Cosmological and Black Hole Apparent Horizons

Faraoni, Valerio

doi:10.1007/978-3-319-19240-6

Cited by 176 publications

(301 citation statements)

References 78 publications

(198 reference statements)

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“…In this approach the first law of thermodynamics for black holes described by metrics (1) is obtained in agreement with the second law as a consequence of the Einstein equations [10][11][12]. A thorough overview of the concept of honrizon is give in [56].…”

Section: Introductionmentioning

confidence: 62%

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

Dymnikova

2018

Universe

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Abstract:We present a systematic review of thermodynamics of horizons in regular spherically symmetric spacetimes of the Kerr-Schild class, ds 2 = g(r)dt 2 − g −1 (r)dr 2 − r 2 dΩ 2 , both asymptotically flat and with a positive background cosmological constant λ. Regular solutions of this class have obligatory de Sitter center. A source term in the Einstein equations satisfies T t t = T r r and represents an anisotropic vacuum dark fluid (p r = −ρ), defined by the algebraic structure of its stress-energy tensor, which describes a time-evolving and spatially inhomogeneous, distributed or clustering, vacuum dark energy intrinsically related to space-time symmetry. In the case of two vacuum scales it connects smoothly two de Sitter vacua, 8πGTIn the range of the mass parameter M cr1 ≤ M ≤ M cr2 it describes a regular cosmological black hole directly related to a vacuum dark energy. Space-time has at most three horizons: a cosmological horizon r c , a black hole horizon r b < r c , and an internal horizon r a < r b , which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. Asymptotically flat regular black holes (λ = 0) can have at most two horizons, r b and r a . We present the basic generic features of thermodynamics of horizons revealed with using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. Quantum evaporation of a regular black hole involves a phase transition in which the specific heat capacity is broken and changes sign while a temperature achieves its maximal value, and leaves behind the thermodynamically stable double-horizon (r a = r b ) remnant with zero temperature and positive specific heat. The mass of objects with the de Sitter center is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context space-time symmetry provides a mechanism for relaxing cosmological constant to a certain non-zero value. We discuss also observational applications of the presented results.

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Section: Introductionmentioning

confidence: 62%

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

Dymnikova

2018

Universe

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“…Our knowledge of energy and mass in general relativity has progressed greatly since the times of Lemaître and Cahill and McVittie, with the introduction of the various quasi-local energies (see [24] for a review), which culminated in the HawkingHayward quasi-local energy [17,18]. In spherical symmetry, the Hawking-Hayward quasi-local energy reduces [18,25] to the Misner-Sharp-Hernandez mass M MSH [20,21], which is defined in a coordinate-invariant way by [18,20,21,25,29,30,35] 1 − 2M MSH R = ∇ c R∇ c R, (2.16) where R is the areal radius (which, being related to the area A of 2-spheres of symmetry by R = A 4π , is a geometrically defined quantity). In coordinates x μ = {T, R, θ, ϕ}, the squared gradient in the right hand side of Eq.…”

Section: Lemaître Geometry and The Mass Of A Sphere Of Symmetrymentioning

confidence: 99%

Lemaître model and cosmic mass

Faraoni

2015

Gen Relativ Gravit

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“…Following Faraoni [28], but also Park [13], the McVittie metric (9) can be reformulated in terms of the areal radius…”

Section: The Mcvittie Metricmentioning

confidence: 99%

“…Using Equation (18) and calculating the Misner-Sharp-Hernandez mass [31,32] of a sphere of proper radius R, one finds [28]:…”

Section: The Mcvittie Metricmentioning

confidence: 99%

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On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

Piattella

2016

Universe

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Abstract:We analyse the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a point-like lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter, H, we derive and approximately solve the null geodesic equations, finding an expression for the bending angle δ, which we expand in powers of the mass-to-closest approach distance ratio and of the impact parameter-to-lens distance ratio. It turns out that the leading order of the aforementioned expansion is the same as the one calculated for the Schwarzschild metric and that cosmological corrections contribute to δ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of the H constant and find that they provide a correction of order 10 −11 on the lens mass estimate.

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Cosmological and Black Hole Apparent Horizons

Cited by 176 publications

References 78 publications

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

Lemaître model and cosmic mass

On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

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