Camilo Angulo

On the existence of certain axisymmetric interior metrics

Journal of Mathematical Physics, 2010

One of the effects of noncommutative coordinate operators is that the delta-function connected to... more One of the effects of noncommutative coordinate operators is that the delta-function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of effects of noncommutativity, this effect is in particular important, as it removes the point singularities of Schwarzschild and Reissner-Nordström solutions. In this context, it seems to be of some importance to probe also into ring-like singularities which appear in the Kerr case. In particular, starting with an anisotropic energymomentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g. Gaussian) we derive the full set of Einstein equations that the Noncommutative Geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by Noncommutative Geometry.

format_quoteNoncommutative approaches yield new black hole geometries, replacing singularities with regular regions as θ approaches zero.format_quote

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On the existence of certain axisymmetric interior metrics

by Davide Batic and Camilo Angulo

Journal of Mathematical Physics, 2010

One of the effects of noncommutative coordinate operators is that the delta-function connected to... more One of the effects of noncommutative coordinate operators is that the delta-function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of effects of noncommutativity, this effect is in particular important, as it removes the point singularities of Schwarzschild and Reissner-Nordström solutions. In this context, it seems to be of some importance to probe also into ring-like singularities which appear in the Kerr case. In particular, starting with an anisotropic energymomentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g. Gaussian) we derive the full set of Einstein equations that the Noncommutative Geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by Noncommutative Geometry.

format_quoteNoncommutative effects replace the singularity in black hole metrics, leading to regular regions in Schwarzschild and Reissner-Nordström geometries.format_quote

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Towards a new cohomology theory for strict Lie 2-groups

Crossed modules enjoyed a lively research activity in the late 1940s after Whitehead introduced t... more Crossed modules enjoyed a lively research activity in the late 1940s after Whitehead introduced them to classify 2-types [Whitehead, 1949]. Said activity was arguably revived after Loday [Loday, 1982] justified the classification of all types using the so-called n-cat Groups. This 1990s revival, spearheaded by [Norrie, 1987], aimed at studying crossed modules as algebraic objects in their own right. This paper is dedicated to crossed modules having a smooth structure, thought of as the global counterpart to Lie 2-algebras [Baez-Crans, 2004]. Recall the definition of a Crossed module (e.g., [Baez-Lauda, 2004]).

format_quoteVan Est's strategy outlines a mapping from Lie algebras to cohomology classes, establishing important connections in the integrability within Lie theory.format_quote

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On the Kodaira Vanishing Theorem

We review the proof and certain consequences of the vanishing theorem due to Kodaira.

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N ov 2 01 8 A cohomology theory for Lie 2-algebras

In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomo... more

Multiplicative Gray stability

In this paper we prove Gray stability for compact contact groupoids and we use it to prove stabil... more

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A cohomological proof for the integrability of strict Lie 2-algebras

of the linear Lie subalgebra ad(g) ≤ gl(g) by the center z(g). Such extensions are classified by ... more of the linear Lie subalgebra ad(g) ≤ gl(g) by the center z(g). Such extensions are classified by H CE(ad(g), z(g)), the Chevalley-Eilenberg cohomology of ad(g) with values on z(g). Recall the following theorem due to van Est: Theorem 1.1. [15] Let G be a Lie group with Lie algebra g and a representation on V . If G is k-connected, then the map that differentiates group cochains into Chevalley-Eilenberg cochains induces isomorphisms Φ : H Gp(G, V ) // H CE(g, V ) (2)

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A cohomology theory for Lie 2-algebras and Lie 2-groups

arXiv: Differential Geometry, 2018

In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new coh... more In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and Lie groups in that their second groups classify extensions. We use this fact together with an adapted van Est map to prove the integrability of Lie 2-algebras anew.

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A new cohomology theory for strict Lie 2-algebras

Communications in Contemporary Mathematics

In this paper, we introduce a new cohomology theory associated to a strict Lie 2-algebra. This co... more

A cohomology theory for Lie 2-algebras

In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomo... more

format_quoteA novel cohomology theory related to Lie 2-algebras extends classical cohomology, impacting the classification of algebraic structures.format_quote

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On the existence of certain axisymmetric interior metrics

One of the effects of noncommutative coordinate operators is that the delta function connected to... more One of the effects of noncommutative coordinate operators is that the delta function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of the effects of noncommutativity, this effect is, in particular, important as it removes the point singularities of Schwarzschild and Reissner-Nordström solutions. In this context, it seems to be of some importance to probe also into ringlike singularities which appear in the Kerr case. In particular, starting with an aniso-tropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution e.g., Gaussian, we derive the full set of Einstein equations that the noncommutative geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by noncommutative geometry.

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