A Relativist's Toolkit, The Mathematics of Black-Hole Mechanics

By B. Whiting. 2004

1,177 citations recorded by the source corpus.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d9414a3186360364377cffd96244c26ed7672851

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Citations in the corpus

Regular Black Holes: A Short Topic Review (2023, background): “Because of this, RBHs are not governed by the Penrose singularity theorem, which can be understood from the Raychaudhuri equation [95,143], dΘ dτ = −Rμνuu , (82)”
Boundary Terms, Variational Principles and Higher Derivative Modified Gravity (2008, background): “The conventions and notation are those of [21].”
Born–Infeld inspired modifications of gravity (2017, background): “The resulting manifold is geodesically complete by construction, but curvature divergences arise at the wormhole throat [304], which is interpreted as a surface layer with an energy-momentum tensor on it.”
Gravitational deflection of light and shadow cast by rotating Kalb-Ramond black holes (2020, background): “The event horizon is a null stationary surface, characterized by the zero expansion for congruence of outgoing null geodesics orthogonal to the surface [17, 18].”
Black-hole binaries, gravitational waves, and numerical relativity (2010, background): “Since numerical relativists want to know when this occurs during the course of a calculation, they rely on a related concept known as an apparent horizon, whose location depends only on the properties of the spacetime at any given time (Poisson, 2004).”
Black hole boundaries (2005, background): “The specific value of the surface gravity depends on the normalization of the Killing vector field, though ifξ is a global Killing vector field, the natural choice is made by requiring that ξ · ξ = −1 “at infinity” [17,18].”
Essential Building Blocks of Dark Energy (2013, positive): “Other relevant equations are the Gauss-Codazzi equations, relating the Ricci tensor and scalar intrinsic to the hypersurface, ((3))Rμν and (3)R, to the four-dimensional ones [28,29], ((3))Rμν = (Rμν)‖ + (n nRμσνρ)‖ −KKμν +KμσKν , (59) ((3))R = R+K(2) −KμνK − 2(Kn − ṅ);μ , (60) where the symbol ‖ mea”
The Raychaudhuri equations: A brief review (2006, methodology): “A recent, nice discussion is available in [18].”
Slowly-Rotating Black Holes in Einstein-Dilaton-Gauss-Bonnet Gravity: Quadratic Order in Spin Solutions (2014, neutral): “(38) into g = 0, which is nothing but gttgφφ − g(2) tφ = 0 [41].”
Calibration of moving puncture simulations (2006, background): “The appropriate quantities are the Bondi quantities [52], which can be defined as taking the limit of the ADM integrals not toward spatial, but rather null, infinity [53, 54, 55], i.”
Theoretical Aspects of Massive Gravity (2011, methodology): “We now go to spacelike ADM variables [97, 98] adapted to the brane (see [99, 100] for detailed derivations and formulae).”
Slowly Rotating Black Holes in Dynamical Chern-Simons Gravity: Deformation Quadratic in the Spin (2012, methodology): “The location of the event horizon can be found by solving the equation gttgφφ − g(2) tφ = 0 for r [44].”
Strong deflection limit analysis and gravitational lensing of an Ellis wormhole (2016, background): “See [70] for the details of the ADM mass.”
Chern-Simons Modified General Relativity (2009, background): “In fact, as we shall see later on, the effacing principle must be corrected in CS modified gravity due to modifications to the junction conditions [107,108,109,110,111,112,113,21,114].”
Energy conditions in $$f(\mathcal {G},T)$$f(G,T) gravity (2016, neutral): “These equations describe the temporal evolution of expansion scalar (θ) as follows [20] dθ dτ = −(1) 3 θ(2) + ωαβω αβ − σαβσ −Rαβuu, (25) dθ dτ = −(1) 2 θ(2) + ωαβω αβ − σαβσ −Rαβkk , (26) where ωαβ, σαβ , u α and k represent the rotation, shear tensor, timelike and null tangent vectors in the congr”