11,349 research outputs found
Unified first law of black-hole dynamics and relativistic thermodynamics
A unified first law of black-hole dynamics and relativistic thermodynamics is
derived in spherically symmetric general relativity. This equation expresses
the gradient of the active gravitational energy E according to the Einstein
equation, divided into energy-supply and work terms. Projecting the equation
along the flow of thermodynamic matter and along the trapping horizon of a
blackhole yield, respectively, first laws of relativistic thermodynamics and
black-hole dynamics. In the black-hole case, this first law has the same form
as the first law of black-hole statics, with static perturbations replaced by
the derivative along the horizon. There is the expected term involving the area
and surface gravity, where the dynamic surface gravity is defined as in the
static case but using the Kodama vector and trapping horizon. This surface
gravity vanishes for degenerate trapping horizons and satisfies certain
expected inequalities involving the area and energy. In the thermodynamic case,
the quasi-local first law has the same form, apart from a relativistic factor,
as the classical first law of thermodynamics, involving heat supply and
hydrodynamic work, but with E replacing the internal energy. Expanding E in the
Newtonian limit shows that it incorporates the Newtonian mass, kinetic energy,
gravitational potential energy and thermal energy. There is also a weak type of
unified zeroth law: a Gibbs-like definition of thermal equilibrium requires
constancy of an effective temperature, generalising the Tolman condition and
the particular case of Hawking radiation, while gravithermal equilibrium
further requires constancy of surface gravity. Finally, it is suggested that
the energy operator of spherically symmetric quantum gravity is determined by
the Kodama vector, which encodes a dynamic time related to E.Comment: 18 pages, TeX, expanded somewhat, to appear in Class. Quantum Gra
A Cosmological Constant Limits the Size of Black Holes
In a space-time with cosmological constant and matter satisfying
the dominant energy condition, the area of a black or white hole cannot exceed
. This applies to event horizons where defined, i.e. in an
asymptotically deSitter space-time, and to outer trapping horizons (cf.
apparent horizons) in any space-time. The bound is attained if and only if the
horizon is identical to that of the degenerate `Schwarzschild-deSitter'
solution. This yields a topological restriction on the event horizon, namely
that components whose total area exceeds cannot merge. We
discuss the conjectured isoperimetric inequality and implications for the
cosmic censorship conjecture.Comment: 10 page
Quasi-local first law of black-hole dynamics
A property well known as the first law of black hole is a relation among
infinitesimal variations of parameters of stationary black holes. We consider a
dynamical version of the first law, which may be called the first law of black
hole dynamics. The first law of black hole dynamics is derived without assuming
any symmetry or any asymptotic conditions. In the derivation, a definition of
dynamical surface gravity is proposed. In spherical symmetry it reduces to that
defined recently by one of the authors (SAH).Comment: Latex, 8 pages; version to appear in Class. Quantum Gra
On the Definition of Averagely Trapped Surfaces
Previously suggested definitions of averagely trapped surfaces are not
well-defined properties of 2-surfaces, and can include surfaces in flat
space-time. A natural definition of averagely trapped surfaces is that the
product of the null expansions be positive on average. A surface is averagely
trapped in the latter sense if and only if its area and Hawking mass
satisfy the isoperimetric inequality , with similar inequalities
existing for other definitions of quasi-local energy.Comment: 4 page
Gravitational radiation from dynamical black holes
An effective energy tensor for gravitational radiation is identified for
uniformly expanding flows of the Hawking mass-energy. It appears in an energy
conservation law expressing the change in mass due to the energy densities of
matter and gravitational radiation, with respect to a Killing-like vector
encoding a preferred flow of time outside a black hole. In a spin-coefficient
formulation, the components of the effective energy tensor can be understood as
the energy densities of ingoing and outgoing, transverse and longitudinal
gravitational radiation. By anchoring the flow to the trapping horizon of a
black hole in a given sequence of spatial hypersurfaces, there is a locally
unique flow and a measure of gravitational radiation in the strong-field
regime.Comment: 5 revtex4 pages. Additional comment
Energy conservation for dynamical black holes
An energy conservation law is described, expressing the increase in
mass-energy of a general black hole in terms of the energy densities of the
infalling matter and gravitational radiation. For a growing black hole, this
first law of black-hole dynamics is equivalent to an equation of Ashtekar &
Krishnan, but the new integral and differential forms are regular in the limit
where the black hole ceases to grow. An effective gravitational-radiation
energy tensor is obtained, providing measures of both ingoing and outgoing,
transverse and longitudinal gravitational radiation on and near a black hole.
Corresponding energy-tensor forms of the first law involve a preferred time
vector which plays the role for dynamical black holes which the stationary
Killing vector plays for stationary black holes. Identifying an energy flux,
vanishing if and only if the horizon is null, allows a division into
energy-supply and work terms, as in the first law of thermodynamics. The energy
supply can be expressed in terms of area increase and a newly defined surface
gravity, yielding a Gibbs-like equation, with a similar form to the so-called
first law for stationary black holes.Comment: 4 revtex4 pages. Many (mostly presentational) changes; emphasizes the
definition of gravitational radiation in the strong-field regim
Black holes, cosmological singularities and change of signature
There exists a widespread belief that signature type change could be used to
avoid spacetime singularities. We show that signature change cannot be utilised
to this end unless the Einstein equation is abandoned at the suface of
signature type change. We also discuss how to solve the initial value problem
and show to which extent smooth and discontinuous signature changing solutions
are equivalent.Comment: 14pages, Latex, no figur
On the semiclassical treatment of Hawking radiation
In the context of the semiclassical treatment of Hawking radiation we prove
the universality of the reduced canonical momentum for the system of a massive
shell self gravitating in a spherical gravitational field within the Painlev\'e
family of gauges. We show that one can construct modes which are regular on the
horizon both by considering as hamiltonian the exterior boundary term and by
using as hamiltonian the interior boundary term. The late time expansion is
given in both approaches and their time Fourier expansion computed to reproduce
the self reaction correction to the Hawking spectrum.Comment: 18 pages, LaTeX, Corrected typo
Construction and enlargement of traversable wormholes from Schwarzschild black holes
Analytic solutions are presented which describe the construction of a
traversable wormhole from a Schwarzschild black hole, and the enlargement of
such a wormhole, in Einstein gravity. The matter model is pure radiation which
may have negative energy density (phantom or ghost radiation) and the
idealization of impulsive radiation (infinitesimally thin null shells) is
employed.Comment: 22 pages, 7 figure
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