Recently there are more and more interest on the gravitational wave of moving sources. This introduces a Lorentz transformation problem of gravitational wave. Although Bondi-Metzner-Sachs (BMS) theory has in principle already included the Lorentz transformation of gravitational wave, the transformation of the three dimensional gravitational wave tensor has not been explicitly calculated before. Within four dimensional spacetime, gravitational wave have property of `boost weight zero' and `spin weight 2'. This fact makes the Lorentz transformation of gravitational wave difficult to understand. In the current paper we adopt the traditional three dimensional tensor description of gravitational wave. Such a transverse-traceless tensor describes the gravitational wave freedom directly. We derive the explicit Lorentz transformation of the gravitational wave tensor. The transformation is similar to the Lorentz transformation for electric field vector and magnetic field vector which are three dimensional vectors. Based on the deduced Lorentz transformation of the gravitational wave three dimensional tensor, we can construct the gravitational waveform of moving source with any speed if only the waveform of the corresponding rest waveform is given. As an example, we apply our method to the effect of kick velocity of binary black hole. The adjusted waveform by the kick velocity is presented.
Generators of Internal Lorentz Transformations and of General Affine Coordinate Transformations in Teleparallel Theory of (2+1)-Dimensional Gravity --- Cases with Static Circularly Symmetric Space-Times---
The fundamental issues of microcausality and energy positivity conditions are important to be investigated in the context of spontaneous Lorentz violating theories. We check the microcausality and energy positivity conditions for a free rank-2 antisymmetric tensor field with spontaneous Lorentz violating term and a classically equivalent vector theory from dispersion relations and propagators, and find that the two theories lead to different conditions. While the antisymmetric tensor theory satisfies energy positivity condition and can satisfy microcausality condition for a particular choice o…
We derive rotation free Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT. We find a general transformation rule between two inertial frames where a speed, invariant under that transformation, arises naturally. This idea first came into light by Mathematician Ignatowski [1] around the year, 1910. Without loss of novelty, here we present our derivation while reviewing more recent literature in this subject.
In the present work, we will derive the expression for the change in direction of the electric field using the Lorentz transformation for inertial frame or un-accelerated frame. The acceleration also influences the observed rate of a moving clock in addition to the influence due to its velocity. So we will also derive the expression for the change in direction of the electric field using the Lorentz-type transformation (as given by Friedman) for non-inertial frame or uniformly accelerated frame.
In three spacetime dimensions, we propose a generally covariant Lorentzian action of the classicalized holographic tensor network (cHTN) as the holographic reduction of the Einstein-Hilbert action of gravity in the presence of a negative cosmological constant. In this article, first, we investigate the properties of this Lorentzian action in the ground state. Next, based on the Euclidean action of the cHTN, we derive the gravity perturbation induced by a massive particle at rest in the cHTN as the Unruh effect. Finally, we view our holographic formulation of spacetime as a non-equilibrium seco…
Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that modifications of general relativity in the teleparallel framework break a certain notion of local Lorentz invariance, which is present in the pure tetrad formulation of such theories, while another notion present in the covariant formulation is preserved. We illuminate these different notions from a geometric perspective, and distinguish them from what is commonly un…
