The energy-momentum tensor of a black hole, or what curves the Schwarzschild geometry?

Balasin, Herbert; Nachbagauer, Herbert

doi:10.1088/0264-9381/10/11/010

Cited by 83 publications

(107 citation statements)

References 9 publications

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“…Notice that the authors [15] chose a very dif f erent function f (r) = r λ than the one chosen above f (r) = r/|r|, and in the limit λ → 0, arrived at similar results for the distribution-valued scalar curvature. A different approach based on Colombeau's nonlinear distributional calculus was undertaken by [14].…”

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confidence: 86%

The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

Castro

2008

Journal of Mathematical Physics

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We argue why the static spherically symmetric (SSS) vacuum solutions of Einstein's equations described by the textbook Hilbert metric g µν (r) is not diffeomorphic to the metric g µν (|r|) corresponding to the gravitational field of a point mass delta function source at r = 0. By choosing a judicious radial function R(r) = r + 2G|M |Θ(r) involving the Heaviside step function, one has the correct boundary condition R(r = 0) = 0 , while displacing the horizon from r = 2G|M | to a location arbitrarily close to r = 0 as one desires, r h → 0, where stringy geometry and quantum gravitational effects begin to take place. We solve the field equations due to a delta function point mass source at r = 0, and show that the Euclidean gravitational action (inh units) is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D ≥ 3 . In the Reissner-Nordsrom (massive-charged) and Kerr-Newman black hole case (massive-rotating-charged) we show that the Euclidean action in a bulk domain bounded by the inner and outer horizons is the same as the black hole entropy. When one smears out the point-mass and point-charge delta function distributions by a Gaussian distribution, the areaentropy relation is modified. We postulate why these modifications should furnish the logarithmic corrections (and higher inverse powers of the area) to the entropy of these smeared Black Holes. To finalize, we analyse the Bars-Witten stringy black hole in 1 + 1 dim and its relation to the maximal acceleration principle in phase spaces and Finsler geometries.

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confidence: 86%

The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

Castro

2008

Journal of Mathematical Physics

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“…Eventually, its distributional limit is computed and-via the field equations-a distributional energy momentum tensor is obtained. This tensor may then be interpreted as distributional source of the Schwarzschild geometry [9,10,11,12,13]. However, using ad-hoc regularizations we are confronted with the problem of regularization independence of the results which may not be suitably addressed within this setting.…”

Section: Prerequisitesmentioning

confidence: 99%

“…In this section we present a first approach to the "Schwarzschild point mass problem", thereby essentially following earlier treatments in the literature ( [9,11,12,13]). However, we are going to use the language of nonlinear distributional geometry introduced above in order to obtain a unified view, which will enable us to carry out a detailed analysis of the previous approaches in the next section.…”

Section: A First Approach To the Problemmentioning

confidence: 99%

“…Representing distributions concentrated at the origin requires a basis regular at the origin. Transforming the results for (R i j ) ε (i.e., (9) and (10)) into Cartesian coordinates associated with the spherical ones (i.e., {r, θ, φ} ↔ {x i }) we obtain, e.g., for the Einstein tensor…”

Section: A First Approach To the Problemmentioning

confidence: 99%

“…We could have replaced (7) by any other smooth ad-hoc regularization of h(r), as has been done, e.g., in [11], by setting h ε (r) 1)-components of the Ricci tensor the result follows from the special form of (9). For the angular components (cf.…”

Section: A First Approach To the Problemmentioning

confidence: 99%

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Remarks on the distributional Schwarzschild geometry

Heinzle

Steinbauer

2002

Journal of Mathematical Physics

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This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a δ-distribution supported at r = 0. Using generalized distributional geometry in the sense of Colombeau's (special) construction the nonlinearities are treated in a mathematically rigorous way. Moreover, generalized function techniques are used as a tool to give a unified discussion of various approaches taken in the literature so far; in particular we comment on geometrical issues.

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Minimum Length Effects in Black Hole Physics

Casadio

Micu

Nicolini

2014

Fundamental Theories of Physics

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We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black holes and how modified dispersion relations affect the Hawking decay, both in four space-time dimensions and in models with extra spatial dimensions. In the latter case, we briefly discuss possible phenomenological signatures. Gravity and minimum lengthPhysics is characterized by a variety of research fields and diversified tools of investigation that strongly depend on the length scales under consideration. As a result, one finds an array of sub-disciplines, spanning from cosmology, to astrophysics, geophysics, molecular and atomic physics, nuclear and particle physics. In a nutshell, we can say that Physics concerns events occurring at scales between the radius of the Universe and the typical size of observed elementary particles. It is not hard to understand that such a rich array of physical phenomena requires specific formalisms. For instance, at macroscopic scales, models of the Universe are obtained in terms of general relativity, while at microscopic scales quantum physics has been proven to be the adequate theory for the miniaturised world.

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The energy-momentum tensor of a black hole, or what curves the Schwarzschild geometry?

Cited by 83 publications

References 9 publications

The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

Remarks on the distributional Schwarzschild geometry

Minimum Length Effects in Black Hole Physics

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