44 research outputs found
Acceleration of particles as universal property of rotating black holes
We argue that the possibility of having infinite energy in the centre of mass
frame of colliding particles is a generic property of rotating black holes. We
suggest a general model-independent derivation valid for "dirty" black holes.
The earlier observations for the Kerr or Kerr-Newman metrics are confirmed and
generalized.Comment: 9 pages. Discussion expande
Static black holes in equilibrium with matter: nonlinear equation of state
We consider a spherically symmetric black hole in equilibrium with
surrounding classical matter that is characterized by a nonlinear dependence of
the radial pressure p_{r} on the density {\rho}. We examine under which
requirements such an equilibrium is possible. It is shown that if the radial
and transverse pressures are equal (Pascal perfect fluid), equation of state
should be approximately linear near the horizon. The corresponding restriction
on ((dp_{r})/(d{\rho})) is a direct generalization of the result, previously
found for an exactly linear equation of state. In the anisotropic case there is
no restriction on equation of state but the horizon should be simple
(nondegenerate).Comment: 6 pages. To appear in PRD
Unified approach to the entropy of an extremal rotating BTZ black hole: Thin shells and horizon limits
Using a thin shell, the first law of thermodynamics, and a unified approach,
we study the thermodymanics and find the entropy of a (2+1)-dimensional
extremal rotating Ba\~{n}ados-Teitelbom-Zanelli (BTZ) black hole. The shell in
(2+1) dimensions, i.e., a ring, is taken to be circularly symmetric and
rotating, with the inner region being a ground state of the anti-de Sitter
(AdS) spacetime and the outer region being the rotating BTZ spacetime. The
extremal BTZ rotating black hole can be obtained in three different ways
depending on the way the shell approaches its own gravitational or horizon
radius. These ways are explicitly worked out. The resulting three cases give
that the BTZ black hole entropy is either the Bekenstein-Hawking entropy,
, or it is an arbitrary function of , , where
is the area, i.e., the perimeter, of the event horizon in (2+1)
dimensions. We speculate that the entropy of an extremal black hole should obey
. We also show that the contributions from the
various thermodynamic quantities, namely, the mass, the circular velocity, and
the temperature, for the entropy in all three cases are distinct. This study
complements the previous studies in thin shell thermodynamics and entropy for
BTZ black holes. It also corroborates the results found for a (3+1)-dimensional
extremal electrically charged Reissner-Nordstr\"om black hole.Comment: 8 pages, 1 table, no figur
Horizons in matter: black hole hair vs. Null Big Bang
It is shown that only particular kinds of matter (in terms of the "radial"
pressure to density ratio ) can coexist with Killing horizons in black-hole
or cosmological space-times. Thus, for arbitrary (not necessarily spherically
symmetric) static black holes, admissible are vacuum matter (, i.e., the
cosmological constant or some its generalization) and matter with certain
values of between 0 and -1, in particular, a gas of disordered cosmic
strings (). If the cosmological evolution starts from a horizon (the
so-called Null Big Bang scenarios), this horizon can co-exist with vacuum
matter and certain kinds of phantom matter with . It is concluded
that normal matter in such scenarios is entirely created from vacuum.Comment: 4 pages, essay written for the Gravity Research Foundation 2009
Awards for Essays on Gravitation, awarded a honorable mentio
Quasiblack holes with pressure: General exact results
A quasiblack hole is an object in which its boundary is situated at a surface
called the quasihorizon, defined by its own gravitational radius. We elucidate
under which conditions a quasiblack hole can form under the presence of matter
with nonzero pressure. It is supposed that in the outer region an extremal
quasihorizon forms, whereas inside, the quasihorizon can be either nonextremal
or extremal. It is shown that in both cases, nonextremal or extremal inside, a
well-defined quasiblack hole always admits a continuous pressure at its own
quasihorizon. Both the nonextremal and extremal cases inside can be divided
into two situations, one in which there is no electromagnetic field, and the
other in which there is an electromagnetic field. The situation with no
electromagnetic field requires a negative matter pressure (tension) on the
boundary. On the other hand, the situation with an electromagnetic field
demands zero matter pressure on the boundary. So in this situation an
electrified quasiblack hole can be obtained by the gradual compactification of
a relativistic star with the usual zero pressure boundary condition. For the
nonextremal case inside the density necessarily acquires a jump on the
boundary, a fact with no harmful consequences whatsoever, whereas for the
extremal case the density is continuous at the boundary. For the extremal case
inside we also state and prove the proposition that such a quasiblack hole
cannot be made from phantom matter at the quasihorizon. The regularity
condition for the extremal case, but not for the nonextremal one, can be
obtained from the known regularity condition for usual black holes.Comment: 18 pages, no figures; improved introduction, added references,
calculations better explaine
Entropy of an extremal electrically charged thin shell and the extremal black hole
There is a debate as to what is the value of the the entropy of extremal
black holes. There are approaches that yield zero entropy , while there
are others that yield the Bekenstein-Hawking entropy , in Planck
units. There are still other approaches that give that is proportional to
or even that is a generic well-behaved function of . Here
is the black hole horizon radius and is its horizon area.
Using a spherically symmetric thin matter shell with extremal electric charge,
we find the entropy expression for the extremal thin shell spacetime. When the
shell's radius approaches its own gravitational radius, and thus turns into an
extremal black hole, we encounter that the entropy is , i.e., the
entropy of an extremal black hole is a function of alone. We speculate
that the range of values for an extremal black hole is .Comment: 11 pages, minor changes, added references, matches the published
versio