arXiv subjects

J. A. Nieto

Publications and source records attributed to J. A. Nieto.

At least 19 recordsLinked to original sources

arXiv2024

Beyond Schwarzschild: New Pulsating Coordinates for Spherically Symmetric Metrics

Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one where tortoise coordinate appears as the unique solution, other that includes Kruskal-Szekeres coordinates as a very specific case, but that also allows other similar transformations, and finally a new set of coordinates with very different properties than the other two. In particular, this represents any causal patch of the spherically symmetric metrics in a compactified form. We analyze some relations, taking the Schwarzschild case as prototype, but also contrasting the cosmological de-Sitter and Anti-de-Sitter solutions for the new proposed pulsating coordinates.

gr-qc↗

arXiv2019

Generalized Elko Theory

By using a totally antisymmetric spinor field we generalize Elko theory. We compare our proposed theory with traditional totally antisymmetric spinor field theory based on the Dirac equation. As an application of our formalism we comment about the possibility to link our generalized Elko theory with matroids, qubits and surreal numbers.

gr-qc↗

arXiv2019

New Reflections on Higher Dimensional Linearized Gravity

We make a number of remarks on linearized gravity with cosmological constant in any dimension, which, we argue, can be useful in a quantum gravity framework. For this purpose we assume that the background space-time metric corresponds to the de Sitter or anti-de Sitter space. Moreover, via the graviton mass and the cosmological constant correspondence, we make some interesting observations, putting special attention on the possible scenario of a graviton-tachyon connection. We compare our proposed formalism with the Novello and Neves approach.

gr-qc↗

arXiv2018

Duality, matroids, qubits, twistors and surreal numbers

We show that via the Grassmann-Plücker relations, the various apparent unrelated concepts, such as duality, matroids, qubits, twistors and surreal numbers are, in fact, deeply connected. Moreover, we conjecture the possibility that these concepts may be considered as underlying mathematical structures in quantum gravity.

physics.gen-ph↗

arXiv2018

Towards a unified Lagrangian formalism for Cosmology and Black Holes

Using a Lagrangian formalism we establish a relationship between the (n + D + d) dimensional cosmology, black-holes and the Polyakov action for strings. Specifically, we identify these physical scenarios as part of a 2-dimensional metric, which arises from a Lagrangian function with constraints, derived from the Einstein-Hilbert action. In particular, we show that the Friedmann-Robertson-Walker cosmological model and the Schwarzschild solution are both consequence of this Lagrangian.

physics.gen-ph↗

arXiv2017

Hyperbolic trajectories around Black Holes

We analyse test particle's trajectories around the geometry of a Schwarzschild black hole. In order to resemble sections of jets in the neighborhood of a black hole, we consider the conserved quantities corresponding to constraints imposed on the trajectories of the test particles, namely conic and hyperboloidic trajectories. As expected, the energy and angular momentum are closely related to the solutions in the non-constrained case.

gr-qc↗

arXiv2016

Some Mathematical and Physical Remarks on Surreal Numbers

We make a number of observations on Conway surreal number theory which may be useful, for further developments, in both in mathematics and theoretical physics. In particular, we argue that the concepts of surreal numbers and matroids can be linked. Moreover, we established a relation between the Gonshor approach on surreal numbers and tensors. We also comment about the possibility to connect surreal numbers with supesymmetry. In addition, we comment about possible relation between surreal numbers and fractal theory. Finally, we argue that the surreal structure may provide a different mathematical tools in the understanding of singularities in both high energy physics and gravitation.

physics.gen-ph↗

arXiv2016

Dirac Equation in Four Time and Four Space Dimensions

The Dirac equation in four time and four space dimensions (or (4+4)-dimensions) is considered. Step by step we show that such an equation admits Majorana and Weyl solutions. In order to obtain the Majorana or Weyl spinors we used a method based on the construction of Clifford algebra in terms of 2x2-matrices. We argue that our approach can be useful in supergravity, superstrings and qubit theory.

physics.gen-ph↗

arXiv2016

Alternative Self-dual Gravity in Eight Dimensions

We develop an alternative Ashtekar formalism in eight dimensions. In fact, using a MacDowell-Mansouri physical framework and a self-dual curvature symmetry we propose an action in eight dimensions in which the Levi-Civita tenor with eight indices plays a key role. We explicitly show that such an action contains number of linear, quadratic and cubic terms in the Riemann tensor, Ricci tensor and scalar curvature. In particular, the linear term is reduced to the Einstein-Hilbert action with cosmological constant in eight dimensions. We prove that such a reduced action is equivalent to the Lovelock action in eight dimensions.

gr-qc↗

arXiv2014

Higher Dimensional Elko Theory

We show that the so called Elko equation can be derived from a 5-dimensional Dirac equation. We argue that this result can be relevant for dark matter and cosmological scenarios. We generalize our procedure to higher dimensions.

gr-qc↗

arXiv2014

Towards an Alternative Gravitational Theory

In 1680 Cassini proposed oval curves as alternative trajectories for the visible planets around the sun. The Cassini ovals were of course overshadow by the Kepler's first law (1609), namely the planets move around the sun describing conic orbits. Here we describe the possibility that the Cassini's idea works at larger or smaller scales. Indeed, we consider the Spiric curves (which are a generalization of the Cassini oval) and present the first steps towards a Spiric gravitational theory. We show that from our formalism an ellipse associated with a planet can be obtained as a particular case.

physics.gen-ph↗

arXiv2014

Phirotopes, Super p-branes and Qubit Theory

The phirotope is a complex generalization of the concept of chirotope in oriented matroid theory. Our main goal in this work is to establish a link between phirotopes, super p-branes and qubit theory. For this purpose we first discuss maximally supersymmetric solutions of 11-dimensional supergravity from the point of view of the oriented matroid theory. We also clarify a possible connection between oriented matroid theory and supersymmetry via the Grassmann-Plücker relations. These links are in turn useful for explaining how our approach can be connected with qubit theory.

hep-th↗

arXiv2013

Geometric Structure of Higher-Dimensional Spheres

We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the recently proposed division-algebras/Poincaré-conjecture correspondence. Moreover, we explore the possibility of a connection between N-qubit system and the Hopf maps. We also discuss the possible links of our work with squashed-spheres in supergravity and pseudo-spheres in oriented matroid theory.

physics.gen-ph↗

arXiv2013

Dirac equation in (1+3) and (2+2) dimensions

We develop a systematic method to derive the Majorana representation of the Dirac equation in (1+3)-dimensions. We compare with similar approach in (2+2)-dimensions . We argue that our formalism can be useful to have a better understanding of possible Majorana fermions.

physics.gen-ph↗

arXiv2013

SL(2,R)-geometric phase space and (2+2)-dimensions

We propose an alternative geometric mathematical structure for arbitrary phase space. The main guide in our approach is the hidden SL(2,R)-symmetry which acts on the phase space changing coordinates by momenta and vice versa. We show that the SL(2,R)-symmetry is implicit in any symplectic structure. We also prove that in any sensible physical theory based on the SL(2,R)-symmetry the signature of the flat target "spacetime" must be associated with either one-time and one-space or at least two-time and two-space coordinates. We discuss the consequences as well as possible applications of our approach on different physical scenarios.

hep-th↗

arXiv2013

Higher dimensional black holes as constrained systems

We construct a Lagrangian and Hamiltonian formulation for charged black holes in a d-dimensional maximally symmetric spherical space. By considering first new variables that give raise to an interesting dimensional reduction of the problem, we show that the introduction of a charge term is compatible with classical solutions to Einstein equations. In fact, we derive the well-known solutions for charged black holes, specially in the case of d=4, where the Reissner-Nordström solution holds, without reference to Einstein field equations. We argue that our procedure may be of help for clarifying symmetries and dynamics of black holes, as well as some quantum aspects.

gr-qc↗

arXiv2013

Division-Alebra/Poncare-Conjecture correspondence

We briefly describe the importance of division algebras and Poincaré conjecture in both mathematical and physical scenarios. Mathematically, we argue that using the torsion concept one can combine the formalisms of division algebras and Poincaré conjecture. Physically, we show that both formalisms may be the underlying mathematical tools in special relativity and cosmology. Moreover, we explore the possibility that by using the concept of n-qubit system, such conjecture may allow generalization the Hopf maps.

physics.gen-ph↗

arXiv2012

Qubits and oriented matroids in four time and four space dimensions

We establish a connection between 4-rebits (real qubits) and the Nambu-Goto action with target `spacetime' of four time and four space dimensions ((4+4)-dimensions)). We motivate the subject with three observations. The first one is that a 4-rebit contains exactly the same number of degree of freedom as a complex 3-qubit and therefore 4-rebits are special in the sense of division algebras. Secondly, the (4+4)-dimensions can be splitted as (4+4)=(3+1)+(1+3) and therefore they are connected with an ordinary (1+3)-spacetime and with changed signature (3+1)-spacetime. Finally, we show how geometric aspects of 4-rebits can be related to the chirotope concept of oriented matroid theory.

hep-th↗