arXiv subjects

Osvaldo L. Santos-Pereira

Publications and source records attributed to Osvaldo L. Santos-Pereira.

11 recordsLinked to original sources

arXiv2026

Shift vector sign reversal in the Alcubierre warp drive spacetime geometry and nonlinear Burgers-type dynamics

This work investigates a sign reversal of the shift vector in the Alcubierre Warp Drive geometry and its effect on the nonlinear reduced structure of the Einstein equations. Previous analyses showed that Burgers-type equations can arise in warp drive spacetimes, leading to vacuum solutions under suitable assumptions on the sign of the shift vector and on matter-source reductions. Here, we analyze the original Alcubierre shift-vector sector and show that, under an appropriate mathematical ansatz, the $\{22\}$ and $\{33\}$ components of the Einstein equations can be formally decomposed into viscous Burgers-type and heat-type equations. The resulting heat-type structure and the constant analogous to a diffusivity coefficient constitute new formal features of the reduced shift-vector dynamics. Since these terms are introduced through an ansatz and are not generated by a specific energy-momentum tensor source, they should not be interpreted as physical diffusivity without an additional matter model. The vacuum reductions of the Einstein equations for the warp-drive geometry come with an important caveat: the shift vector must depend only on time and on one spatial coordinate, namely $β(t,x)$. Consequently, the Alcubierre regulating function no longer retains its original spherical dependence on $r_s(t)$, and the resulting solutions should be interpreted as lower-dimensional shift-sector reductions rather than complete spherically symmetric warp bubble configurations.

gr-qc↗

arXiv2025

Matching the Alcubierre and Minkowski spacetimes

This work analyzes the Darmois junction conditions matching an interior Alcubierre warp drive spacetime to an exterior Minkowski geometry. The joining hypersurface requires that the shift vector of the warp drive spacetime must satisfy the solution of a particular inviscid Burgers equation, namely, the gauge where the shift vector is not a function of the $y$ and $z$ spacetime coordinates. Such a gauge connects the warp drive metric to shock waves via a Burgers-type equation, which was previously found to be an Einstein equations vacuum solution for the warp drive geometry. It is also shown that not all Ricci and Riemann tensors components are zero at the joining hypersurface, but for that to happen they depend on the shift vector solution of the inviscid Burgers equation at the joining wall. This means that the warp drive geometry is not globally flat.

gr-qc↗

arXiv2025

Roullete curves, coin paradox and Aristotle's wheel paradox

This work discusses the concept of roulette, the generated curves that occur when one curve rolls without slipping along another, tracing the path of a fixed point. The coin paradox and Aristotle's wheel paradox are used as pedagogical motivations to discuss the parametric equations of epicycloids and hypocycloids, providing a geometrical intuition for the mathematical derivations and computational implementation of those curves. Python code is provided to motivate the application of the derived parametric equations, resulting in concrete visualizations and animations.

physics.soc-ph↗

arXiv2025

The Warp Drive: Superluminal Travel within General Relativity

In 1994, Miguel Alcubierre proposed that the well-known special relativistic limitation that particles cannot travel with velocities higher than light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks, using a warped region of spacetime in the shape of a bubble that transports particles with mass traveling through spacetime with superluminal speed. Although initial results indicated this scenario as nonphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such a nonphysical situation may not always be true. This thesis presents newfound solutions for the Einstein field equations, considering the Alcubierre warp drive spacetime metrics. The central premise is to study the fluid matter as the gravity source, rather than the more common vacuum or negative energy sources, to explore the potential for generating superluminal velocities, or \textit{warp speeds}, through a warped region in the spacetime. Such solutions have various matter-energy sources: dust particles, perfect fluid, quasi-perfect fluid with anisotropic pressures, charged dust, and a perfect fluid within a cosmological constant spacetime. A connection between some of these solutions featuring shock waves described by a Burgers-type equation with a term on the right-hand side of the equation purely dependent on time is also shown. This could mean warp drives are closely related to vacuum energy and possibly have topological effects such as shock waves.

gr-qc↗

arXiv2025

Experimental Physics Laboratory 2: Calculating the Value of Water Density using Metal Rod and Water Container

This article presents a detailed analysis of an undergraduate physics laboratory experiment designed to determine the density of water using fundamental measurement techniques and data analysis methods. The experimental setup consists of a precision scale, a graduated container filled with water, and a suspended metal rod held by a crank, allowing for controlled displacement measurements. The primary objective of this experiment is to reinforce essential concepts in experimental physics, particularly in deriving physical models that correlate measurable quantities, performing precise measurements, and analyzing data using regression techniques via ordinary least squares methods for fitting data into linear models. This article aims to provide students with a theoretical and computational aid to explore the physical interpretations of this experiment. I developed a theoretical framework to introduce the fundamental concepts of hydrostatics, Newtonian mechanics, and the primary equations used in the experiment. I supplied Python code with thorough explanations that performs analysis on the experiment.

physics.ed-ph↗

arXiv2025

Galaxy Mergers in a Fractal Cosmology

This work discusses the influence of galaxy mergers in the evolution of a parabolic Lema\^ıtre-Tolman-Bondi (LTB) cosmology with simultaneous big bang endowed with two consecutive single fractal galaxy distributions systems possessing fractal dimension $D$. Based on recent empirical findings, it is assumed that the resulting galaxy mass from mergers can be expressed by a redshift dependent decaying power law. The proposed cosmological model modifies the relativistic fractal number counts distribution by including a merger rate evolution that estimates the model's radial density. Numerical solutions for the first order small-merger-rate approximation (SMRA) are found and the results show that a fractal galaxy distribution having $D=1.5$ in the range $0.1<z<1.0$, and $D=0.5$ for $1<z<6$, as suggested by recent empirical findings, the SMRA allows consistent description of the model for a merger rate power law exponent up to $q=0.2$ considering a fractal galaxy distribution starting from the Local Group. Consistent values were also found up to $q=2.5$ and $z=7$ from a scale smaller than the Local Supercluster. These results show that galaxy mergers can be successfully incorporated into the dynamics of a parabolic LTB fractal cosmology.

astro-ph.CO↗

arXiv2021

Warp drive dynamic solutions considering different fluid sources

Alcubierre proposed in 1994 that the well known special relativistic limitation that particles cannot travel with velocities bigger than the light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks. Although initial results indicated this scenario as being unphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such an unphysical situation may not always be necessarily true. In this paper we review some solutions of the Einstein equations using the original Alcubierre warp drive metric endowed with various matter-energy sources, namely dust, perfect fluid, anisotropic fluid, and perfect fluid with a cosmological constant. A connection of some of these solutions featuring shock waves described by the Burgers equation is also shown.

gr-qc↗

arXiv2021

Perfect fluid warp drive solutions with the cosmological constant

The Alcubierre metric describes a spacetime geometry that allows a massive particle inside a spacetime distortion, called warp bubble, to travel with superluminal global velocities. In this work we advance solutions of the Einstein equations with the cosmological constant for the Alcubierre warp drive metric having the perfect fluid as source. We also consider the particular dust case with the cosmological constant, which generalizes our previous dust solution (arXiv:2008.06560) and led to vacuum solutions connecting the warp drive with shock waves via the Burgers equation, as well as our perfect fluid solution without the cosmological constant (arXiv:2101.11467). All energy conditions are also analyzed. The results show that the shift vector in the direction of the warp bubble motion creates a coupling in the Einstein equations that requires off-diagonal terms in the energy-momentum source. Therefore, it seems that to achieve superluminal speeds by means of the Alcubierre warp drive spacetime geometry one may require a complex configuration and distribution of energy, matter and momentum as source in order to produce a warp drive bubble. In addition, warp speeds seem to require more complex forms of matter than dust for stable solutions and that negative matter may not be a strict requirement to achieve global superluminal speeds.

gr-qc↗

arXiv2021

Charged dust solutions for the warp drive spacetime

The Alcubierre warp drive metric is a spacetime construction where a massive particle located inside a spacetime distortion, called warp bubble, travels at velocities arbitrarily higher than the velocity of light. This theoretically constructed spacetime geometry is a consequence of general relativity where global superluminal velocities, also known as warp speeds, are possible, whereas local speeds are limited to subluminal ones as required by special relativity. In this work we analyze the solutions of the Einstein equations having charged dust energy-momentum tensor as source for warp velocities. The Einstein equations with the cosmological constant are written and all solutions having energy-momentum tensor components for electromagnetic fields generated by charged dust are presented, as well as the respective energy conditions. The results show an interplay between the energy conditions and the electromagnetic field such that in some cases the former can be satisfied by both positive and negative matter density. In other cases the dominant and null energy conditions are violated. A result connecting the electric energy density with the cosmological constant is also presented, as well as the effects of the electromagnetic field on the bubble dynamics.

gr-qc↗

arXiv2021

Fluid dynamics in the warp drive spacetime geometry

The Alcubierre warp drive metric is a spacetime geometry featuring a spacetime distortion, called warp bubble, where a massive particle inside it acquires global superluminal velocities, or warp speeds. This work presents solutions of the Einstein equations for the Alcubierre metric having fluid matter as gravity source. The energy-momentum tensor considered two fluid contents, the perfect fluid and the parametrized perfect fluid (PPF), a tentative more flexible model whose aim is to explore the possibilities of warp drive solutions with positive matter density content. Santos-Pereira et al. (2020; arXiv:2008.06560) have already showed that the Alcubierre metric having dust as source connects this geometry to the Burgers equation, which describes shock waves moving through an inviscid fluid, but led the solutions back to vacuum. The same happened for two out of four solutions subcases for the perfect fluid. Other solutions for the perfect fluid indicate the possibility of warp drive with positive matter density, but at the cost of a complex solution for the warp drive regulating function. Regarding the PPF, solutions were also obtained indicating that warp speeds could be created with positive matter density. Weak, dominant, strong and null energy conditions were calculated for all studied subcases, being satisfied for the perfect fluid and creating constraints in the PPF quantities such that positive matter density is also possible for creating a warp bubble. Summing up all results,energy-momentum tensors describing more complex forms of matter, or field, distributions generate solutions for the Einstein equations with the warp drive metric where negative matter density might not be a strict precondition for attaining warp speeds.

gr-qc↗

arXiv2020

Dust content solutions for the Alcubierre warp drive spacetime

The Alcubierre metric is a spacetime geometry where a massive particle inside a spacetime distortion, called warp bubble, is able to travel at velocities arbitrarily higher than the velocity of light, a feature known as the warp drive. This is a consequence of general relativity, which allows global superluminal velocities but restricts local speeds to subluminal ones as required by special relativity. In this work we solved the Einstein equations for the Alcubierre warp drive spacetime geometry considering the dust matter distribution as source, since the Alcubierre metric was not originally advanced as a solution of the Einstein equations, but as a spacetime geometry proposed without a source gravity field. We found out that all Einstein equations solutions of this geometry containing pressureless dust lead to vacuum solutions. We also concluded that these solutions connect the Alcubierre metric to the Burgers equation, which describes shock waves moving through an inviscid fluid. Our results also indicated that these shock waves behave as plane waves.

gr-qc↗