable constituents: the height and the relevant reference surface. The definition of the height differs according to the appointed reference surface. Global Navigation Satellite Systems (GNSS) ensure ellipsoidal heights relative to a geodetic reference ellipsoid surface. However, many field applications require heights that are related to a physically meaningful surface (e.g. the geoid). Such physically meaningful heights often provided in terms of orthometric heights. The geoid undulation is the relation between the ellipsoidal and orthometric heights. The ellipsoidal heights can be transformed to orthometric heights via two principal approaches: a gravimetric geoid model, and geometrical interpolation between geoid undulations where GNSS observations have been collocated with benchmarks. The purpose of this study is investigating the applicability of a back propagation artificial neural network as a height transformation tool