اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExtensions of GR using Projective-Invariance
182
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We show that the unification of electromagnetism and gravity into a single geometrical entity can be beautifully accomplished in a theory with non-symmetric affine connection (${Gamma}_{mu u}^{lambda} eq{Gamma}_{ umu}^{lambda}$), and the unifying symmetry being projective symmetry. In addition, we show that in a purely-affine theory where there are no constrains on the symmetry of ${Gamma}_{mu u}^{lambda}$, the electromagnetic field can be interpreted as the field that preserves projective-invariance. The matter Lagrangian breaks the projective-invariance, generating classical relativistic gravity and quantum electromagnetism. We notice that, if we associate the electromagnetic field tensor with the second Ricci tensor and ${Gamma}_{[mu u]}^{ u}$ with the vector potential, then the classical Einstein-Maxwell equation can be obtained. In addition, we explain the geometrical interpretation of projective transformations. Finally, we discuss the importance of the role of projective-invariance in f(R) gravity theories.
قيم البحث
اقرأ أيضاً
In four dimensions complexified General Relativity (GR) can be non-trivially deformed: There exists an (infinite-parameter) set of modifications all having the same count of degrees of freedom. It is trivial to impose reality conditions that gi
Current limits on violation of local Lorentz invariance in the photon sector are derived mainly from experiments that search for a spatial anisotropy in the speed of light. The presently operating gravitational wave detectors are Michelson interferom
eters with long effective arms, 4e5 m, and sensitive to a fringe shift 2e-9. Therefore they can be used to test for a difference in the speed of light in the two arms, as modulated bi-annualy by the orientation of the Earths velocity with respect to the direction of motion of the local system. A limit can be set on the Robertson-Mansouri-Sexl parameter PMM < 10e-15, as compared to its present limit of PMM < 2e-10, an improvement of five orders of magnitude.
For the purpose of searching for Lorentz-invariance violation in the minimal Standard-Model Extension, we perfom a reanalysis of data obtained from the $^{133}text{Cs}$ fountain clock operating at SYRTE. The previous study led to new limits on eight
components of the $tilde{c}_{mu u}$ tensor, which quantifies the anisotropy of the proton kinetic energy. We recently derived an advanced model for the frequency shift of hyperfine Zeeman transition due to Lorentz violation and became able to constrain the ninth component, the isotropic coefficient $tilde{c}_{TT}$, which is the least well-constrained coefficient of $tilde{c}_{mu u}$. This model is based on a second-order boost Lorentz transformation from the laboratory frame to the Sun-centered frame, and it gives rise to an improvement of five orders of magnitude on $tilde{c}_{TT}$ compared to the state of the art.
A topological extension of general relativity is presented. The superposition principle of quantum mechanics, as formulated by the Feynman path integral, is taken as a starting point. It is argued that the trajectories that enter this path integral a
re distinct, despite any quantum uncertainty in geometry, and thus that space-time topology is multiply connected. Specifically, space-time at the Planck scale consists of a lattice of three-tori that facilitates many distinct paths for particles to travel along. To add gravity, mini black holes are attached to this lattice. These mini black holes represent Wheelers quantum foam and result from the fact that GR is not conformally invariant. The stable creation of such mini black holes is found to be caused by the existence of macroscopic (so long-lived) black holes. This connection, by which macroscopic black holes induce mini black holes, is a topological expression of Machs principle. The proposed topological extension of GR can be tested because, if correct, the dark energy density of the universe should be linearly proportional to the total number of macroscopic black holes in the universe at any time. This prediction, although strange, agrees with current astrophysical observations.
Effective field theory methods suggest that some rather-general extensions of General Relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary. Thus, the
tantalizing prospect to test the fundamental nature of gravity with gravitational-wave observations, in a systematic way, emerges naturally. Here, we build black hole solutions in such a framework and study their main properties. Once rotation is included, we find the first purely gravitational example of geometries without $mathbb{Z}_2$-symmetry. Despite the higher-order operators of the theory, we show that linearized fluctuations of such geometries obey second-order differential equations. We find nonzero tidal Love numbers. We study and compute the quasinormal modes of such geometries. These results are of interest to gravitational-wave science but also potentially relevant for electromagnetic observations of the galactic center or $X$-ray binaries.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
