No-Hair Theorem for Spontaneously Broken Abelian Models in Static Black Holes

The vanishing of the electromagnetic field, for purely electric configurations of spontaneously broken Abelian models, is established in the domain of outer communications of a static asymptotically flat black hole. The proof is gauge invariant, and is accomplished without any dependence on the model. In the particular case of the Abelian Higgs model, it is shown that the only solutions admitted for the scalar field become the vacuum expectation values of the self-interaction.Comment: 8 pages, 2 figures, RevTeX; some changes to match published versio

The Height of a Giraffe

A minor modification of the arguments of Press and Lightman leads to an estimate of the height of the tallest running, breathing organism on a habitable planet as the Bohr radius multiplied by the three-tenths power of the ratio of the electrical to gravitational forces between two protons (rather than the one-quarter power that Press got for the largest animal that would not break in falling over, after making an assumption of unreasonable brittleness). My new estimate gives a height of about 3.6 meters rather than Press's original estimate of about 2.6 cm. It also implies that the number of atoms in the tallest runner is very roughly of the order of the nine-tenths power of the ratio of the electrical to gravitational forces between two protons, which is about 3 x 10^32.Comment: 12 pages, LaTe

Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity

International audienc

On the Status of Highly Entropic Objects

It has been proposed that the entropy of any object must satisfy fundamental (holographic or Bekenstein) bounds set by the object's size and perhaps its energy. However, most discussions of these bounds have ignored the possibility that objects violating the putative bounds could themselves become important components of Hawking radiation. We show that this possibility cannot a priori be neglected in existing derivations of the bounds. Thus this effect could potentially invalidate these derivations; but it might also lead to observational evidence for the bounds themselves.Comment: 6 pages, RevTex, a few editorial change

Cosmic Censorship, Area Theorem, and Self-Energy of Particles

The (zeroth-order) energy of a particle in the background of a black hole is given by Carter's integrals. However, exact calculations of a particle's {\it self-energy} (first-order corrections) are still beyond our present reach in many situations. In this paper we use Hawking's area theorem in order to derive bounds on the self-energy of a particle in the vicinity of a black hole. Furthermore, we show that self-energy corrections {\it must} be taken into account in order to guarantee the validity of Penrose cosmic censorship conjecture.Comment: 11 page

Variational description of multi-fluid hydrodynamics: Uncharged fluids

We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems containing an arbitrary number of interacting fluids and superfluids. In addition to spatial variations we use ``time shifts'' in the variational principle, which allows us to describe dissipative processes with entropy creation, such as chemical reactions, friction or the effects of external non-conservative forces. The resulting framework incorporates the generalization of the entrainment effect originally discussed in the case of the mixture of two superfluids by Andreev and Bashkin. In addition to the conservation of energy and momentum, we derive the generalized conservation laws of vorticity and helicity, and the special case of Ertel's theorem for the single perfect fluid. We explicitly discuss the application of this framework to thermally conducting fluids, superfluids, and superfluid neutron star matter. The equations governing thermally conducting fluids are found to be more general than the standard description, as the effect of entrainment usually seems to be overlooked in this context. In the case of superfluid He4 we recover the Landau--Khalatnikov equations of the two-fluid model via a translation to the ``orthodox'' framework of superfluidity, which is based on a rather awkward choice of variables. Our two-fluid model for superfluid neutron star matter allows for dissipation via mutual friction and also ``transfusion'' via beta-reactions between the neutron fluid and the proton-electron fluid.Comment: uses RevTeX 4; 20 pages. To appear in PRD. v2: removed discussion of charged fluids and coupling to electromagnetic fields, which are submitted as a separate paper for a clearer presentation v3: fixed typo in Eq.(9), updated some reference

Scalar hairy black holes and solitons in asymptotically flat spacetimes

A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\phi)$ of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations for the minimal coupling case, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture. For the nonminimal coupling case, the stability will be analyzed in a forthcoming paper.Comment: 7 pages, 10 postscript figures, file tex, new postscript figs. and references added, stability analysis revisite

Entropy of Lovelock Black Holes

A general formula for the entropy of stationary black holes in Lovelock gravity theories is obtained by integrating the first law of black hole mechanics, which is derived by Hamiltonian methods. The entropy is not simply one quarter of the surface area of the horizon, but also includes a sum of intrinsic curvature invariants integrated over a cross section of the horizon.Comment: 15 pages, plain Latex, NSF-ITP-93-4

On Relativistic Material Reference Systems

This work closes certain gaps in the literature on material reference systems in general relativity. It is shown that perfect fluids are a special case of DeWitt's relativistic elastic media and that the velocity--potential formalism for perfect fluids can be interpreted as describing a perfect fluid coupled to a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is carried out and the constraints that arise when the system is coupled to gravity are studied. When the Hamiltonian constraint is resolved with respect to the clock momentum, the resulting true Hamiltonian is found to be a functional only of the gravitational variables. The true Hamiltonian is explicitly displayed when the medium is dust, and is shown to depend on the detailed construction of the clocks.Comment: 18 pages, ReVTe