Gravity and Sunspots.

Sunspots are disturbances in the electro-magnetic field surrounding the photosphere, or top surface of the Sun's convection zone. They are believed to be caused by the differential rotation of the outer convective layer. The rotation period of the Sun at the equator is 25.6 days and at the poles is 30 days. The magnetic field wraps around itself and produces loops, which are forced out through the photosphere. Where these loops form is the location of the sunspots.

Previously it was thought that filaments of gas parallel to the surface and marking the path of the magnetic field only extended into the penumbra, or outer region of the sunspot. However, astronomer William Livingston of the National Solar Observatory in Tucson produced long-exposure photographs showing the filaments bridging the penumbra from one side to the other (1).

The magnetic fields have a fluctuation based on an 11-year cycle, which means that after 22 years the sunspot will return to it's original configuration. The sunspot temperature at 4000 K/6680 *F is also lower than the surrounding photosphere.

Gravity and General Relativity

In his seminal 1915 paper Einstein introduced the idea of gravity being formed by warps in the space-time continuum.

Previous to this Newton's Law of Gravitation specified gravity as the force of attraction between two bodies. This force is inversely proportional to the square of the distance between them. Newton quantified the concept in the equation F=Gm1m2/r^2 where

G=6.6742x10^11Nm^2/kg^2(gravitational constant), m1 and m2 are masses of the objects, and r is the distance between them.

Gravity and General Relativity

With the introduction of General Relativity gravity was now treated as a "dent or "warp" in the fabric of space-time.

This fabric is measured by three-dimensional world lines that bend and stretch with warps formed by gravity. The mathematics used to measure world lines is Riemannian geometry, which traces lines along a three-dimensional surface.

The world lines of the diagram trace the path of the arrows following the folds. This section of the continuum is referred to as a manifold, or reference frame, as used in Special Relativity. Each reference frame is independent, and can have forces acting on it that do not act on adjacent frames.

The equations of General Relativity are field equations that treat gravity in a similar way as electro-magnetism. They are based on tensors. A tensor is an object that corresponds to a position in space-time. A tensor of rank=0 is a scalar, or point in time. A tensor of rank=1 is a vector, which has magnitude and direction. A rank k tensor has a value of k dimensions. For a coordinate system X,Y,Z there are indices to denote the position of the tensor in this system. Special Relativity introduced the time constant T so that a tensor in the space-time continuum will include a T index.

Gravity and General Relativity

Einstein needed to define position in space-time due to the failure of the Michelson-Morley experiment to detect any medium or "ether" that gravity exits in. Time is treated as a fourth coordinate. The field equation that defines General Relativity and the curvature due to gravity is:

R1-gR2/2+ CCg=8piG/c^4T

Where R1= the Ricci curvature tensor, R2= the scalar curvature, g= the metric tensor, CC=8piG/3c^2p(Einstein's cosmological constant),T= the stress-energy tensor non-gravitational matter, energy, and forces at any given point in space-time, c= the speed of light in a vacuum, G= the gravitational constant from Newton's Law of Gravitation, and pi=3.1415

The cosmological constant was developed by Einstein to balance the equation. He later stated it was the worst mistake of his life. The metric tensor gdescribes the metric of the manifold and is a symmetric 4x4 tensor, which means it is a matrix with 10 independent components, but with freedom of choice for 4, so that the independent equations that make up the Einstein field equation are reduced to 6.

The basic tenant of the Einstein field equation is that the curvature of space-time is directly affected by the force of gravity applied by the mass of the object. It also takes into account the measurement of the curvature (g), the non-gravitational forces (T), and the interrelations of fields. In an over-simplified way it states, "curvature tells matter how to move, and matter tells space how to curve" (2).

Gravity and Sunspots

As stated earlier, sunspots are perturbations in the sun's electro-magnetic field due to differential rotation of the poles and equators. Sunspots can cause severe disturbances in the electro-magnetic field here on earth, disrupt satellite communications and bombard passenger jets with large amounts of gamma-ray radiation.

Because of General Relativity we now understand that space-time is warped by massive objects in the form of gravity. The force of electro-magnetism also affects the curvature of space-time defined by the T tensor. What this effect is has been the subject of experiments performed attempting to link sunspot activity with changes in the earth's tidal periods (3).

These results of these effects have so far proven to be inconsequential. However, there is extensive evidence of the curvature of light represented by red or blue shift in the spectrum when bodies are either moving towards or away from the observer. This is how stellar astronomers measure distances between the earth and stars, and is used to determine if the universe is either expanding or contracting.

At this point in time, there needs to be more research both experimentally and theoretically on this subject. I will continue to probe other's work and perhaps join a solar astronomer's society such as the American Association of Variable Star Observers (AAVSO). In addition, I will look for research associates in the Society of Amateur Scientists, and look into building or purchasing instrumentation to measure sunspot activity.

References

1. http://www.goodfelloweb.com/nature/cgbi/sn030991.html

2. http://en.wikipedia.org/wiki/General_relativity

3. http://perso.wanadoo.fr/jpdesm/sunspots/sun3.html