General Definition of Gravitational Tension
T. Harmark, N. A. Obers
TL;DR
This paper introduces a general definition of gravitational tension applicable to various space-times, extending existing concepts and verifying consistency with known formulas, especially for Kaluza-Klein black holes and near-extremal branes.
Contribution
It provides a unified, extrinsic curvature-based definition of gravitational tension that applies to both asymptotically flat and non-flat space-times.
Findings
Consistency with ADM tension formulas for asymptotically-flat space-times
Application to Kaluza-Klein black holes confirms validity
Extension to near-extremal branes demonstrates broader applicability
Abstract
In this note we give a general definition of the gravitational tension in a given asymptotically translationally-invariant spatial direction of a space-time. The tension is defined via the extrinsic curvature in analogy with the Hawking-Horowitz definition of energy. We show the consistency with the ADM tension formulas for asymptotically-flat space-times, in particular for Kaluza-Klein black hole solutions. Moreover, we apply the general tension formula to near-extremal branes, constituting a check for non-asymptotically flat space-times.
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