Influence of anisotropic matter on the Alcubierre metric and other related metrics: revisiting the problem of negative energy

Abellán, Gabriel; Bolivar, Nelson; Vasilev, Ivaylo T.

doi:10.1007/s10714-023-03105-8

Cited by 5 publications

(5 citation statements)

References 28 publications

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“…As we have shown in previous work [30], spherical symmetry allows us to find a neater system of equations, eliminating the redundant relations from Einstein equations of warp-like systems. This is particularly useful when dealing with problems involving material distributions, where one can clearly read the links with matter and the energy conditions involved.…”

Section: Final Remarksmentioning

confidence: 86%

“…Nonetheless, there are regions of the domain in r where all the conditions can be said to be satisfied; although they are clearly not satisfied for the whole domain. However, as we have shown in a previous study [28,30], the energy conditions should be evaluated by considering the complete set of Einstein equations. Thus, the observance of the energy conditions is much more subtle and must be treated with care.…”

Section: Final Remarksmentioning

confidence: 99%

“…For example, by working in cylindrical coordinates we have been able to write the Einstein equations in a simple enough form to be able to see that there is a relationship between the energy density and the tangential pressures. In particular, we have found that for dust-like fluids, isotropic fluids, or fluids where the tangential pressures are equal, the energy density is necessarily zero [30]. All these works have in common the interest of studying the complete set of Einstein equations in order to extract constraints and relations between the different degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

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Spherical warp-based bubble with non–trivial lapse function and its consequences on matter content

Abellán,

Bolívar,

Vasilev

2024

Class. Quantum Grav.

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In the present work, we study the consequences of including the lapse function as an additional degree of freedom for a general spherical warp-based geometry. By allowing a non-uniform lapse function to evolve, we find that it is possible to accommodate a fluid that includes heat flow. This broadens the range of fluid types that have been studied in these systems and is consistent with the spherical warp metric. Having added the lapse function, we solved the system of equations using an anisotropic fluid with heat flow. In this way, we can examine the different characteristics of the variables of the system. Next, we study the energy conditions and establish how these are modified by including heat flux for an appropriate generic observer in a locally flat spacetime. Finally, we explore all energy conditions using the numerical solutions and verify the regions where they are satisfied.

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Section: Final Remarksmentioning

confidence: 86%

Section: Final Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spherical warp-based bubble with non–trivial lapse function and its consequences on matter content

Abellán,

Bolívar,

Vasilev

2024

Class. Quantum Grav.

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“…( 7), dictates the local shear stress, corresponding to the off-diagonal components of T αβ which in turn sources a shear curvature (warping) of spacetime (in the case of the Alcubierre metric this curvature is predefined). The stress-energy-momentum tensor can exhibit off-diagonal components in scenarios involving anisotropic fluids [22][23][24][25][26][27][28][29], which may arise due to fluid viscosity, or when observing a perfect fluid from a non-comoving frame, or in heat transfer. An electromagnetic field can also serve as a source in this context.…”

Section: Preliminaries: Tensor Definitionsmentioning

confidence: 99%

Visualization and analysis of the curvature invariants in the Alcubierre warp-drive spacetime

Rodal

2023

Gen Relativ Gravit

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In the Alcubierre warp-drive spacetime, we investigate the following scalar curvature invariants: the scalar I, derived from a quadratic contraction of the Weyl tensor, the trace R of the Ricci tensor, and the quadratic r1 and cubic r2 invariants from the trace-adjusted Ricci tensor. In four-dimensional spacetime the trace-adjusted Einstein and Ricci tensors are identical, and their unadjusted traces are oppositely signed yet equal in absolute value. This allows us to express these Ricci invariants using Einstein's curvature tensor, facilitating a direct interpretation of the energy-momentum tensor. We present detailed plots illustrating the distribution of these invariants. Our findings underscore the requirement for four distinct layers of an anisotropic stress-energy tensor to create the warp bubble. Additionally, we delve into the Kretschmann quadratic invariant decomposition. We provide a critical analysis of the work by Mattingly et al., particularly their underrepresentation of curvature invariants in their plots by 8 to 16 orders of magnitude. A comparison is made between the spacetime curvature of the Alcubierre warp-drive and that of a Schwarzschild black hole with a mass equivalent to the planet Saturn. The paper addresses potential misconceptions about the Alcubierre warp-drive due to inaccuracies in representing spacetime curvature changes and clarifies the classification of the Alcubierre spacetime, emphasizing its distinction from class B warped product spacetimes.

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“…In 2021 Bobrick and Martire further reduced the magnitude of negative mass-energy required by Alcubierre's super-luminal drive as well as proposed a model for a sub-luminal warp-drive that utilizes only positive energy density [15]. From 2010 to 2023 several researchers have considered the effects of altering the stressenergy tensor by utilizing various different fluids: in 2010 Smolyaninov-bi-anisotropic nonreciprocal magnetoelectric metamaterials [16]; in 2020 Béatrix-Drouhet-exotic equations of state [17]; in 2023 Abellan et al-anisotropic matter [18]. Also in 2021, Erik Lentz proposed a super-luminal warp-drive model that does not violate the WEC.…”

Section: Introductionmentioning

confidence: 99%

Membrane models as a means of propulsion in general relativity: super-luminal warp-drive that satisfies the weak energy condition

Huey

2024

Class. Quantum Grav.

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Presented are toy-models for sub-luminal and super-luminal warp-drives in 3+1 dimensions. The models are constructed in a chimeric manner - as different bulk space-times separated by thin membranes. The membranes contain perfect-fluid-like stress-energy tensors. The Israel junction conditions relate this stress-energy to a jump in extrinsic curvature across the brane, which in turn manifests as apparent acceleration in the bulk space-times. The acceleration on either side of the brane may be set individually by choice of model parameters. The Weak Energy Condition (WEC) is shown to be satisfied everywhere in both models. Although the branes in these toy models are not compact, it is demonstrated that super-luminal warp-drive is possible that satisfies the WEC. Additionally, the nature of these models provides framework for speculation on a mechanism for transition from sub-luminal to super-luminal warp. Neither quantum effects nor stability of the models is considered.

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Influence of anisotropic matter on the Alcubierre metric and other related metrics: revisiting the problem of negative energy

Cited by 5 publications

References 28 publications

Spherical warp-based bubble with non–trivial lapse function and its consequences on matter content

Spherical warp-based bubble with non–trivial lapse function and its consequences on matter content

Visualization and analysis of the curvature invariants in the Alcubierre warp-drive spacetime

Membrane models as a means of propulsion in general relativity: super-luminal warp-drive that satisfies the weak energy condition

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