Search results for "Field equation"
showing 10 items of 31 documents
The nonadiabatic general-relativistic stellar oscillations
1990
We have derived the equations which govern the linear nonadiabatic general-relativistic radial oscillations. The perturbation produces a heat flux that is coupled with the geometry, through the Einstein field equations of a stellar configuration. The classical limit is recovered. The stability conditions are examined by means of a simplified one-zone model.
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…
Method to obtain shear-free two-fluid solutions of Einstein's equations.
1989
We use the Einstein equations, stated as an initial-value problem (3+1 formalism), to present a method for obtaining a class of solutions which may be interpreted as the gravitational field produced by a mixture of two perfect fluids. The four-velocity of one of the components is assumed to be a shear-free, irrotational, and geodesic vector field. The solutions are given up to a set of a hyperbolic quasilinear system.
Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
2004
A renormalization group (RG) improvement of the Einstein-Hilbert action is performed which promotes Newton's constant and the cosmological constant to scalar functions on spacetime. They arise from solutions of an exact RG equation by means of a ``cutoff identification'' which associates RG scales to the points of spacetime. The resulting modified Einstein equations for spherically symmetric, static spacetimes are derived and analyzed in detail. The modifications of the Newtonian limit due to the RG evolution are obtained for the general case. As an application, the viability of a scenario is investigated where strong quantum effects in the infrared cause Newton's constant to grow at large …
The Scherk-Schwarz mechanism as a flux compactification with internal torsion
2005
The aim of this paper is to make progress in the understanding of the Scherk-Schwarz dimensional reduction in terms of a compactification in the presence of background fluxes and torsion. From the eleven dimensional supergravity point of view, we find that a general E6(6) S-S phase may be obtained by turning on an appropriate background torsion, together with suitable fluxes, some of which can be directly identified with certain components of the four-form field-strength. Furthermore, we introduce a novel (four dimensional) approach to the study of dualities between flux/torsion compactifications of Type II/M-theory. This approach defines the action that duality should have on the backgroun…
Importance of torsion and invariant volumes in Palatini theories of gravity
2013
We study the field equations of extensions of general relativity formulated within a metric-affine formalism setting torsion to zero (Palatini approach). We find that different (second-order) dynamical equations arise depending on whether torsion is set to zero (i) a priori or (ii) a posteriori, i.e., before or after considering variations of the action. Considering a generic family of Ricci-squared theories, we show that in both cases the connection can be decomposed as the sum of a Levi-Civita connection and terms depending on a vector field. However, while in case (i) this vector field is related to the symmetric part of the connection, in (ii) it comes from the torsion part and, therefo…
A scenario for critical scalar field collapse in $AdS_3$
2014
We present a family of exact solutions, depending on two parameters $\alpha$ and $b$ (related to the scalar field strength), to the three-dimensional Einstein-scalar field equations with negative cosmological constant $\Lambda$. For $b=0$ these solutions reduce to the static BTZ family of vacuum solutions, with mass $M = -\alpha$. For $b\neq0$, the solutions become dynamical and develop a strong spacelike central singularity. The $\alpha0$ agrees qualitatively with that observed in numerical simulations of subcritical collapse. We analyze the linear perturbations of the threshold solution, $\alpha=0$, in the $\Lambda=0$ approximation, and find that it has only one unstable growing mode, whi…
On cosmic quantum tunneling from “nothing”
2015
We extend to a general Λ-Eriedmann-Lemaitre-Robertson-Walker (ΛFLRW) a previous result by Vilenkin and others according to which a closed de Sitter universe could be created from "nothing". More specifically, our main result is that only the closed ΛFLRW universe (but not the open and flat ones) could be created from a corresponding instanton, that is, from the corresponding solution with signature +4 of the Einstein field equations. Before getting this result the suitable corresponding instantons are calculated. The result is in accordance with previous results by another authors obtained by different methods.
Comparison between the fCCZ4 and BSSN formulations of Einstein equations in spherical polar coordinates
2015
Recently, we generalized a covariant and conformal version of the Z4 system of the Einstein equations using a reference metric approach, that we denote as fCCZ4. We successfully implemented and tested this approach in a 1D code that uses spherical coordinates and assumes spherical symmetry, obtaining from one to three orders of magnitude reduction of the Hamiltonian constraint violations with respect to the BSSN formulation in tests involving neutron star spacetimes. In this work, we show preliminary results obtained with the 3D implementation of the fCCZ4 formulation in a fully 3D code using spherical polar coordinates.
A Lemaitre-Tolman-Bondi cosmological wormhole
2010
We present a new analytical solution of the Einstein field equations describing a wormhole shell of zero thickness joining two Lema{\i}tre-Tolman-Bondi universes, with no radial accretion. The material on the shell satisfies the energy conditions and, at late times, the shell becomes comoving with the dust-dominated cosmic substratum.