Search results for "classical"
showing 10 items of 2294 documents
The Quantum Scalar Field in Spherically Symmetric Loop Quantum Gravity
2013
We consider the quantization of a spherically symmetric gravitational system coupled to a massless scalar field within the loop quantum gravity framework. Our results rely on the uniform discretizations method developed during the last years. We minimize the associated discrete “master constraint” using a trial state whose gravitational part is peaked around the classical Schwarzschild solution.
Numerical 3+1 general relativistic magnetohydrodynamics: a local characteristic approach
2005
We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e. Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jac…
The Palatini Approach Beyond Einstein’s Gravity
2014
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these theories, governed by second-order equations and having no new degrees of freedom, makes them specially suitable to address certain aspects of quantum gravity phenomenology, construct nonsingular bouncing cosmologies, and explore black hole interiors, which in the Reissner-Nordstrom case develop a compact core of finite density instead of a point-like singularity.
New methods for approximating general relativity in numerical simulations of stellar core collapse
2006
We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented. Such an effective relativistic potential can be used in an otherwise standard Newtonian hydrodynamic code. An alternative approximation of general relativity is the assumption of conformal flatness for the three-metric, and its extension by adding second post-Newtonian order terms. Using a code which evolves the coupled system of metric and fluid equations, we apply the various approximation methods to numerically simulate axisymmetric models for the col…
CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations
2004
Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core collapse in general relativity have been done using approximations of the Einstein field equations. As recently shown by Dimmelmeier et al (2002a,b), one of the most interesting such approximation is the so-called conformal flatness condition (CFC) of Isenberg, Wilson and Mathews. Building on this previous work we present here new results from numerical simulations of relativistic rotational core collapse in axisymmetry, aiming at improving the dynamics and the gravitational waveforms. The computer code used for these simulations evolves th…
Gravitational waves from the collapse and bounce of a stellar core in tensor-scalar gravity
1999
Tensor-scalar theory of gravity allows the generation of gravitational waves from astrophysical sources, like Supernov\ae{}, even in the spherical case. That motivated us to study the collapse of a degenerate stellar core, within tensor-scalar gravity, leading to the formation of a neutron star through a bounce and the formation of a shock. We discuss in this paper the effects of the scalar field on the evolution of the system, as well as the appearance of strong non-perturbative effects of this scalar field (the so-called ``spontaneous scalarization''). As a main result, we describe the resulting gravitational monopolar radiation (form and amplitude) and discuss the possibility of its dete…
Zur Frage der Charakterisierung stationärer Bewegungen in der Hydrodynamik
1958
Helmholtz andKorteweg propose that the steady motion of a viscous fluid under constant extraneous forces having a single-valued potential dissipates—for any given region and assuming that inertia terms in the dynamic equations can be neglected—less energy than any other motion with the same values of velocity at the boundary.—A generalization of this proposition is here given, and an application discussed. The application deals with the motion of a simple macromolecule model in an inhomogeneous field of flow—a motion caused only by the influence ofStokes' friction.
A kinematic method to obtain conformal factors
2000
Radial conformal motions are considered in conformally flat space-times and their properties are used to obtain conformal factors. The geodesic case leads directly to the conformal factor of Robertson-Walker universes. General cases admitting homogeneous expansion or orthogonal hypersurfaces of constant curvature are analyzed separately. When the two conditions above are considered together a subfamily of the Stephani perfect fluid solutions, with acceleration Fermi-Walker propagated along the flow of the fluid, follows. The corresponding conformal factors are calculated and contrasted with those associated with Robertson-Walker space-times.
Kinematic relative velocity with respect to stationary observers in Schwarzschild spacetime
2013
We study the kinematic relative velocity of general test particles with respect to stationary observers (using spherical coordinates) in Schwarzschild spacetime, obtaining that its modulus does not depend on the observer, unlike Fermi, spectroscopic and astrometric relative velocities. We study some fundamental particular cases, generalizing some results given in other work about stationary and radial free-falling test particles. Moreover, we give a new result about test particles with circular geodesic orbits: the modulus of their kinematic relative velocity with respect to any stationary observer depends only on the radius of the circular orbit, and so, it remains constant.
Geons in Palatini Theories of Gravity
2017
An explicit implementation of geons in the context of gravitational theories extending general relativity is discussed in detail. Such extensions are formulated in the Palatini approach, where metric and affine connection are regarded as independent entities. This formulation is inspired on the macroscopic description of the physics of crystalline structures with defects in the context of solid-state physics, whose study can provide valuable lessons for going beyond GR. We discuss several theories for the gravitational field including additional contributions of the Ricci tensor in four and higher dimensions. As opposed to the standard metric approach, the Palatini formulation generates gho…