110 research outputs found
Rotating black hole hair
A Kerr black hole sporting cosmic string hair is studied in the context of the abelian Higgs model vortex. It is shown that such a system displays much richer phenomenology than its static Schwarzschild or Reissner-Nordstrom cousins, for example, the rotation generates a near horizon ‘electric’ field. In the case of an extremal rotating black hole, two phases of the Higgs hair are possible: large black holes exhibit standard hair, with the vortex piercing the event horizon. Small black holes on the other hand, exhibit a flux-expelled solution, with the gauge and scalar field remaining identically in their false vacuum state on the event horizon. This solution however is extremely sensitive to confirm numerically, and we conjecture that it is unstable due to a supperradiant mechanism similar to the Kerr-adS instability. Finally, we compute the gravitational back reaction of the vortex, which turns out to be far more nuanced than a simple conical deficit. While the string produces a conical effect, it is conical with respect to a local co-rotating frame, not with respect to the static frame at infinity
Applications of hidden symmetries to black hole physics
This work is a brief review of applications of hidden symmetries to black
hole physics. Symmetry is one of the most important concepts of the science. In
physics and mathematics the symmetry allows one to simplify a problem, and
often to make it solvable. According to the Noether theorem symmetries are
responsible for conservation laws. Besides evident (explicit) spacetime
symmetries, responsible for conservation of energy, momentum, and angular
momentum of a system, there also exist what is called hidden symmetries, which
are connected with higher order in momentum integrals of motion. A remarkable
fact is that black holes in four and higher dimensions always possess a set
(`tower') of explicit and hidden symmetries which make the equations of motion
of particles and light completely integrable. The paper gives a general review
of the recently obtained results. The main focus is on understanding why at all
black holes have something (symmetry) to hide.Comment: This is an extended version of the talks at NEB-14 conference
(June,Ioannina,Greece) and JGRG20 meeting (September, Kyoto, Japan
Symmetries of the Dirac operator with skew-symmetric torsion
In this paper, we consider the symmetries of the Dirac operator derived from
a connection with skew-symmetric torsion. We find that the generalized
conformal Killing-Yano tensors give rise to symmetry operators of the massless
Dirac equation, provided an explicitly given anomaly vanishes. We show that
this gives rise to symmetries of the Dirac operator in the case of strong
Kahler with torsion (KT) and strong hyper-Kahler with torsion (HKT) manifolds
Exactly solvable strings in Minkowski spacetime
We study the integrability of the equations of motion for the Nambu-Goto
strings with a cohomogeneity-one symmetry in Minkowski spacetime. A
cohomogeneity-one string has a world surface which is tangent to a Killing
vector field. By virtue of the Killing vector, the equations of motion can be
reduced to the geodesic equation in the orbit space. Cohomogeneity-one strings
are classified into seven classes (Types I to VII). We investigate the
integrability of the geodesic equations for all the classes and find that the
geodesic equations are integrable. For Types I to VI, the integrability comes
from the existence of Killing vectors on the orbit space which are the
projections of Killing vectors on Minkowski spacetime. For Type VII, the
integrability is related to a projected Killing vector and a nontrivial Killing
tensor on the orbit space. We also find that the geodesic equations of all
types are exactly solvable, and show the solutions.Comment: 11 pages, a reference added, some points clarifie
Do Killing-Yano tensors form a Lie Algebra?
Killing-Yano tensors are natural generalizations of Killing vectors. We
investigate whether Killing-Yano tensors form a graded Lie algebra with respect
to the Schouten-Nijenhuis bracket. We find that this proposition does not hold
in general, but that it does hold for constant curvature spacetimes. We also
show that Minkowski and (anti)-deSitter spacetimes have the maximal number of
Killing-Yano tensors of each rank and that the algebras of these tensors under
the SN bracket are relatively simple extensions of the Poincare and (A)dS
symmetry algebras.Comment: 17 page
Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
We investigate the critical behaviour of charged and rotating AdS black holes
in d spacetime dimensions, including effects from non-linear electrodynamics
via the Born-Infeld action, in an extended phase space in which the
cosmological constant is interpreted as thermodynamic pressure. For
Reissner-Nordstrom black holes we find that the analogy with the Van der Walls
liquid-gas system holds in any dimension greater than three, and that the
critical exponents coincide with those of the Van der Waals system. We find
that neutral slowly rotating black holes in four space-time dimensions also
have the same qualitative behaviour. However charged and rotating black holes
in three spacetime dimensions do not exhibit critical phenomena. For
Born-Infeld black holes we define a new thermodynamic quantity B conjugate to
the Born-Infeld parameter b that we call Born-Infeld vacuum polarization. We
demonstrate that this quantity is required for consistency of both the first
law of thermodynamics and the corresponding Smarr relation.Comment: 23 pages, 32 figures, v2: minor changes, upgraded reference
Pressure and volume in the first law of black hole thermodynamics
The mass of a black hole is interpreted, in terms of thermodynamic
potentials, as being the enthalpy, with the pressure given by the cosmological
constant. The volume is then defined as being the Legendre transform of the
pressure and the resulting relation between volume and pressure is explored in
the case of positive pressure. A virial expansion is developed and a van der
Waals like critical point determined. The first law of black hole
thermodynamics includes a PdV term which modifies the maximal efficiency of a
Penrose process. It is shown that, in four dimensional space-time with a
negative cosmological constant an extremal charged rotating black hole can have
an efficiency of up to 75%, while for an electrically neutral rotating back
hole this figure is reduced to 52%, compared to the corresponding values of 50%
and 29% respectively when the cosmological constant is zero.Comment: 20 pages, 4 figures, minor typos corrected and references updated in
v
Separability of Black Holes in String Theory
We analyze the origin of separability for rotating black holes in string
theory, considering both massless and massive geodesic equations as well as the
corresponding wave equations. We construct a conformal Killing-Stackel tensor
for a general class of black holes with four independent charges, then identify
two-charge configurations where enhancement to an exact Killing-Stackel tensor
is possible. We show that further enhancement to a conserved Killing-Yano
tensor is possible only for the special case of Kerr-Newman black holes. We
construct natural null congruences for all these black holes and use the
results to show that only the Kerr-Newman black holes are algebraically special
in the sense of Petrov. Modifying the asymptotic behavior by the subtraction
procedure that induces an exact SL(2)^2 also preserves only the conformal
Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black
hole possesses a conformal Killing-Stackel tensor but has no further
enhancements.Comment: 27 page
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