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Curvature Invariants and Lower Dimensional Black Hole Horizons
General Relativity and Quantum Cosmology · Submitted 14 Feb 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The suitable Cartan invariants employed for detecting the horizon can be interpreted as a local extremum of the tidal force suggesting that the horizon of a black hole is a genuine special hypersurface within the full manifold, contrary to the usual claim that there is nothing special at the horizon, which is said to be a consequence of the equivalence principle.
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The abstract, sentence by sentence
It is known that the event horizon of a black hole can often be identified from the zeroes of some curvature invariants. The situation in lower dimensions has not been thoroughly clarified. In this work we investigate both (2+1)- and (1+1)-dimensional black hole horizons of static, stationary and dynamical black holes, identified with the zeroes of scalar polynomial and Cartan curvature invariants, with the purpose of discriminating the different roles played by the Weyl and Riemann curvature tensors. The situations and applicability of the methods are found to be quite different from that in 4-dimensional spacetime. The suitable Cartan invariants employed for detecting the horizon can be interpreted as a local extremum of the tidal force suggesting that the horizon of a black hole is a genuine special hypersurface within the full manifold, contrary to the usual claim that there is nothing special at the horizon, which is said to be a consequence of the equivalence principle.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is known that the event horizon of a black hole can often be identified from the zeroes of some curvature invariants. | background 1.00 | 0.03 | 0.03 | asserted 0.73 |
| s1 | The situation in lower dimensions has not been thoroughly clarified. | gap 1.00 | 0.03 | 0.02 | asserted 0.96 |
| s2 | In this work we investigate both (2+1)- and (1+1)-dimensional black hole horizons of static, stationary and dynamical black holes, identified with the zeroes of scalar polynomial and Cartan curvature invariants, with the purpose of discriminating the different roles played by the Weyl and Riemann curvature tensors. | contribution 1.00 | 0.86 | 0.07 | asserted 0.79 |
| s3 | The situations and applicability of the methods are found to be quite different from that in 4-dimensional spacetime. | result 1.00 | 0.86 | 0.15 | asserted 1.00 |
| s4 | The suitable Cartan invariants employed for detecting the horizon can be interpreted as a local extremum of the tidal force suggesting that the horizon of a black hole is a genuine special hypersurface within the full manifold, contrary to the usual claim that there is nothing special at the horizon, which is said to be a consequence of the equivalence principle. | interpretation 0.96 | 0.82 | 0.73 | hedged possibility 0.81 |
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The paper
Original abstract
It is known that the event horizon of a black hole can often be identified from the zeroes of some curvature invariants. The situation in lower dimensions has not been thoroughly clarified. In this work we investigate both (2+1)- and (1+1)-dimensional black hole horizons of static, stationary and dynamical black holes, identified with the zeroes of scalar polynomial and Cartan curvature invariants, with the purpose of discriminating the different roles played by the Weyl and Riemann curvature tensors. The situations and applicability of the methods are found to be quite different from that in 4-dimensional spacetime. The suitable Cartan invariants employed for detecting the horizon can be interpreted as a local extremum of the tidal force suggesting that the horizon of a black hole is a genuine special hypersurface within the full manifold, contrary to the usual claim that there is nothing special at the horizon, which is said to be a consequence of the equivalence principle.
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How the literature uses it
5 arXiv papers cite this in 7 sentences
Papers citing it · 4 sentences without a confident label
Compares with it 1 paper
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This is the same result found in [ref] where the horizon of the BTZ black hole was studied in a massless gravity theory.
On the Curvature Invariants of the Massive Banados-Teitelboim-Zanelli Black Holes and Their Holographic Pictures · Locating the event horizon in terms of the zeroes of curvature invariants · 0.92
Cites it as support 1 paper
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Therefore, we have explicitly shown that the horizon constitutes a local property of the manifold (in agreement with the core principles of any relativistic field theory), and that a curvature invariant can be constructed for its detection once the geometrical symmetries of the spacetime are known regardless the gravitational theory behind it: this is consistent with the geometric horizon conjecture [ref] .
A Critical Assessment of Black Hole Solutions With a Linear Term in Their Redshift Function · Curvature syzygys · 0.98
Cites it as background 1 paper
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See [ref] for further discussions and implications.], then it should start small or even zero at the Big Bang, and then monotonically grow as structures like stars and galaxies and eventually black holes formed.
Thermodynamics of Shearing Massless Scalar Field Spacetimes is Inconsistent With the Weyl Curvature Hypothesis · Discussion: What Is Gravitational Entropy? · 0.89
What it cites · 46 sentences without a confident label
Contests 1 paper
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This implies that the argument proposed in [ref] , contrary to the cases of $(3+1)$- and higher dimensional gravity theories, cannot be used for locating the horizon of the corresponding lower dimensional Schwarzschild, Kerr, and Schwarzschild-(anti-)de Sitter black holes because the geometry does not admit enough degrees of freedom.
Cartan Invariants and Event Horizon Detection, Extended Version · On the use of curvature invariants for detecting a black hole horizon: the peculiar case of lower dimensional Einstein t · contest 0.82
Uses the method or tool of 1 paper
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Thus we must fix the triad in such a way that the curvature is in its canonical form, i.e. with the smallest possible number of non-zero independent components, which can be done applying the Newman-Penrose formalism. 3-dimensional spacetimes admits at most 5 independent Ricci scalars defined as [ref] [equation] Then, we construct ([ref]) setting the appropriate components to zero or equal (or proportional to each other) following eqs (5.44)-(5.51) of [ref] according to the isotropy group of the black hole in hand.
Equivalence of three-dimensional spacetimes · A first explicit example: the case of the BTZ black hole with electric charge · 0.98
Cites as support 1 paper
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We propose that this behavior of the tidal forces can be a valuable technique for distinguishing black holes from other star-like objects which do not have an horizon and therefore according to [ref] do not exhibit this property of the Cartan invariants (that is having a spacetime point in which a Cartan invariant connected to the tidal tensor vanishes).
Cartan Invariants and Event Horizon Detection, Extended Version · Physical interpretation of the horizon-detecting Cartan invariants · 0.96
Cites as background 7 papers
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In fact, it is well known that the Weyl tensor identically vanishes for any spacetime in (2+1)-dimensional gravity, implying that the Riemann tensor $R_μνρσ$ can be fully written in terms of the Ricci tensor $R_μν$, the Ricci scalar $R$ and the metric tensor $g_μν$ as follows [ref] : [equation] The ingredients of ([ref]) must be obtained from the Einstein equations
Lectures in (2+1)-Dimensional Gravity · On the use of curvature invariants for detecting a black hole horizon: the peculiar case of lower dimensional Einstein t · 0.93
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They are a useful technique for classifying known solutions of the Einstein field equations in reference to the so-called equivalence problem, in which one has to check whether two very different looking solutions (derived in different coordinate systems) are in fact one and the same [ref] .
Spacetimes characterized by their scalar curvature invariants · Basic properties of the black hole horizon: a very short review · 0.95
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Even though lower-dimensional gravity is a pure topological theory, it admits black hole solutions, the first example was found in (2+1) dimensions in the presence of a negative cosmological constant [ref] .
The Black Hole in Three Dimensional Space Time · Introduction: Locating the Event Horizon of a Black Hole · 0.86
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