General Definition of Gravitational Tension

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.

17 pages, v2: Appendix added on deriving ADM-type tension formula from general tension formula

References in corpus (2)

• The Dynamics of General Relativity
• A critical dimension in the black-string phase transition

Cited by in corpus (66)

• The Phase Transition between Caged Black Holes and Black Strings - A Review
• AdS Bubbles, Entropy and Closed String Tachyons
• Instabilities of Black Strings and Branes
• Black Hole Thermodynamics with Conical Defects
• Extremal vacuum black holes in higher dimensions
• Higher-dimensional Rotating Charged Black Holes
• New Horizons for Black Holes and Branes
• Heating up the BIon
• New nonuniform black string solutions
• Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes
• Thermodynamics of static black objects in D dimensional Einstein-Gauss-Bonnet gravity with D-4 compact dimensions
• Conserved gravitational charges from Yano tensors
• Thermodynamics of the hot BIon
• New Phases of Near-Extremal Branes on a Circle
• Black Holes in Higher-Dimensional Gravity
• G2 Dualities in D=5 Supergravity and Black Strings
• Non-uniform black strings and the critical dimension in the $1/D$ expansion
• Phases of Kaluza-Klein Black Holes: A Brief Review
• Blackfolds in (Anti)-de Sitter Backgrounds
• Emergence and Expansion of Cosmic Space in BIonic system
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Stresses and Strains in the First Law for Kaluza-Klein Black Holes
• On squashed black holes in Godel universes
• Thermodynamics of Squashed Kaluza-Klein Black Holes and Black Strings -- A Comparison of Reference Backgrounds --
• Thermal string probes in AdS and finite temperature Wilson loops
• Mass and Free energy in Thermodynamics of Squashed Kaluza-Klein Black Holes
• Quasilocal equilibrium condition for black ring
• A General Black String and its Microscopics
• New stable phase of non-uniform charged black strings
• Kaluza-Klein models: can we construct a viable example?
• Harrison transformation and charged black objects in Kaluza-Klein theory
• The First Law for Boosted Kaluza-Klein Black Holes
• 1/2 BPS Geometries of M2 Giant Gravitons
• Magnetized configurations with black holes and Kaluza-Klein bubbles: Smarr-like relations and first law
• Charged Kaluza-Klein double-black holes in five dimensions
• Lattice Black Branes: Sphere Packing in General Relativity
• New Phases of Thermal SYM and LST from Kaluza-Klein Black Holes
• Charged black holes on a Kaluza-Klein bubble
• Gravitational Tension, Spacetime Pressure and Black Hole Volume
• Shockwaves in black hole microstate geometries
• Thermodynamics of the Near-Extremal NS5-brane
• D-brane Construction of the 5D NHEK Dual
• Three-Charge Black Holes on a Circle
• A bridge between unified cosmic history by $f(R)$-gravity and BIonic system
• Remarks on gravitational interaction in Kaluza-Klein models
• Black branes and black strings in the astrophysical and cosmological context
• Geometrical properties of the trans-spherical solutions in higher dimensions
• Einstein-Gauss-Bonnet black strings at large $\alpha$
• Significance of tension for gravitating masses in Kaluza-Klein models
• Many-body problem in Kaluza-Klein models with toroidal compactification
• Genuine Cosmic Hair
• Exact and asymptotic black branes with spherical compactification
• A Generalised Garfinkle-Vachaspati Transform
• Sum Rule for the ADM Mass and Tensions in Planar AdS Spacetimes
• The Flowing BIon
• Weak field limit of higher dimensional massive Brans-Dicke gravity: Observational constraints
• First Law of p-brane Thermodynamics
• String or branelike solutions in four-dimensional Einstein gravity in the presence of cosmological constant
• The Angular Tension of Black Holes
• Holographic Cosmology from a System of M2-M5 Branes
• First Law and a Variational Principle for Static Asymptotically Randall-Sundrum Black Holes
• Entropy of Three-Charge Black Holes on a Circle
• Tension term, interchange symmetry, and the analogy of energy and tension laws of the AdS soliton solution
• Weak-field limit of Kaluza-Klein models with spherically symmetric static scalar field: observational constraints
• Squashed black holes at large $D$
• Exact Solutions and Black Hole Stability in Higher Dimensional Supergravity Theories