Non-stationary Energy in General Relativity

Abstract

Using the time evolution equations of (cosmological) General Relativity in the first order Fischer-Marsden form, we construct an integral that measures the amount of non-stationary energy on a given spacelike hypersurface in $D$ dimensions. The integral vanishes for stationary spacetimes; and with a further assumption, reduces to Dain's invariant on the boundary of the hypersurface which is defined with the Einstein constraints and a fourth order equation defining approximate Killing symmetries.

arXiv comment16 pages,dedicated to the memory of Rahmi Guven (1948-2019) who spent a life in gravity research in a region quite timid about science

References in corpus (7)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• The Dynamics of General Relativity
• Killing Initial Data
• Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem
• Killing vectors in asymptotically flat space--times: II. Asymptotically translational Killing vectors and the rigid positive energy theorem in higher dimensions
• A new geometric invariant on initial data for Einstein equations
• Dain's invariant on non-time symmetric initial data sets

Cited by in corpus (8)

• Dain's invariant for black hole initial data
• Bowen-York Model Solution Redux
• Non-stationary Energy of Perfect Fluid Sources in General Relativity
• Basics of Apparent Horizons in Black Hole Physics
• Approximate analytical description of apparent horizons for initial data with momentum and spin
• Constraints and Time Evolution in Generic $f$(Riemann) Gravity
• Perturbative solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen-York formalism
• Perturbative Analytical Construction of Bowen-York Initial Data for Binary Black Holes up to Third Order in Spin and Linear Momentum