8,550 research outputs found
Angular momentum conservation for uniformly expanding flows
Angular momentum has recently been defined as a surface integral involving an
axial vector and a twist 1-form, which measures the twisting around of
space-time due to a rotating mass. The axial vector is chosen to be a
transverse, divergence-free, coordinate vector, which is compatible with any
initial choice of axis and integral curves. Then a conservation equation
expresses rate of change of angular momentum along a uniformly expanding flow
as a surface integral of angular momentum densities, with the same form as the
standard equation for an axial Killing vector, apart from the inclusion of an
effective energy tensor for gravitational radiation.Comment: 5 revtex4 pages, 3 eps figure
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
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
Dynamic wormholes
A new framework is proposed for general dynamic wormholes, unifying them with
black holes. Both are generically defined locally by outer trapping horizons,
temporal for wormholes and spatial or null for black and white holes. Thus
wormhole horizons are two-way traversible, while black-hole and white-hole
horizons are only one-way traversible. It follows from the Einstein equation
that the null energy condition is violated everywhere on a generic wormhole
horizon. It is suggested that quantum inequalities constraining negative energy
break down at such horizons. Wormhole dynamics can be developed as for
black-hole dynamics, including a reversed second law and a first law involving
a definition of wormhole surface gravity. Since the causal nature of a horizon
can change, being spatial under positive energy and temporal under sufficient
negative energy, black holes and wormholes are interconvertible. In particular,
if a wormhole's negative-energy source fails, it may collapse into a black
hole. Conversely, irradiating a black-hole horizon with negative energy could
convert it into a wormhole horizon. This also suggests a possible final state
of black-hole evaporation: a stationary wormhole. The new framework allows a
fully dynamical description of the operation of a wormhole for practical
transport, including the back-reaction of the transported matter on the
wormhole. As an example of a matter model, a Klein-Gordon field with negative
gravitational coupling is a source for a static wormhole of Morris & Thorne.Comment: 5 revtex pages, 4 eps figures. Minor change which did not reach
publisher
Kerr black holes in horizon-generating form
New coordinates are given which describe non-degenerate Kerr black holes in
dual-null foliations based on the outer (or inner) horizons, generalizing the
Kruskal form for Schwarzschild black holes. The construction involves an area
radius for the transverse surfaces and a generalization of the Regge-Wheeler
radial function, both functions of the original radial coordinate only.Comment: 4 revtex4 page
How to make a traversable wormhole from a Schwarzschild black hole
The theoretical construction of a traversable wormhole from a Schwarzschild
black hole is described, using analytic solutions in Einstein gravity. The
matter model is pure phantom radiation (pure radiation with negative energy
density) and the idealization of impulsive radiation is employed.Comment: 4 pages, 4 figure
Radiation from the LTB black hole
Does a dynamical black hole embedded in a cosmological FRW background emit
Hawking radiation where a globally defined event horizon does not exist? What
are the differences to the Schwarzschild black hole? What about the first law
of black hole mechanics? We face these questions using the LTB cosmological
black hole model recently published. Using the Hamilton-Jacobi and radial null
geodesic-methods suitable for dynamical cases, we show that it is the apparent
horizon which contributes to the Hawking radiation and not the event horizon.
The Hawking temperature is calculated using the two different methods giving
the same result. The first law of LTB black hole dynamics and the thermal
character of the radiation is also dealt with.Comment: 9 pages, revised version, Europhysics Letter 2012 97 2900
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