The Shield Proposal

Title: On the Problems of Hazardous Matter and Radiation for

Interstellar Craft using a Warp Drive Space-time C. B. Hart R. Held* P. K. Hoiland+ S. Jenks Martins J. Nyman J. P. Pertierra# P. A. Santos M. Stabano T. O. M. Teage

F. Loup** D. M. A. Shore R. Sims

Rev. 1 1 January 2003 of original that appeared in gr-qc/0207109 27 July 2002 Email: *[email protected] [email protected] **[email protected] #[email protected] abstract: The Problems of both hazardous radiation and collisions with matter on any sub-light or superluminal drive craft pose considerable obstacles to this possibility for interstellar travel. They also pose problems when it comes to survival of the human species on this planet as historical geological records show. A solution to these problems lies in the Broeck metric. It will be demonstrated that both treats to the ship will be greatly reduced and that an application of this type of field could be deployed to protect the planet earth itself.

1.) INTRODUCTION A Warp driven craft traveling at either a high sub-light or faster than light condition may collide with objects in front of the craft, which would be hazardous to the ship and its crew. Additionally, another problem exists in that photons arriving at the front of the ship’s region are blueshifted to very high energies by the Pfenning warped region effects. This high energy radiation can pose radiation dangers to the ship’s crew. It is desirable to find a solution that protects the ship’s crew from both of these threats,while maintaining a stable warp drive or sub-warp method of propulsion.

2.) BROECK WARP DRIVE METRIC AND BROECK WARPED REGIONS The warp drive metric in [1] was used to create a new metric. This variant of the Broeck warp drive metric differs from the previous metric of [6] in that it contains two warped regions. One is the usual Pfenning warped region representing the behavior of the function f(rs) going from 1 to 0, and the other is the Broeck warped region, which will decrease the energy of both photons and matter in the neighborhood of the ship. For the remote frame observer, the new metric is: Ds2=1-B2[dx-vsf(rs)dt]2

(1)

In the ship’s frame of reference, the metric can be written as, Ds2=1-B2[dx1+vsg(rs)dt]2 The symbols have the following definitions:

(2)

f(rs)=tanh[delta(rs+R)]-tanh[delta(rs-R)]/2tanh[delat(R)]

(3)

f(rs) is the Top Hat shaped function related to the Pfenning Warped region R-delta to R+delta B={1+tanh[delta(rs-D)]2/2}-p

(4)

Where D is the radius of the Broeck warped region, R is the radius of the warp bubble. Rs=sqrt[(x-xs)2+y2+z2]

(5)

Vs=dxs/dt

(6)

X1=x-xs

(7)

g(rs)=1-f(rs)

(8)

The general behavior of B is 1 at the ship and far from it since both regions remain C limited lightcone regions, while large in the vicinity of D. The exponent P is a free parameter. A more convenient form of the metric is:

ds2=[1-(Bvsg(rs))2]dt2-2vsg(rs)(B2)dx1dt-(B2)dx/2

(11)

3.) BEHAVIOR OF PHOTONS IN SHIP FRAME Solving equation 11 for photons(ds2=0), produces two solutions: v1=-vsg(rs)+1/B

(12)

v2=-vsg(rs)-1/B

(13)

v3=-vsg(rs)-1/B

(14)

v1 represents the energy of photons being emitted in the direction of motion, and v2 represents photons emitted toward the rear, as seen from the craft, and v3 is the energy of the photons coming towards the ship from the front. A 1 here represents the value for a velocity case where V=186300 mps. A qualitative analysis of the photon’s energy can be broken up into five regions: near the ship, the Broeck region, between the Broeck and Pfenning regions, the Pfenning region, and finally outside of the Pfenning region. At the location of the ship g(rs)=0, and B=1, so v1=1 and v2=-1. At a distance D from the craft, the Broeck warped region, g(rs)=0 and B is large. For a large enough B, both v1 and v2 can be made proportionally small due to v1=1/B and v2=-1/b. In between the Broeck and Pfenning warped regions, the space is effectively flat, so g(rs)=0 and B=1, therefore v1=1 and v2=-1. In the

Pfenning Warped region g(rs) is between 0 and 1. Here v2 is still negative, but v1 changes sign at g(rs)=1/vs. One can note that the photons entering the Pfenning region having been accelerated by the warp effect undergo a blueshift or increase in energy. The Broeck warped region is designed to decreases their energy. It performs the function of a shield not only against the high energies of incoming photons, but any other object in the path of the craft. Any object entering will encounter a region at distance D from the ship where B will have its maximum value, while being normal again at the ship itself. By proper placement of D relatively close to the ship, photons or incoming particles can have their kinetic energy dampened, thus reducing the over all impact effect of such collisions. 4.) THE BEHAVIOR OF MATTER COMING TOWARDS A SHIELD FIELD EFFECT REGION The exact description of what happens to matter entering the shield field effected region is quite complex. Since a time-like interval is appropriate to matter, the equations in section 2 would have the = replaced by I for equations with v3. The descriptions are still qualitatively the same. Pieces of matter too small to be disrupted by the tidal forces will have their inertia energy greatly reduced in the Broeck warped region. For large pieces of matter, they will become tidally disrupted in this region and broken up under this effect due to gravitational gradients in the Broeck region. It is this effect that we the authors believe to hold an answer to our survival of large incoming objects towards the earth itself. 5.) ENERGY NEEDED TO SUSTAIN A WARPED FIELD EFFECT Recently Krasnikov[4] demonstrated that a Broeck warp field can be obtained with approximately 10 kg of exotic matter if we use classical scalar fields instead of quantum fields. This was also noted in papers by Ford Roman[5}, Visser-Barcelo[3}, and LoboCrawford[2}. The paper of Ford-Roman 2000, they found at equation 15 and energy of 3*1017 gmcm2/s2, this amount can be generated using a massless scalar non-minimally coupled. If the assumptions Kransikov derived from his own formula are correct, then no astronomical amount of negative energy is needed to create a basic warp field with shields. Such a field could be deployed even from a stationary position to disrupt a large incoming body on a path towards the earth or any other space station or craft we have in service. REFERENCES [1] C. Van Den Broeck A ‘warped drive’ with more reasonable total energy requirements Class. Quant. Grav. 16 1999 3973-79 gr-qc/9905084 [2] F. Lobo and Paulo Crawford Weak energy condition violation and superluminal travel 16 2002 gr-qc/0204038

[3] Matt Visser and Carlos Barcelo Energy conditions and their cosmological implications 16 2000 gr-qc/0001099 [4] Serguei Krasnikov The quantum inequalities do not forbid space-time short-cuts 16 2002 gr-qc/0207057 [5] Lawrence Ford and Thomas Roman Classical Scalar Fields and the Generalized Second Law 16 20000 gr-qc/0009076 [6] F. Loup, D. Waite, and E. Halerwicz, Jr. Reduced Total Energy Requirements for a Modified Alcubierre Warp Drive Spacetime gr-qc/0107097