Fernando Loup

Abstract: Warp Drives are solutions of the Einstein Field Equations that allows Superluminal Travel within the framework of General Relativity. There are at the present moment two known solutions: The Alcubierre Warp Drive discovered in 1994 and the Natario Warp Drive discovered in 2001. However as stated by both Alcubierre and Natario themselves the Warp Drive violates all the known energy conditions because the stress energy momentum tensor(the right side of the Einstein Field Equations) for the Einstein tensor G00 is negative implying in a negative energy density. While from a classical point of view the negative energy is forbidden the quantum theory allows the existence of very small amounts of it being the Casimir effect a good example as stated by Alcubierre himself. But the stress energy momentum tensor of both Alcubierre and Natario Warp Drives have the speed of the ship raised to the square inside its mathematical structure which means to say that as fast the ship goes by then more and more amounts of negative energy are needed in order to maintain the Warp Drive. Since the total energy requirements to maintain the Warp Drive are enormous and since quantum theory only allows small amounts of it,many authors regarded the Warp Drive as unphysical and impossible to be achieved. We compute the negative energy density requirements for a Warp Bubble with a radius of 100 meters(large enough to contain a ship) moving with a speed of 200 times light speed(fast enough to reach stars at 20 light-years away in months not in years)and we verify that the negative energy density requirements are of about 1045 times the positive energy density of Earth!!!(We multiply the mass of Earth by c2 and divide by Earth volume for a radius of 6300km). However both Alcubierre and Natario Warp Drives as members of the same family of the Einstein Field Equations requires the so-called Shape Functions in order to be mathematically defined. We present in this work two new Shape Functions one for the Alcubierre and another for the NatarioWarp Drive Spacetimes that allows arbitrary Superluminal speeds while keeping the negative energy density at "low" and "affordable" levels. We do not violate any known law of quantum physics and we maintain the original geometries of both Alcubierre and Natario Warp Drive Spacetimes.

Abstract: Although both Alcubierre and Natario Spacetimes belongs to the same family of Einstein Field Equations of General Relativity and both have many resemblances between each other ,the Energy Density distribution in the Alcubierre Warp Drive is different than the one found in the Natario Warp Drive.The Horizons will arise in both Spacetimes when approaching Superluminal(Warp) speeds however due to a different distribution of Energy Density the Natario Warp Drive behaves slightly different when compared to the Alcubierre one. The major differences between the Natario and Alcubierre Warp Drive Spacetimes occurs when we study the Infinite Doppler Blueshifts that affect the Alcubierre Spacetime but not affect the Natario one because while in Alcubierre Spacetime the Negative Energy is distributed in a toroidal region above and below the ship perpendicular to the direction of the motion while in front of the ship.the space is empty having nothing to prevent a photon to reach the Horizon because in this case the Horizon lies on empty space,in the Natario Spacetime the Energy Density is distributed in a spherical shell that covers the entire ship and a photon sent to the front will be deflected by this shell of Negative Energy before reaching the Horizon because the Horizon also lies inside this shell and not on "empty" space.This shell avoids the occurrence of Infinite Doppler Blueshifts in the Natario Warp Drive Spacetime.We examine in this work the major differences between both Natario and Alcubierre Spacetimes outlining the repulsive character of the Negative Energy Density.The creation of a Warp Bubble in Alcubierre or Natario Spacetimes is beyond the scope of Classical General Relativity and will have to wait until the arrival of a real Quantum Gravity theory that must encompass Superluminal Non-Local Quantum Entanglement Effects in order to deal with the Horizon problem added to the Geometrical features of Classical General Relativity plus it must also provide a way to generate large outputs of Negative Energy Densities.Since this theory is ahead of our scientific capabilities,we discuss in the end of this work an approach that could be performed by our science in a short period of term.to increase our knowledge about the Warp Drive as a Dynamical Spacetime.

Abstract: Natario Warp Drive is one of the most exciting Spacetimes of General Relativity.It was the second Spacetime Metric able to develop Superluminal Velocities.However in the literature about Warp Drives the Natario Spacetime is only marginally quoted. Almost all the available literature covers the Alcubierre Warp Drive. It is our intention to present here the fully developed Natario Warp Drive Spacetime and its very interesting features.Our presentation is given in a more accessible mathematical formalism following the style of the current Warp Drive literature destined to graduate students of physics since the original Natario Warp Drive paper of 2001 was presented in a sophisticated mathematical formalism not accessible to average students. Like the Alcubierre Warp Drive Spaceime that requires a continuous function f(rs) in order to be completely analyzed or described we introduce here the Natario Shape Function n(r) that allows ourselves to study the amazing physical features of the Natario Warp Drive. The non-existence of a continuous Shape Function for the Natario Warp Drive in the original 2001 work was the reason why Natario Warp Drive was not covered by the standard literature in the same degree of coverage dedicated to the Alcubierre Warp Drive. We hope to change the situation because the Natario Warp Drive looks very promising

Abstract: We use the Conformal Metric as described in Kar-Sinha work on Gravitational Bending of Light in a $5D$ Spacetime to recompute the equations of the $5D$ Force in Basini-Capozziello-Leon Formalism and we arrive at a result that possesses some advantages. The equations of the Extra Force as proposed by Leon are now more elegant in Conformal Formalism and many algebraic terms can be simplified or even suppressed. Also we recompute the Kar-Sinha Gravitational Bending of Light affected by the presence of the Extra Dimension and analyze the Superluminal Chung-Freese Features of this Formalism describing the advantages of the Chung-Freese BraneWorld when compared to other Superluminal spacetime metrics(eg:Warp Drive) and we describe why the Extra Dimension is invisible and how the Extra Dimension could be made visible at least in theory.We also examine the Maartens-Clarkson Black Holes in $5D$(Black Strings) coupled to massive Kaluza-Klein graviton modes predicted by Extra Dimensions theories and we study experimental detection of Extra Dimensions on-board LIGO and LISA Space Telescopes.We also propose the use of International Space Station(ISS) to measure the additional terms(resulting from the presence of Extra Dimensions) in the Kar-Sinha Gravitational Bending of Light in Outer Space to verify if we really lives in a Higher Dimensional Spacetime.Also we demonstrate that Particle $Z$ can only exists if the $5D$ spacetime exists.

Abstract: We use the 5D Extra Dimensional Force according to Basini-Capozziello-Ponce De Leon,Overduin-Wesson and Mashoon-Wesson-Liu Formalisms to study the behaviour of the Chung-Freese Superluminal BraneWorld compared to the Alcubierre Warp Drive and we arrive at some interesting results from the point of view of the Alcubierre ansatz although we used a diferent Shape Function f(rs) with a behaviour similar to the Natario Warp Drive. We introduce here the Casimir Warp Drive. We also demonstrate that in flat 5D Minkowsky Spacetime or weak Gravitational Fields we cannot tell if we live in a 5D or a 4D Universe according to Basini-Capozziello-Ponce De Leon,Overduin-Wesson and Mashoon-Wesson-Liu Dimensional Reduction but in the extreme conditions of Strong Gravitational Fields we demonstrate that the effects of the 5D Extra Dimension becomes visible and perhaps the study of the extreme conditions in Black Holes can tell if we live in a Higher Dimensional Universe. We use a 5D Maartens-Clarkson Schwarzschild Cosmic Black String centered in the Sun coupled to the 5D Extra Force from Ponce De Leon together with Mashoon-Wesson-Liu and the definitions of Basini-Capozziello and Bertolami-Paramos for the Warp Fields in order to demonstrate that the Anomalous Effect disturbing two American space probes known as the Pioneer Anomaly is a force of 5D Extra Dimensional Nature. As a matter of fact the Pioneer Anomaly is the first experimental evidence of the "Fifth Force" predicted years ago by Mashoon-Wesson-Liu and we also demonstrate that this Extra Force is coming from the Sun.

Abstract: If the Universe have more than $4$ Dimensions then its Extra Dimensional Nature generates in our $4D$ Spacetime a projection of a $5D$ Bulk Weyl Tensor. We demonstrate that this happens not only in the Randall-Sundrum BraneWorld Model where this idea appeared first(developed by Shiromizu,Maeda and Sasaki)but also occurs in the Kaluza-Klein $5D$ Induced Matter Formalism.As a matter of fact this $5D$ Bulk Weyl Tensor appears in every Extra Dimensional Formalism (eg Basini-Capozziello-Wesson-Overduin Dimensional Reduction From $5D$ to $4D$) because this Bulk Weyl tensor is being generated by the Extra Dimensional Nature of the Universe regardless and independently of the Mathematical Formalism used and the Dimensional Reduction From $5D$ to $4D$ of the Einstein and Ricci Tensors in both Kaluza-Klein and Randall-Sundrum Formalisms are similar.Also as in the Randall-Sundrum Model this $5D$ Bulk Weyl Tensor generates in the Kaluza-Klein formalism a Tidal "Electric" Charge "seen" in $4D$ as an Extra Term in the Schwarzschild Metric resembling the Reissner-Nordstrom Metric. We analyze the Gravitational Bending Of Light in this BraneWorld Black Hole Metric(known as the Dadhich,Maartens,Papadopolous and Rezania) affected by an Extra Term due to the presence of the Tidal Charge compared to the Bending Of Light in the Reissner-Nordstrom Metric with the Electric Charge also being generated by the Extra Dimension in agreement with the point of view of Ponce De Leon (explaining in the generation process how and why antiparticles have the same rest mass $m_{0}$ but charges of equal modulus and opposite signs when compared to particles)and unlike the Reissner-Nordstrom Metric the terms $G/(c^4)$ do not appear in the Tidal Charge Extra Term.Thereby we conclude that the Extra Term produced by the Tidal Charge in the Bending Of Light due to the presence of the Extra Dimensions is more suitable to be detected than its Reissner-Nordstrom counterpart and this line of reason is one of the best approaches to test the Higher Dimensional Nature of the Universe and we describe a possible experiment using Artificial Satellites and the rotating BraneWorld Black Hole Metric to do so