On asymptotically flat solutions of Einstein's equations periodic in time: I
نویسندگان
چکیده
By an argument similar to that of Gibbons and Stewart (1984 Absence of asymptotically flat solutions of Einstein’s equations which are periodic and empty near infinity Classical General Relativity (London, 1983) ed W Bonnor, J N Islam and M A H Callum (Cambridge: Cambridge University Press) pp 77– 94), but in a different coordinate system and less restrictive gauge, we show that any weakly asymptotically simple, analytic vacuum or electrovacuum solutions of the Einstein equations which are periodic in time are necessarily stationary. PACS numbers: 04.20.−q, 04.20.Cv, 04.20.Ha
منابع مشابه
Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth
In this paper, we consider the following Kirchhoff-type equations: $-left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}, quad mbox{in }mathbb{R}^{3},$ $u(x)>0, quad mbox{in }mathbb{R}^{3},$ $uin H^{1}(mathbb{R}^{3}) ,$ where $a,b>0$ are constants and $lambda$ is a positive parameter. The aim of this paper is to study the existence of positive ...
متن کاملOn analytic asymptotically-flat vacuum and electrovac metrics, periodic in time
By an argument similar to that of Gibbons and Stewart [5], we show that there are no weakly-asymptotically-simple, analytic vacuum or electrovac solutions of the Einstein equations which are periodic in time.
متن کاملJa n 19 98 Interpretation of the Siklos solutions as exact gravitational waves in the anti - de Sitter universe
The Siklos class of solutions of Einstein's field equations is investigated by analytical methods. By studying the behaviour of free particles we reach the conclusion that the space-times represent exact gravitational waves propagating in the anti-de Sitter universe. The presence of a negative cosmological constant implies that the 'background' space is not asymptotically flat and requires a 'r...
متن کاملProbing Quantum Gravity Through Exactly Soluble Midi - Superspaces
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar fields. We first reexamine the quantization of this midi-superspace paying special attention to the asymptotically flat boundary conditions and to certain functi...
متن کاملScalar field collapse in three - dimensions
Scalar field collapse in three-dimensions. Abstract We study an analytical solution to the Einstein's equations in 2 + 1-dimensions, representing the collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters , this solution exhibits all three, known, end states of a collapse situation: Minkowski space-time after a bouncing, naked...
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 2010