57 research outputs found

### Black holes cannot support conformal scalar hair

It is shown that the only static asymptotically flat non-extrema black hole
solution of the Einstein-conformally invariant scalar field equations having
the scalar field bounded on the horizon, is the Schwarzschild one. Thus black
holes cannot be endowed with conformal scalar hair of finite length.Comment: 15 pages, Te

### 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 Jang equation, apparent horizons, and the Penrose inequality

The Jang equation in the spherically symmetric case reduces to a first order
equation. This permits an easy analysis of the role apparent horizons play in
the (non)existence of solutions. We demonstrate that the proposed derivation of
the Penrose inequality based on the Jang equation cannot work in the
spherically symmetric case. Thus it is fruitless to apply this method, as it
stands, to the general case. We show also that those analytic criteria for the
formation of horizons that are based on the use of the Jang equation are of
limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte

### Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data

We establish necessary conditions for the appearance of both apparent
horizons and singularities in the initial data of spherically symmetric general
relativity when spacetime is foliated extrinsically. When the dominant energy
condition is satisfied these conditions assume a particularly simple form. Let
$\rho_{Max}$ be the maximum value of the energy density and $\ell$ the radial
measure of its support. If $\rho_{Max}\ell^2$ is bounded from above by some
numerical constant, the initial data cannot possess an apparent horizon. This
constant does not depend sensitively on the gauge. An analogous inequality is
obtained for singularities with some larger constant. The derivation exploits
Poincar\'e type inequalities to bound integrals over certain spatial scalars. A
novel approach to the construction of analogous necessary conditions for
general initial data is suggested.Comment: 15 pages, revtex, to appear in Phys. Rev.

### Trapped surfaces and the Penrose inequality in spherically symmetric geometries

We demonstrate that the Penrose inequality is valid for spherically symmetric
geometries even when the horizon is immersed in matter. The matter field need
not be at rest. The only restriction is that the source satisfies the weak
energy condition outside the horizon. No restrictions are placed on the matter
inside the horizon. The proof of the Penrose inequality gives a new necessary
condition for the formation of trapped surfaces. This formulation can also be
adapted to give a sufficient condition. We show that a modification of the
Penrose inequality proposed by Gibbons for charged black holes can be broken in
early stages of gravitational collapse. This investigation is based exclusively
on the initial data formulation of General Relativity.Comment: plain te

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