Brans-Dicke theory in general space-time with torsion

We present a Petrov type II general space–time which violates causality in the sense that it allows for the formation of closed timelike curves that appear after a definite instant of time. The metric, which is axially symmetric, admits an expansion-free, twist-free and shear-free null geodesic congruence. From the general metric, we obtain two particular type II metrics. One is a vacuum solution while the other represents a Ricci flat solution with a negative cosmological constant.

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Positivity of the Total Mass of a General Space-Time

Physical Review Letters ◽

10.1103/physrevlett.43.1457 ◽

1979 ◽

Vol 43 (20) ◽

pp. 1457-1459 ◽

Cited By ~ 104

Author(s):

Richard Schoen ◽

Shing-Tung Yau

Keyword(s):

Total Mass ◽

Space Time ◽

General Space

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Toward error estimates for general space-time discretizations of the advection equation

Computing and Visualization in Science ◽

10.1007/s00791-020-00328-z ◽

2020 ◽

Vol 23 (1-4) ◽

Author(s):

Martin J. Gander ◽

Thibaut Lunet

Keyword(s):

Error Estimates ◽

Time Discretization ◽

Space Time ◽

Error Tolerance ◽

Advection Equation ◽

Order Of Accuracy ◽

One Dimensional ◽

General Space ◽

Discretization Schemes ◽

The One

AbstractWe develop new error estimates for the one-dimensional advection equation, considering general space-time discretization schemes based on Runge–Kutta methods and finite difference discretizations. We then derive conditions on the number of points per wavelength for a given error tolerance from these new estimates. Our analysis also shows the existence of synergistic space-time discretization methods that permit to gain one order of accuracy at a given CFL number. Our new error estimates can be used to analyze the choice of space-time discretizations considered when testing Parallel-in-Time methods.

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Continued Gravitational Collapse for Newtonian Stars

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-020-01580-w ◽

2020 ◽

Cited By ~ 1

Author(s):

Yan Guo ◽

Mahir Hadžić ◽

Juhi Jang

Keyword(s):

Gravitational Collapse ◽

Classical Model ◽

Space Time ◽

Poisson System ◽

Leading Order ◽

Singular Behavior ◽

Infinite Dimensional ◽

General Space ◽

Continuous Mass ◽

Gaseous Star

Abstract The classical model of an isolated selfgravitating gaseous star is given by the Euler–Poisson system with a polytropic pressure law $$P(\rho )=\rho ^\gamma $$ P ( ρ ) = ρ γ , $$\gamma >1$$ γ > 1 . For any $$1<\gamma <\frac{4}{3}$$ 1 < γ < 4 3 , we construct an infinite-dimensional family of collapsing solutions to the Euler–Poisson system whose density is in general space inhomogeneous and undergoes gravitational blowup along a prescribed space-time surface, with continuous mass absorption at the origin. The leading order singular behavior is described by an explicit collapsing solution of the pressureless Euler–Poisson system.

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