The Gauss Map and 2+1 Gravity
نویسنده
چکیده
We prove that the Gauss map of a surface of constant mean curvature embedded in Minkowski space is harmonic. This fact will then be used to study 2+1 gravity for surfaces of genus higher than one. By considering the energy of the Gauss map, a canonical transform between the ADM reduced variables and holonomy variables can be constructed. This allows one to solve (in principle) for the evolution in the ADM variables without having to explicitly solve the constraints first.
منابع مشابه
L_1 operator and Gauss map of quadric surfaces
The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...
متن کاملسیاهچالههای نظریه گوس- بونه در حضور شاره کامل
In this paper, the solutions of the Gauss-Bonnet theory of gravity was proposed in the presence of a perfect fluid with thermodynamic pressure P and energy gravity ρ in n-dimension. Accordingly, perfect fluid tensor was regarded as energy-momentum tensor and the static and radiating solutions for the linear equation of state p = wρ was calculated. This solution contains all the solutions alread...
متن کامل/ 03 11 26 7 v 1 2 7 N ov 2 00 3 Gauss - Bonnet gravity renders negative tension branewolds unstable
We show that the Gauss-Bonnet correction to Einstein gravity induces a gravitational tachyon mode, namely an unstable spin 2 fluctuation, in the Randall-Sundrum I model. We demonstrate that this instability is generically related to the presence of a negative tension brane in the set-up, with or without Z2-symmetry across it. Indeed it is shown that the tachyon mode is a bound state localised o...
متن کاملNUT-Charged Black Holes in Gauss-Bonnet Gravity
We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in d dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at r = N , there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter α goes to zero. Fur...
متن کاملTesting the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
This is the final fifth paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. Here we consider interacting quantum field theories, specifically we consider the non – Abelean Gauss constraints of Einstein – Yang – Mills theory and 2+1 gravity. Interestingly, while Yang – Mills theory in 4D is not yet rigorousl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008