Higher dimensional black holes as constrained systems

Abstract

We construct a Lagrangian and Hamiltonian formulation for charged black holes in a d-dimensional maximally symmetric spherical space. By considering first new variables that give raise to an interesting dimensional reduction of the problem, we show that the introduction of a charge term is compatible with classical solutions to Einstein equations. In fact, we derive the well-known solutions for charged black holes, specially in the case of d=4, where the Reissner-Nordström solution holds, without reference to Einstein field equations. We argue that our procedure may be of help for clarifying symmetries and dynamics of black holes, as well as some quantum aspects.

15 pages, no figures, some minor changes made, one reference added

References in corpus (6)

• Conditional Symmetries and the Canonical Quantization of Constrained Minisuperspace Actions: the Schwarzschild case
• Negative Horizon Mass for Rotating Black Holes
• Higher Dimensional Cosmology: Relations among the radii of two homogeneous spaces
• A Link Between Black Holes and the Golden Ratio
• SO(n + 1) Symmetric Solutions of the Einstein Equations in Higher Dimensions
• Hidden Structures of Black Holes

Cited by in corpus (5)

• Minisuperspace Canonical Quantization of the Reissner-Nordstrom Black Hole via Conditional Symmetries
• The golden ratio in Schwarzschild-Kottler black holes
• Gyroscope precession frequency analysis of a five dimensional charged rotating Kaluza-Klein black hole
• Hyperbolic trajectories around Black Holes
• Towards a unified Lagrangian formalism for Cosmology and Black Holes