Search results for "General Relativity"
showing 10 items of 1057 documents
Dynamics for a 2-vertex Quantum Gravity Model
2010
We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global …
The Einstein field equation in a multidimensional universe
1988
String theory [4] predicts that the universe has 10 or 26 dimensions. A salient problem is how the Einstein field equation should be written in terms of these revivified Kaluza-Klein cosmologies. The answer is by now well-known, yet nobody seems to have rewritten the seminal computation in [6] where an unnecessarily involved Euler-Lagrange variational method is employed and, curiously enough, no allusion to the Gauss-Bonnet-Chern theorem is made. We provide a more straightforward argument, which has been inspired by Hilbert's original derivation of the Einstein field equation [5].
T-model field equations: the general solution
2021
We analyze the field equations for the perfect fluid solutions admitting a group G$_3$ of isometries acting on orbits S$_2$ whose curvature has a gradient that is tangent to the fluid flow (T-models). We propose several methods to integrate the field equations and we present the general solution without the need to calculate any integral.
Computational Approach to Gravitational Waves Forms in Stellar Systems as Complex Structures through Keplerian Parameters
2009
In this paper we investigate the gravitational waves emission by stellar dynamical structures as complex systems in the quadrupole approximation considering bounded and unbounded orbits. Precisely, after deriving analytical expressions for the gravitational wave luminosity, the total energy output and gravitational radiation amplitude, we present a computational approach to evaluate the gravitational wave-forms from elliptical, circular, parabolic and hyperbolic orbits as a function of Keplerian parameters.
L-Rigidity in Newtonian approximation
2008
Newtonian limit of L-Rigidity is obtained. In this formalism, L-Rigidity is reduced to steady Newtonian rigid motions in a Newtonian frame of reference in which the observer is at rest.
Mass dimension one fermions and their gravitational interaction
2019
We investigate in detail the interaction between the spin-${1/2}$ fields endowed with mass dimension one and the graviton. We obtain an interaction vertex that combines the characteristics of scalar-graviton and Dirac's fermion-graviton vertices, due to the scalar-dynamic attribute and the fermionic structure of this field. It is shown that the vertex obtained obeys the Ward-Takahashi identity, ensuring the gauge invariance for this interaction. In the contribution of the mass dimension one fermion to the graviton propagator at one-loop, we found the conditions for the cancellation of the tadpole term by a cosmological counter-term. We calculate the scattering process for arbitrary momentum…
Reply to Comment on Measurement of quantum states of neutrons in the Earth's gravitational field
2003
Physical review / D 68(10), 108702 (2003). doi:10.1103/PhysRevD.68.108702
Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes
2005
The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this paper is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides…
Asymptotic Safety in Quantum Einstein Gravity: Nonperturbative Renormalizability and Fractal Spacetime Structure
2007
The asymptotic safety scenario of Quantum Einstein Gravity, the quantum field theory of the spacetime metric, is reviewed and it is argued that the theory is likely to be nonperturbatively renormalizable. It is also shown that asymptotic safety implies that spacetime is a fractal in general, with a fractal dimension of 2 on sub-Planckian length scales.
Intrinsic, deductive, explicit, and algorithmic characterization of the Szekeres-Szafron solutions
2018
We write the known invariant definition of the Szekeres-Szafron family of solutions in an intrinsic, deductive, explicit and algorithmic form. We also intrinsically characterize the two commonly considered subfamilies, and analyze other subclasses, also defined by first-order differential conditions. Furthermore, we present a Rainich-like approach to these metrics.