105 research outputs found
Black holes in which the electrostatic or scalar equation is solvable in closed form
We show that the method used in the Schwarzschild black hole for finding the
elementary solution of the electrostatic equation in closed form cannot extend
in higher dimensions. By contrast, we prove the existence of static,
spherically symmetric geometries with a non-degenerated horizon in which the
static scalar equation can be solved in closed form. We give the explicit
results in 6 dimensions. We determine moreover the expressions of the
electrostatic potential and of the static scalar field for a point source in
the extremal Reissner-Nordstrom black holes in higher dimensions.Comment: 20 pages, no figur
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
Electrostatic self-energy and Bekenstein entropy bound in the massive Schwinger model
We obtain the electrostatic energy of two opposite charges near the horizon
of stationary black-holes in the massive Schwinger model. Besides the confining
aspects of the model, we discuss the Bekenstein entropy upper bound of a
charged object using the generalized second law. We show that despite the
massless case, in the massive Schwinger model the entropy of the black hole and
consequently the Bekenstein bound are altered by the vacuum polarization.Comment: 14 pages, accepted for publication in "Gen. Rel. Grav. (2005)
On Black Hole Scalar Hair in Asymptotically Anti de Sitter Spacetimes
The unexpected discovery of hairy black hole solutions in theories with
scalar fields simply by considering asymptotically Anti de-Sitter, rather than
asymptotically flat, boundary conditions is analyzed in a way that exhibits in
a clear manner the differences between the two situations.
It is shown that the trivial Schwarzschild Anti de Sitter becomes unstable in
some of these situations, and the possible relevance of this fact for the
ADS/CFT conjecture is pointed out.Comment: 12 pages. Published versio
A New Class of Exact Hairy Black Hole Solutions
We present a new class of black hole solutions with minimally coupled scalar
field in the presence of a negative cosmological constant. We consider a
one-parameter family of self-interaction potentials parametrized by a
dimensionless parameter . When , we recover the conformally invariant
solution of the Martinez-Troncoso-Zanelli (MTZ) black hole. A non-vanishing
signals the departure from conformal invariance. All solutions are
perturbatively stable for negative black hole mass and they may develop
instabilities for positive mass. Thermodynamically, there is a critical
temperature at vanishing black hole mass, where a higher-order phase transition
occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch
of hairy solutions which undergo a first-order phase transition at a second
critical temperature which depends on and it is higher than the MTZ
critical temperature. As , this second critical temperature diverges.Comment: 18 pages, 6 figures, minor changes, references added, published
versio
Algebraic approach to quantum black holes: logarithmic corrections to black hole entropy
The algebraic approach to black hole quantization requires the horizon area
eigenvalues to be equally spaced. As shown previously, for a neutral
non-rotating black hole, such eigenvalues must be -fold degenerate if
one constructs the black hole stationary states by means of a pair of creation
operators subject to a specific algebra. We show that the algebra of these two
building blocks exhibits symmetry, where the area
operator generates the U(1) symmetry. The three generators of the SU(2)
symmetry represent a {\it global} quantum number (hyperspin) of the black hole,
and we show that this hyperspin must be zero. As a result, the degeneracy of
the -th area eigenvalue is reduced to for large , and
therefore, the logarithmic correction term should be added to the
Bekenstein-Hawking entropy. We also provide a heuristic approach explaining
this result, and an evidence for the existence of {\it two} building blocks.Comment: 15 pages, Revtex, to appear in Phys. Rev.
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 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
Highly damped quasinormal modes of Kerr black holes
Motivated by recent suggestions that highly damped black hole quasinormal
modes (QNM's) may provide a link between classical general relativity and
quantum gravity, we present an extensive computation of highly damped QNM's of
Kerr black holes. We do not limit our attention to gravitational modes, thus
filling some gaps in the existing literature. The frequency of gravitational
modes with l=m=2 tends to \omega_R=2 \Omega, \Omega being the angular velocity
of the black hole horizon. If Hod's conjecture is valid, this asymptotic
behaviour is related to reversible black hole transformations. Other highly
damped modes with m>0 that we computed do not show a similar behaviour. The
real part of modes with l=2 and m<0 seems to asymptotically approach a constant
value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of
a. For any perturbing field, trajectories in the complex plane of QNM's with
m=0 show a spiralling behaviour, similar to the one observed for
Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the
asymptotic separation in the imaginary part of consecutive modes with m>0 is
given by 2\pi T_H (T_H being the black hole temperature). We conjecture that
for all values of l and m>0 there is an infinity of modes tending to the
critical frequency for superradiance (\omega_R=m) in the extremal limit.
Finally, we study in some detail modes branching off the so--called
``algebraically special frequency'' of Schwarzschild black holes. For the first
time we find numerically that QNM multiplets emerge from the algebraically
special Schwarzschild modes, confirming a recent speculation.Comment: 19 pages, 11 figures. Minor typos corrected. Updated references to
take into account some recent development
Hairy black holes in theories with massive gravitons
This is a brief survey of the known black hole solutions in the theories of
ghost-free bigravity and massive gravity. Various black holes exist in these
theories, in particular those supporting a massive graviton hair. However, it
seems that solutions which could be astrophysically relevant are the same as in
General Relativity, or very close to them. Therefore, the no-hair conjecture
essentially applies, and so it would be hard to detect the graviton mass by
observing black holes.Comment: References added. 20 pages, 3 figures, based on the talk given at the
7-th Aegean Summer School "Beyond Einstein's theory of gravity", September
201
- …