No Scalar-Haired Cauchy Horizon Theorem in Charged Gauss-Bonnet Black Holes

Recently, a ``no inner (Cauchy) horizon theorem" for static black holes with non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories and also in Einstein-Maxwell-Horndeski theories with the non-minimal coupling of a charged (complex) scalar field to Einstein tensor. In this paper, we study an extension of the theorem to the static black holes in Einstein-Maxwell-Gauss-Bonnet-scalar theories, or simply, charged Gauss-Bonnet (GB) black holes. We find that no inner horizon with charged scalar hairs is allowed for the planar (k=0) black holes, as in the case without GB term. On the other hand, for the non-planar (k=+1,-1) black holes, we find that the haired inner horizon can not be excluded due to GB effect generally, though we can not find a simple condition for its existence. As some explicit examples of the theorem, we study numerical GB black hole solutions with charged scalar hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good agreements with the theorem. As a byproduct, we find a ``no-go theorem" for charged de Sitter GB black holes with charged scalar hairs in arbitrary dimensions.Comment: 21 pages, 8 figure

Symmetries and Conservation Laws in Horava Gravity

Horava gravity has been proposed as a renormalizable quantum gravity without the ghost problem through anisotropic scaling dimensions which break Lorentz symmetry in UV. In the Hamiltonian formalism, due to the Lorentz-violating terms, the constraint structure looks quite different from that of general relativity (GR) but we have recently found that "there exists the case where we can recover the same number of degrees of freedom as in GR", in a rather general set-up. In this paper, we study its Lagrangian perspectives and examine the full diffeomorphism (Diff) symmetry and its associated conservation laws in Horava gravity. Surprisingly, we find that the full Diff symmetry in the action can also be recovered when a certain condition, called "super-condition", which super-selects the Lorentz-symmetric sector in Horava gravity, is satisfied. This indicates that the broken Lorentz symmetry, known as "foliation-preserving" Diff, is just an "apparent" symmetry of the Horava gravity action and rather its "full action symmetry can be as large as the Diff in GR ". The super-condition exactly corresponds to the tertiary constraint in Hamiltonian formalism which is the second-class constraint and provides a non-trivial realization of the Lorentz symmetry otherwise being absent apparently. From the recovered Lorentz symmetry in the action, we obtain the conservation laws with the Noether currents as in covariant theories. The general formula for the conserved Noether charges reproduces the mass of four-dimensional static black holes with an "arbitrary" cosmological constant in Horava gravity, and is independent of ambiguities associated with the choice of asymptotic boundaries. We also discuss several challenging problems, including its implications to Hamiltonian formalism, black hole thermodynamics, radiations from colliding black holes.Comment: 18 pages, no figure

The Hamiltonian Dynamics of Horava Gravity

We consider the Hamiltonian formulation of Horava gravity in arbitrary dimensions, which has been proposed as a renormalizable gravity model for quantum gravity without the ghost problem. We study the "full" constraint analysis of the "non-projectable" Horava gravity whose potential, V(R), is an arbitrary function of the (intrinsic) Ricci scalar R. We find that there exist generally distinct cases of this theory, depending on (i) whether the Hamiltonian constraint generates new (second-class) constraints (Cases A, C) or just fixes the associated Lagrange multipliers (Case B), or (ii) whether the IR Lorentz-deformation parameter \lambda is at the conformal point (Case C) or not (Cases A, B). It is found that, for Cases A and C, the dynamical degrees of freedom are the same as in general relativity, while, for Case B, there is "one additional phase-space degree of freedom", representing an extra (odd) scalar graviton mode. This would resolve the long-standing debates about the extra graviton modes and achieves the dynamical consistency of the Horava gravity, at the "fully non-linear" level. Several exact solutions are also considered as some explicit examples of the new constraints. The structure of the newly obtained, "extended" constraint algebra seems to be generic to Horava gravity and its general proof would be a challenging problem. Some other challenging problems, which include the path integral quantization and the Dirac bracket quantization are discussed also.Comment: Matches published version, Typos correcte

Plasma Levels of Plasminogen Activator Inhibitor Type 1 and Vitronectin in Children With Cancer

Background: The plasminogen activator system controls intravascular fibrin deposition; besides, it also participates in a wide variety of physiologic and pathologic processes, including cancer