431 research outputs found
PP-waves as Exact Solutions to Ghost-free Infinite Derivative Gravity
We construct exact pp-wave solutions of ghost-free infinite derivative
gravity. These waves described in the Kerr-Schild form also solve the
linearized field equations of the theory. We also find an exact gravitational
shock wave with non-singular curvature invariants and with a finite limit in
the ultraviolet regime of non-locality which is in contrast to the divergent
limit in Einstein's theory.Comment: 13 pages, references added, version published in Phys. Rev.
On memory effect in modified gravity theories
In this note, we discuss the gravitational memory effect in higher derivative
and infinite derivative gravity theories and give the detailed relevant
calculations whose results were given in our recent works. We show that the
memory effect in higher derivative gravity takes the same form as in pure GR at
large distances, whereas at small distances, the results are different. We also
demonstrated that, in infinite derivative gravity, the memory is reduced via
error function as compared to Einstein's gravity. For the lower bound on the
mass scale of non-locality, the memory is essentially reproduces the usual GR
result at distances above at very small distances.Comment: 14 pages, references added, published in Turkish Journal of Physic
Graviton Mass and Memory
Gravitational memory, a residual change, arises after a finite gravitational
wave pulse interacts with free masses. We calculate the memory effect in
massive gravity as a function of the graviton mass and show that it is
discretely different from the result of general relativity: the memory is
reduced not just via the usual expected Yukawa decay but by a numerical factor
which survives even in the massless limit. For the strongest existing bounds on
the graviton mass, the memory is essentially wiped out for the sources located
at distances above 10 Mpc. On the other hand, for the weaker bounds found in
the LIGO observations, the memory is reduced to zero for distances above 0.1
Pc. Hence, we suggest that careful observations of the gravitational wave
memory effect can rule out the graviton mass or significantly bound it. We also
show that adding higher curvature terms reduces the memory effect.Comment: 6 pages, matches the published versio
More on Cotton Flow
Cotton flow tends to evolve a given initial metric on a three manifold to a
conformally flat one. Here we expound upon the earlier work on Cotton flow and
study the linearized version of it around a generic initial metric by employing
a modified form of the DeTurck trick. We show that the flow around the flat
space, as a critical point, reduces to an anisotropic generalization of
linearized KdV equation with complex dispersion relations one of which is an
unstable mode, rendering the flat space unstable under small perturbations. We
also show that Einstein spaces and some conformally flat non-Einstein spaces
are linearly unstable. We refine the gradient flow formalism and compute the
second variation of the entropy and show that generic critical points are
extended Cotton solitons. We study some properties of these solutions and find
a Topologically Massive soliton that is built from Cotton and Ricci solitons.
In the Lorentzian signature, we also show that the pp-wave metrics are both
Cotton and Ricci solitons.Comment: 22 pages, typos corrected, version to appear in JHE
Weyl-gauging of Topologically Massive Gravity
We construct a Weyl-invariant extension of topologically massive gravity
which, remarkably, turns out to include topologically massive electrodynamics,
with a Proca mass term, conformally coupled to a scalar field. The action has
no dimensionful parameters, therefore, the masses are generated via symmetry
breaking either radiatively in flat backgrounds or spontaneously in constant
curvature backgrounds. The broken phase of the theory, generically, has a
single massive spin-2 and a massive spin-1 excitation. Chiral gravity in
asymptotically anti-de Sitter spacetimes does not arise as a low energy theory,
while chiral gravity in de Sitter spacetime is not ruled out.Comment: 10 pages, minor changes made, version to appear in Phys. Rev.
Solutions with pure radiation and gyratons in 3D massive gravity theories
We find exact solutions of topologically massive gravity (TMG) and new
massive gravity (NMG) in dimensions (3D) with an arbitrary cosmological
constant, pure radiation, and gyratons, i.e., with possibly non-zero
and in canonical coordinates. Since any `reasonable' geometry in 3D
(i.e., admitting a null geodesic congruence) is either expanding
Robinson-Trautman () or Kundt (), we focus on these
two classes. Assuming expansions (`GR-like' Robinson-Trautman)
or (general Kundt), we systematically integrate the field
equations of TMG and NMG and identify new classes of exact solutions. The case
of NMG contains an additional assumption of being quadratic in ,
which is automatically enforced in TMG as well as in 3D GR. In each case, we
reduce the field equations as much as possible and identify new classes of
solutions. We also discuss various special subclasses and study some explicit
solutions.Comment: 16 page
Exotic Massive Gravity: Causality and a Birkhoff-like Theorem
We study the local causality issue via the Shapiro time-delay computations in
the on-shell consistent exotic massive gravity in three dimensions. The theory
shows time-delay as opposed to time-advance despite having a ghost at the
linearized level both for asymptotically flat and anti-de Sitter spacetimes. We
also prove a Birkhoff-like theorem: any solution with a hypersurface orthogonal
non-null Killing vector field is conformally flat; and find some exact
solutions.Comment: 14 pages, 1 figure, typos corrected, matches the published versio
Predict Vehicle Collision by TTC From Motion Using a Single Video Camera
The objective of this paper is the instantaneous computation of time-to-collision (TTC) for potential collision only from the motion information captured with a vehicle borne camera. The contribution is the detection of dangerous events and degree directly from motion divergence in the driving video, which is also a clue used by human drivers. Both horizontal and vertical motion divergence are analyzed simultaneously in several collision sensitive zones. The video data are condensed to the motion profiles both horizontally and vertically in the lower half of the video to show motion trajectories directly as edge traces. Stable motion traces of linear feature components are obtained through filtering in the motion profiles. As a result, this avoids object recognition and sophisticated depth sensing in prior. The fine velocity computation yields reasonable TTC accuracy so that a video camera can achieve collision avoidance alone from the size changes of visual patterns. We have tested the algorithm for various roads, environments, and traffic, and shown results by visualization in the motion profiles for overall evaluation
Causality in 3D Massive Gravity Theories
We study the constraints coming from local causality requirement in various
dimensional dynamical theories of gravity. In topologically massive
gravity, with a single parity non-invariant massive degree of freedom, and in
new massive gravity, with two massive spin- degrees of freedom, causality
and unitarity are compatible with each other and both require the Newton's
constant to be negative. In their extensions, such as the Born-Infeld gravity
and the minimal massive gravity the situation is similar and quite different
from their higher dimensional counterparts, such as quadratic (e.g.,
Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in
conflict. We study the problem both in asymptotically flat and asymptotically
anti-de Sitter spaces.Comment: This version has significant improvements: causality discussion of
all the well-known gravity theories in flat space is extended to the AdS
space, references added, 29 pages, latest version matches the published on
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