Staticity Theorem for Higher Dimensional Generalized Einstein-Maxwell System

Abstract

We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the topology of (n-2)-sphere we obtained the generalized first law of black hole thermodynamics. Supposing that a black hole evevt horizon comprisesw a bifurcation Killing horizon with a bifurcate surface we find that the solution is static in the exterior world, when the Killing timelike vector field is normal to the horizon and has vanishing electric or magnetic fields on static slices.

10 pages, REVTEX, to published in Phys.Rev. D15

References in corpus (2)

• Uniqueness Theorem for Generalized Maxwell Electric and Magnetic Black Holes in Higher Dimensions
• Uniqueness theorem for stationary black hole solutions of σ-models in five dimensions

Cited by in corpus (28)

• Black Holes in Higher Dimensions
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• The Role of Dipole Charges in Black Hole Thermodynamics
• Black hole uniqueness theorems in higher dimensional spacetimes
• Evolution of a Self-interacting Scalar Field in the spacetime of a Higher Dimensional Black Hole
• On the uniqueness of extremal vacuum black holes
• The Decay of Dirac Hair around a Dilaton Black Hole
• Decay of Massive Dirac Hair on a Brane-World Black Hole
• Decay of Dirac Massive Hair in the Background of Spherical Black Hole
• Uniqueness of photon sphere for Einstein-Maxwell-dilaton black holes with arbitrary coupling constant
• Decay of massive hair on brane black hole
• Uniqueness theorem for stationary black ring solution of $\sigma$-models in five dimensions
• Black Rings and the Physical Process Version of the First Law of Thermodynamics
• First Law of Black Rings Thermodynamics in Higher Dimensional Dilaton Gravity with p + 1 Strength Forms
• Uniqueness of charged static asymptotically flat black holes in dynamical Chern-Simons gravity
• First Law of Black Rings Thermodynamics in Higher Dimensional Chern-Simons Gravity
• Abelian-Higgs hair on stationary axisymmetric black hole in Einstein-Maxwell-axion-dilaton gravity
• First Law of Black Saturn Thermodynamics
• Physical Process Version of the First Law of Thermodynamics for Black Holes in Higher Dimensional Gravity
• Decay of massive scalar hair in the background of a dilaton gravity black hole
• Uniqueness of dilaton Melvin-Schwarzschild solution
• Matter ouside a Static Higher-dimensional Black Hole
• Static black holes and strictly static spacetimes in Einstein-Gauss-Bonnet gravity with gauge field
• First Law of p-brane Thermodynamics
• Uniqueness of dark matter magnetized static black hole spacetime
• Evolution of Massive Scalar Fields in the Spacetime of a Tense Brane Black Hole
• Dark matter influence on black hole objects thermodynamics
• Mass formulae and staticity condition for dark matter charged black holes