Horizons| Horizons |
In General > s.a. black holes;
black-hole thermodynamics; event
horizon;
killing horizons; Rigidity;
rindler space.
* Remark: As originally
defined, the event horizon is a highly non-local object,
defined in terms of the causal past of future null infinity; Alternative, (quasi)local
definitions of horizons are often used, which include apparent, trapping,
isolated and dynamical horizons, and are closely associated with 2-surfaces
of zero outward null expansion.
@ General references: Mäkelä gq/01 [microscopic
properties]; Chrusciel et al JGP(02)
[differentiability]; Hubeny & Rangamani
JHEP(02)ht [stability];
Aros JHEP(03)gq/02 [diffeomorphism
algebra]; Booth & Fairhurst CQG(05)gq [energy
and angular momentum]; Korzynski PRD(06)gq;
't Hooft IJMPD(06)gq-in
[black hole, as a dynamical system].
@ Evolving: Nielsen & Visser CQG(06)gq/05 [spherically
symmetric, relation to various approaches]; Kavanagh & Booth PRD(06)gq [slowly].
@ Thermodynamics: Padmanabhan MPLA(02)gq,
gq/02, CQG(02)gq,
GRG(02)gq,
PRP(05)gq/03 [intro];
Jacobson & Parentani FP(03)gq;
Padmanabhan
MPLA(04)gq [observer-dependent,
and
tunneling]; Wang PRD(05)gq [entropy
in modified gravity].
@ Trapping horizons: Nielsen
a0802-in; Hayward
et al CQG(09)-a0806 [spherical,
local temperature]; Nielsen IJMPD(08)-a0809,
GRG(09)-a0809
[and black holes]; Hayward a0810-ASL
[rev].
> Related topics: > s.a. black hole
laws; semiclassical
general relativity [reliability
horizon]; entropy.
Isolated Horizon > s.a. black-hole
laws; multipoles; numerical
relativity;
quasilocal general relativity.
* Relationships: A Killing horizon is always an isolated horizon.
@
General references: Ashtekar et al CQG(99)gq/98,
ATMP(00)gq/99 [phase
space],
CQG(00)gq/99 [mechanics],
AdP(00)gq/99,
PRL(00)gq, CQG(02)gq/01 [geometry];
Date CQG(00)gq [spin
coefficients]; Ashtekar et al ATMP(02)gq [2+1];
Gourgoulhon & Jaramillo PRP(06)gq/05
[3+1 view].
@ With matter: Ashtekar & Corichi CQG(00)gq/99 [dilaton];
Corichi et al PRD(00)gq [Einstein-Yang-Mills];
Ashtekar et al CQG(03)gq [scalar];
Corichi et al PRD(06)gq/05 [hairy
Einstein-Higgs black holes]; Liko & Booth CQG(08)-a0712 [Einstein-Maxwell-Chern-Simons
in odd D 
5];
Liko PRD(09)-a0901 [p-form matter fields].
@ Properties: Corichi & Sudarsky gq/00-in
[hair]; Date CQG(01)gq [and
Killing horizons]; Dreyer et
al PRD(03)gq/02 [numerical];
Lewandowski & Pawlowski CQG(03)gq/02 [uniqueness];
Pawlowski et al CQG(04)gq/03 [spacetime
foliations]; Ashtekar & Corichi
CQG(03)gq [entropy];
Booth & Fairhurst PRD(08)-a0708 [extremality];
Basu et al a0907 [entropy].
@ Quantum: Ashtekar et al CQG(05)gq/04 [with
distortion and rotation]; Bojowald & Swiderski PRD(05)
[spherical]; Engle JPCS(05)gq
[distorted, rotating, entropy].
@ Asymptotically AdS: Ashtekar et al CQG(07)gq/06 [covariant
phase space, first law];
Booth & Liko PLB(08)-a0808 [supersymmetric].
@ Higher-dimensional spacetimes:
Korzynski et al CQG(05)gq/04;
Liko & Booth CQG(07)-a0705 [in
Einstein-Gauss-Bonnet
gravity].
@ Other types of spacetimes: Lewandowski CQG(00)gq/99 [vacuum];
Lewandowski & Pawlowski
IJMPD(02)gq/01 [Kerr];
Ashtekar et al PRD(01)gq [rotating];
Senovilla JHEP(03)ht [with
no trapped surfaces]; > s.a. born-infeld
theory; Skyrmions.
Dynamical Horizon > s.a. constraints
in general relativity; numerical
relativity.
@ General references: Ashtekar & Krishnan PRL(02)gq,
PRD(03)gq [fluxes,
laws], LRR(04)gq [review,
applications]; Hayward PRL(04)gq [first
law]; Ashtekar & Galloway ATMP(05)gq [uniqueness,
isometries]; Andersson et al PRL(05)
[local existence]; Bartnik & Isenberg CQG(06)gq/05 [spherical,
nasc]; Hayward gq/06 [conservation
laws]; Booth & Fairhurst PRD(08)-a0708 [extremality].
@ Specific spacetimes: Sawayama PRD(06)gq/05 [evaporating
Vaidya black hole].
@ Related topics: Di Criscienzo & Vanzo EPL(08)-a0803 [fermion
tunneling]; Nielsen & Yoon CQG(08)
[surface gravity].
Apparent Horizon > s.a. models
in numerical relativity; Penrose
Inequality.
$ Def: Given a spacelike
hypersurface
, the apparent horizon
is the boundary of the region of containing
trapped surfaces lying in
; In terms of the
advanced time v, it is defined by dr/dv = 0.
* Relationships: A marginally-trapped
surface; It need not coincide with the event horizon, since some light rays
may start out
diverging
and reconverge again later, but it
either
coincides or is contained in the event horizon; (Not true? York in Corvallis:
light rays may start out converging but not be trapped, e.g., for an evaporating
hole).
@ General references: Gundlach PRD(98)gq/97,
Alcubierre et al CQG(00)
[algorithms]; Dasgupta ht/03 [entropy];
Zhou et al PLB(07)
[thermodynamics]; Andersson & Metzger CMP(09)-a0708 [area
estimate].
@ Specific spacetimes: Wang GRG(05)gq/03 [no
outer ones with 2 Killing vector fields]; Goncalves
PRD(03)gq,
CQG(03)gq [none
with isometries].
Cauchy Horizon > s.a. censorship; gowdy
spacetime;
Rigidity.
$ Def: The future and
past Cauchy horizons are given, respectively, by 
+/–(S):=
bdry{D+/–(S)}
– I+/–(D+/–(S)),
the boudary of the region where evolution can be predicted from data on S.
* Existence of isometry groups: & Isenberg and Moncrief.
@ Differentiability: Królak & Beem gq/97; Chrusciel CQG(98)gq;
Budzynski et al JMP(99)gq.
@ Other properties: Borde PLA(84)
[compact]; Beem GRG(95)
[stability]; Burko gq/97-in, PRL(97)gq [singularity,
Klein-Gordon-perturbed
Reissner-Nordström]; Beem & Królak gq/97 [endpoints];
Budzynski et al gq/00-in
[properties]; Rácz gq/01-MG9
[spacetime rigidity].
Particle (Cosmological) Horizon > s.a. Horizon
Problem.
* Idea: The particle
horizon of a point p in spacetime, given a congruence of
timelike lines (particles), is the boundary of the set of world-lines that p can
see; One
does not expect an entropy associated to this type of horizon to be meaningful.
* Example: If the particles
are geodesics, there are particle horizons iff past null infinity is spacelike
(e.g., de Sitter).
@ References: in Hawking & Ellis 73, p128; Ellis & Rothman AJP(93)oct;
Boya et al PRD(02)gq [graphical
approach]; Melia MNRAS-a0711.
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aug
2009