The energy-momentum tensor of a black hole, or what curves the Schwarzschild geometry?
Open accessAbstract
Using distributional techniques we calculate the energy-momentum tensor of the Schwarzschild geometry. It turns out to be a well defined tensor distribution concentrated on the r=0 region which is usually excluded from spacetime. This provides a physical interpretation for the curvature of this geometry.
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The Oppenheimer-Snyder model of gravitational collapse does not smoothly lead to the Schwarzschild black hole because its energy-momentum tensor is dust of the contracting FLRW Universe and thus a perfect fluid.
“This suggests that the model of the gravitational collapse proposed by Oppenheimer-Snyder[27] does not smoothly lead to the Schwarzschild BH, since their EMT is the dust of the contracting FLRW Universe and thus the perfect fluid.”
From Is energy conserved in general relativity? (2025) · cites this paper as [27]
For a static point-like quantum system of mass m, its gravitational field is described by the Schwarzschild metric, and the prescription of [42] yields dim H_G = e^{4π(m/m_Pl)^2}, in coherence with (4.7).
“It is instructive to analyse a static point-like quantum system of mass m.Its gravitational field is then described by the Schwarzschild metric [75], hence the prescription of [42] yields the formula dim H G = e 4π(m/m Pl ) 2 , in coherence with (4.7).”
From Conformal Cyclic Cosmology, gravitational entropy and quantum information (2023) · cites this paper as [75]
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“This metric is the “regularized” Schwarzschild metric as a distribution, which leads to the non-zero EMT at the origin as[1] This EMT agrees with the one obtained by the distributional approach[26], and corresponds to the non-perfect fluid.”
- Authors
- Balasin, H., & Nachbagauer, H.
- Affiliations
- TU Wien (AT)
- ORCID
- Balasin, H
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1993-11-01
- Volume
- 10
- Issue
- 11
- Pages
- 2271-2278
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2087477702
- Cited by
- 90
- References
- 0
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 7 · 2023: 5 · 2022: 2 · 2021: 5 · 2020: 3 · 2019: 4 · 2018: 6 · 2017: 3 · 2016: 3 · 2015: 2 · 2014: 2 · 2013: 1 · 2012: 2
- FWCI
- 5.41
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- energy-momentum tensor, Schwarzschild geometry, black holes, distributional methods, spacetime curvature
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