Perturbative Solutions of the Extended Constraint Equations in General Relativity
نویسندگان
چکیده
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface Z in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on Z , and are equivalent to the usual constraint equations that Z satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that is used to solve the usual constraint equations.
منابع مشابه
Elliptic systems
Elliptic problems appear naturally in physics mainly in two situations: as equations which describe equilibrium (for example, stationary solutions in General Relativity) and as constraints for the evolutions equations (for example, constraint equations in Electromagnetism and General Relativity). In addition, in General Relativity they appear often as gauge conditions for the evolutions equatio...
متن کاملRenormalization Group Running of Newton ’ s G : The Static Isotropic Case
Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is argued, related to the observed effective cosmo-lo...
متن کاملBulk Viscous Bianchi Type VI0 Cosmological Model in the Self-creation Theory of Gravitation and in the General Theory of Relativity
In the second self-creation theory of gravitation and in the general theory of relativity, Bianchi type VI0 cosmological model in the presence of viscous fluid is studied. An exact solution of the field equations is given by considering the cosmological model yields a constant decelerations parameter q=constant and the coefficients of the metric are taken as A(t)=[c1t+c<su...
متن کاملDark matter as integration constant in Hořava-Lifshitz gravity
In the non-relativistic theory of gravitation recently proposed by Hořava, the Hamiltonian constraint is not a local equation satisfied at each spatial point but an equation integrated over a whole space. The global Hamiltonian constraint is less restrictive than its local version, and allows a richer set of solutions than in general relativity. We show that a component which behaves like press...
متن کاملApplication of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation
In recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. One such method is known as the new extended (G'/G)-expansion method and was proposed by Roshid et al. In this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (NLPDEs), namely the Benjamin-Ono equation. It is est...
متن کامل