Charged shells in Lovelock gravity: Hamiltonian treatment and physical implications

Abstract

Using a Hamiltonian treatment, charged thin shells in spherically symmetric spacetimes in d dimensional Lovelock-Maxwell theory are studied. The coefficients of the theory are chosen to obtain a sensible theory, with a negative cosmological constant appearing naturally. After writing the action and the Lagrangian for a spacetime comprised of an interior and an exterior regions, with a thin shell as a boundary in between, one finds the Hamiltonian using an ADM description. For spherically symmetric spacetimes, one reduces the relevant constraints. The dynamic and constraint equations are obtained. The vacuum solutions yield a division of the theory into two branches, d-2k-1>0 (which includes general relativity, Born-Infeld type theories) and d-2k-1=0 (which includes Chern-Simons type theories), where k gives the highest power of the curvature in the Lagrangian. An additional parameter, chi, gives the character of the vacuum solutions. For chi=1 the solutions have a black hole character. For chi=-1 the solutions have a totally naked singularity character. The integration through the thin shell takes care of the smooth junction. The subsequent analysis is divided into two cases: static charged thin shell configurations, and gravitationally collapsing charged dust shells. Physical implications are drawn: if such a large extra dimension scenario is correct, one can extract enough information from the outcome of those collapses as to know, not only the actual dimension of spacetime, but also which particular Lovelock gravity, is the correct one.

arXiv comment25 pages, 9 figures

References in corpus (13)

• The Hierarchy Problem and New Dimensions at a Millimeter
• Phenomenology, Astrophysics and Cosmology of Theories with Sub-Millimeter Dimensions and TeV Scale Quantum Gravity
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
• Black Holes in Theories with Large Extra Dimensions: a Review
• Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World
• Black Hole Scan
• Dimensionally Continued Black Holes
• Black hole and brane production in TeV gravity: A review
• Black hole particle emission in higher-dimensional spacetimes
• Hamiltonian Treatment of the Gravitational Collapse of Thin Shells
• Lagrangian and Hamiltonian formalism for discontinuous fluid and gravitational field
• Hamiltonian treatment of Collapsing Thin Shells in Lanczos-Lovelock's theories
• Charged Rotating Black Hole Formation from Thin Shell Collapse in Three Dimensions

Cited by in corpus (13)

• Thin accretion disks onto brane world black holes
• `Mass without mass' from thin shells in Gauss-Bonnet gravity
• The relation between F(R) gravity and Einstein-conformally invariant Maxwell source
• New solutions of charged regular black holes and their stability
• Collapsing and static thin massive charged dust shells in a Reissner-Nordström black hole background in higher dimensions
• Bonnor stars in d spacetime dimensions
• Theorem to generate Einstein-Non Linear Maxwell Fields
• Extremal Myers-Perry black holes coupled to Born-Infeld electrodynamics in five dimensions
• All fundamental electrically charged thin shells in general relativity: From star shells to tension shell black holes and regular black holes and beyond
• Electrically charged spherical matter shells in higher dimensions: Entropy, thermodynamic stability, and the black hole limit
• Solution for Static, Spherically Symmetric Lovelock Gravity Coupled with Yang-Mills Hierarchy
• Gravitational collapse of charged dust cloud in the Lovelock gravity
• Thin shell dynamics in Lovelock gravity