Black-Hole Geometry and Topology  

Black-Hole Interior > s.a. quantum black holes.
@ General references: Krori et al PLA(88) [higher-dimensional, Schwarzschild-like]; Frolov et al PRD(90); Poisson & Israel PRD(90); Balbinot et al PLA(91); Bonanno et al PRD(94)gq; Burnett PRD(95)gq [journey inside a black hole]; Donets et al PRD(97) [Einstein-Yang-Mills]; Artemova & Novikov ap/02 [intro]; Novikov gq/03; Hamilton & Pollack PRD(05)gq/04, PRD(05)gq/04 [self-similar, accreting, charged]; Culetu IJMPA(09)ht/07; Lewis & Kwan PASA(07)-a0705 [maximizing survival time]; Hamilton & Polhemus a0903 [view from the inside]; Hamilton & Polhemus PRD(11)-a1010, Hamilton PRD(11)-a1010, PRD(11)-a1010, a1108 [realistic accreting, rotating black holes]; Dokuchaev CQG(11)-a1103 [interior bound periodic orbits], G&C(12)-a1203 [life inside?]; Culetu PLA(12) [Rindler-type geometry]; Smith & Mann CQG(14)-a1309 [probing the interior with an Unruh-DeWitt detector outside the horizon]; Nomura et al PRL(15)-a1412 [in quantum gravity]; Ganguly et al CQG(15)-a1411 [global structure, dynamical systems approach]; Brustein & Medved a1701 [and the detection of gravitational waves].
@ Appearance: news disc(11)jun [Andrew Hamilton's visualization].
@ Volume: DiNunno & Matzner GRG(10)-a0801; Christodoulou & Rovelli PRD(15)-a1411; Bengtsson & Jakobsson MPLA(15)-a1502 [large interiors]; Ong JCAP(15)-a1503 [volume not necessarily a monotonically increasing function of surface area].
@ Charged black holes: Dafermos CPAM(03)gq; Hwang & Yeom PRD(11); Henry et al a1512 [rotating, plots of all independent curvature invariants].

Geometry in General > s.a. black-hole solutions [including deformed black holes]; Supertranslations.
* Hawking's theorem: If Λ = 0, the constant time sections of the horizon of stationary black holes are topologically spheres.
* Angular momentum-area inequality: The angular momentum J of an axially symmetric black hole with surface area A satisfies

\[ \vert J\vert \le {A\over8\pi}\sqrt{\left(1-{\Lambda A\over4\pi}\right)\left(1-{\Lambda A\over12\pi}\right)} .\]

where Λ is the cosmological constan; The bound is saturated for the extreme Kerr-de Sitter family of metrics.
* Firewall: 2012, The idea that information escaping from a black hole ignites a firewall at the event horizon that would consume anything falling in, a claim which contradicts the general relativity assumption ("no drama" scenario) that locally nothing happens at the horizon; 2014, Hawking claims that black holes have apparent horizons rather than event horizons, thus avoiding the paradox; 2017, There is no concrete model for a firewall yet, but some phenomenological consequences from accreting matter and emitted radiation and neutrinos have been worked out.
@ Near-horizon geometry: Balasubramanian & Larsen NPB(98) [4D]; Cvetič & Larsen NPB(98) [5D]; Medved et al CQG(04)gq [static 4D]; Kang et al PRD(04)ht [any dimension]; Kunduri CQG(11)-a1104-GR19 [in 4D and 5D]; Kunduri & Lucietti LRR(13) [extremal black holes]; Susskind a1403 [and computational complexity]; Chruściel et al a1707 [uniqueness]; > s.a. black-hole entropy.
@ Inequalities: Dain in(09)-a0911 [angular momentum-mass inequality]; Jaramillo et al PRD(11)-a1106 [non-vacuum spacetimes]; Dain et al CQG(12)-a1109, Simon CQG(12)-a1109 [area-charge inequality]; Yazadjiev PRD(13)-a1210 [including charge, Einstein-Maxwell-dilaton theory]; Dain GRG(14)-a1401 [rev]; Gabach Clement et al CQG(15)-a1501 [in cosmological spacetimes]; Dain PRD(15)-a1506 [between size, charge, angular momentum and energy]; Csukás a1607 [using quasilocal mass, spherical symmetry]; Alaee et al AHP-a1608 [mass-angular momentum-charge, in 5D minimal supergravity]; > s.a. gravitating bodies.
@ Area product formulae: Cvetič et al PRL(11)-a1011; Page & Shoom a1504 [universal area product].
@ Firewall: Almheiri et al JHEP(13); Marolf & Polchinski PRL(13) + Karch Phy(13); Mathur & Turton NPB(14)-a1306; Nomura PRD(13)-a1308 [theory of horizons]; news SA(13)oct; Berenstein & Dzienkowski a1311 [numerical evidence]; Hossenfelder PRD(15)-a1401 [a local observer does not notice the presence of the boundary and does not encounter a firewall]; Devin a1401 [rev]; Hawking a1401 + news ns(14)jan, sa(14)mar; Israel a1403 [the horizon as a hot massless shell, 2D model]; Abramowicz et al PRL(14) [upper limit of 1/(8πM) to the surface density of a firewall]; Moffat & Toth a1404 [and Karlhede's invariant]; Stoltenberg & Albrecht PRD(15)-a1408 [questioning firewalls]; Dündar MS-a1409 [overview]; Germani & Sarkar FdP-a1502 [firewalls as artefacts]; Hotta & Sugita PTEP(15)-a1505 [firewalls generically do not emerge]; Chen et al PRL(16)-a1511 [firewalls outside the horizon]; Ori GRG(16) [alternative viewpoint based on semiclassical gravity]; Thanjavur & Israel a1601; Nomura & Salzetta PLB(16)-a1602 [firewalls need not exist]; Bryan & Medved AHEP-a1603 [and information]; > s.a. entanglement in field theory; matter near black holes.
@ Related topics: Anderson & Mull gq/97, gq/97-MG8 [constraints on static geometry]; Abramowicz & Sonego 02 [optical geometry]; Parikh PRD(06)ht/05 [3-volume]; Álvarez NPPS(09)-a0904 [without coordinates]; Gibbons AIP(12)-a1201 [results and conjectures for 4 and higher dimensions]; Bini et al IJGMP(15)-a1509 [stationary spacelike slicings]; > s.a. Smarr Formula.
> Singularities: see cosmic censorship; models for topology change [censorship, genus].
> Related topics: see event horizons; horizons [isolated, dynamical, trapping]; Mass Inflation.

Other Topologies and Higher Dimensionalities
* Black strings: Gregory & Laflamme argued that an instability along the extra dimension causes the Schwarzschild black string to break up into disjoint black holes; Horowitz and Maeda derived bounds on the rate at which the smallest sphere can pinch off.
@ Black rings: Emparan & Reall CQG(06) [rev]; Elvang et al JHEP(06)ht [dynamics, instability]; Iizuka & Shigemori PRD(08) [in 4D]; Chruściel & Cortier JDG-a0807 [geometry]; Astefanesei et al JHEP(09)-a0909 [equilibrium conditions]; Kleihaus et al a1205PLB(13) [6D]; Dadras et al EPL(12)-a1207; Armas & Blau JHEP(15)-a1504 [helicoidal black rings and black tori]; Chervonyi PRD(15)-a1510 [in D > 5]; > s.a. laws of black-hole dynamics.
@ Black strings: Gregory & Laflamme PRL(93)ht, NPB(94)ht, Horowitz & Maeda PRL(01)ht, Choptuik et al PRD(03)gq, Kol & Sorkin CQG(04)gq [instability]; Kol & Wiseman CQG(03)ht; Kol et al PRD(04)ht/03 [and black holes]; Cardoso & Dias PRL(06)ht [and membrane]; Kleihaus et al JHEP(06)ht [non-uniform]; Chowdhury et al NPB(07) [phase transition]; Yoo et al IJGMP(11) [slowly rotating, Gregory-Laflamme instability]; Gregory a1107-ch [rev]; Lehner & Pretorius a1106-ch [Gregory-Laflamme instability, final state]; Ida a1609 [no arbitrarily long black strings].
@ In higher dimensions: Helfgott et al JHEP(06)ht/05; Galloway & Shoen CMP(06); Rácz CQG(08)-a0806 [proof of generalized Hawking theorem]; Hollands et al AHP(11)-a1002 [5D, restrictions on topology]; Ida & Okamoto PTP(12)-a1105; Galloway a1111-ch; Lessel a1210; Taliotis PRD(12); > s.a. higher-dimensional solutions; uniqueness and hair.
@ Other topology: Galloway CMP(93); Chruściel & Wald CQG(94)gq; Chruściel et al CQG(06) [no degenerate components for static vacuum]; Bambi & Modesto PLB(11)-a1107 [in lqg and other gravity theories]; Monte IJMPCS(12)-a1111 [Schwarzschild black hole]; Klemm PRD(14)-a1401 [non-compact manifolds with finite volume]; Bohn et al a1606 [toroidal topology, binary merger simulation]; > s.a. horizons; modified theories; black-hole phenomenology.

Other References > s.a. Antigravity; particle effects and models; thermodynamics [phase transitions]; black-hole phenomenology; wormholes.
@ Membrane paradigm: & Damour (78); Price & Thorne PRD(86), SA(88)apr; Thorne et al 86; Carter in(92)ht/04 [equilibrium geometry]; Parikh & Wilczek PRD(98)gq/97; Straumann in(98)ap/97; Parikh PhD(98)ht/99; Cardoso et al IJMPD(08)-a0705 [black objects in higher dimensions]; Mathur GRG(10)-a1005-GRF = IJMPD(10) [realized by degrees of freedom just outside the horizon].
@ Membrane paradigm, alternative gravity theories: Chatterjee et al CQG(12)-a1012 [in f(R) gravity]; Jacobson et al PRD(17)-a1107 [in Einstein-Gauss-Bonnet gravity, D ≥ 5]; Kolekar & Kothawala JHEP(12)-a1111 [Lanczos-Lovelock gravity].
@ Other approaches / models: Abramowicz & Sonego 02 [optical geometry]; Gourgoulhon & Jaramillo NAR(08)-a0803-proc [hypersurfaces foliated by trapped surfaces]; Skenderis & Taylor PRP(08)-a0804 [fuzzball proposal]; Hamilton & Lisle AJP(08)jun [river model]; Caldarelli et al JHEP(09)-a0901 [lump of fluid].
@ Non-singular: Newman GRG(89); Berman gq/04; Hayward PRL(06) [formation + evaporation]; Pérez et al IJTP(14) [instability of Mbonye-Kazanas regular interior model]; Barceló et al CQG(15)-a1409 [time-symmetric bounce]; > s.a. 4D and modified solutions.
@ Related topics: Laughlin IJMPA(03)gq-fs [vacuum phase boundaries]; Mei et al JHEP(13)-a1305 [effective action for a fluctuating horizon].


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