2007
DOI: 10.1016/j.aop.2006.07.005
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Geometric obstruction of black holes

Abstract: We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The latter result is used to rigorously prove the absence of static spherically symmetric black holes in more than three dimensions. The proofs of these new results are preceded by a detailed exposition of the local aspects of sectional curvature bounds for Lorentzian manifolds, … Show more

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Cited by 14 publications
(21 citation statements)
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“…The result then follows by substituting (8) in (2) and by noticing that η µν Φ G,µν = η µν k α Γ α µν = 0 by virtue of (1) and (5) and (6) are the byproduct of covariance (minimal coupling) and, ultimately, of Lorentz invariance and can therefore be applied to general relativity, in particular to theories in which acceleration has an upper limit [15][16][17][18][19][20][21][22] and that therefore allow the resolution of astrophysical [23][24][25][26] and cosmological singularities in quantum theories of gravity [27,28]. They also are relevant to those theories of asymptotically safe gravity that can be expressed as Einstein gravity coupled to a scalar field [29].…”
Section: Introductionmentioning
confidence: 99%
“…The result then follows by substituting (8) in (2) and by noticing that η µν Φ G,µν = η µν k α Γ α µν = 0 by virtue of (1) and (5) and (6) are the byproduct of covariance (minimal coupling) and, ultimately, of Lorentz invariance and can therefore be applied to general relativity, in particular to theories in which acceleration has an upper limit [15][16][17][18][19][20][21][22] and that therefore allow the resolution of astrophysical [23][24][25][26] and cosmological singularities in quantum theories of gravity [27,28]. They also are relevant to those theories of asymptotically safe gravity that can be expressed as Einstein gravity coupled to a scalar field [29].…”
Section: Introductionmentioning
confidence: 99%
“…According to (28), complete alignment Γ = 1 can be achieved only at T = 0 which plays the role of a critical temperature in the model. The results given above also apply to a two-dimensional Ising model because the partition function (27) remains unchanged under the same conditions.…”
Section: The Lattice Gas Modelmentioning
confidence: 86%
“…The model can be solved exactly [1] by introducing the transfer matrix < s|M |s ′ >= exp(βεss ′ ), where β ≡ 1/T and ε ≡ mγ/4 contains the gravitational contribution due to γ µν . Equation (27) can be rewritten as Z = s1 < s 1 |M N |s 1 >= T r(M N ) = λ N + + λ N − and the eigenvalues ofM are λ + = 2 cosh(βε) and λ − = 2 sinh(βε). As N → ∞, only λ + is relevant, N −1 ln Z → ln(λ + ) and the Helmholtz free energy per site is F/N = −(N β) −1 ln Z → −β −1 ln(λ + ).…”
Section: The Lattice Gas Modelmentioning
confidence: 99%
“…For each channel and mass range, each BDT output variable is required to exceed a value determined by maximizing the quantity S/(1.5 + √ B) [28], where S and B are the expected numbers of signal and background events, respectively, based on simulation.…”
Section: -18 Event Shape Variablesmentioning
confidence: 99%