# Relativistic effects on interior of our sun?

1. Dec 4, 2006

### chemisttree

Last night I watched a program on TV that made the statement that in the interior of our sun the gravity is so intense that a photon of light can travel only several thousandths of an inch per minute. It takes hundreds of thousands of years for a photon of light to travel from the interior of the sun (near the core) to the surface.

Thats the first time I've heard anything like that about our sun. But, I'm no expert...

Is it true?

If it is true, does the magnetic field in the interior respond as slowly? It should...

Is the center of the sun rotating with approximately the same radial velocity as is observed at the surface? If so, does the mass near the center therefore travel (by rotation alone) at close to the same speed as does a photon? Is that mass travelling at near relativistic speed?

If the interior is not travelling as fast (radially) as the surface, does this dampen the rotation of the sun?

I found the following abstract:

"The hypothesis stating that a chemically inhomogeneous convectively neutral zone is present in the sun, in the region where the angular velocity is at a minimum, is considered. A preliminary study of the 5-min mode frequency splitting is carried out. The results are in qualitative agreement with the experimental data, indicating a large decrease of the rotational velocity at a distance of about 1/4 of the radius from the center."

Could relativistic effects near the core explain the observations mentioned in the abstract?

2. Dec 4, 2006

### Staff: Mentor

That was badly worded. It isn't the gravity itself, but the density of the sun (caused by gravity) that makes the energy take so long to get to the surface.

3. Dec 6, 2006

### Chris Hillman

Hi, chemisttree,

I'd add to what russ watters told you specific mention of the essential point: the fact that a photon can rarely if ever propagate from deep inside a star to deep space is due to nongravitional physics (very very rougly speaking, the photon quickly encounters star stuff so it doesn't propagate freely; that is why we cannot see optical images from very far inside a star). Having said that, I should probably add that the process by which material becomes concentrated in a gaseous ball does involve gravitation. The process by which, when pressures and temperatures becomes sufficiently high, this ball ignites to form a star, involves nuclear physics.

Chris Hillman

Last edited: Dec 6, 2006
4. Dec 8, 2006

### chemisttree

I get it... thanks Russ and Chris.

5. Dec 10, 2006

### estel

Of course, at the centre of the sun, gravitation itself is very low in comparison to that at the surface.
However, as has been mentioned, due to the pressure of the sun, the core has a very high particle density for such a high temperature.

Pretty sure Chris nailed the rest - and can I just add that quantum effects also keep the sun active, not just standard nuclear physics.

6. Dec 12, 2006

### Chris Hillman

Gravitation minimal at the center?

Hi, estel,

Not sure what you mean by "gravitation", but just to be clear: if we model a star, according to gtr, as a static spherically symmetric perfect fluid solution of the Einstein field equation (EFE), or ssspf for short, then:

1. "the acceleration due to gravity" (that is, the acceleration of a bit of fluid at the center due the gravitational attraction of the rest of our fluid ball) vanishes at the center of the ball, just as in Newtonian theory; this is obvious from symmetry considerations (the only vector which doesn't pick out a preferred direction by pointing in said direction is the zero vector!),

2. the curvature is in general maximal at the center, where "curvature" can stand for "typical" components of the Einstein curvature tensor, "typical" components of the electrogravitic tensor (analog of the tidal tensor of Newtonian gravitation), the Kretschmann scalar, and so on,

3. in a stellar model in gtr, one generally matches an "interior solution" (often a ssspf) across the surface of the fluid ball to a "exterior solution" (neccessarily part of the Schwarzschild vacuum solution, if matching to a ssspf),

4. the pressure and (mass-energy) density are in general monotonically decreasing functions of radius, with the surface of the star at the zero pressure surface, where the density in general is positive in the limit as you approach the surface radially from inside the star, but of course zero as you approach from outside,

5. interestingly enough, the maximal acceleration of a bit of fluid can occur somewhat below the surface (zero pressure locus) of a static spherically symmetric perfect fluid solution, so that "the acceleration due to gravity" need not be monotonically increasing inside the star (outside, the acceleration of static test particles of course is decreasing with "radius'),

6. in general, to relate these variables to the temperature of the star, one must assume some equation of state (giving pressure as a function of density), most often, a "polytropic" equation of state, a type of model which was extensively developed by Chandrasekhar first in Newtonian and later in relativistic models; then one can for instance show that for a polytrope of index n, the mass density $$\mu$$, the pressure $$p$$, and the mass-energy density $$\varepsilon$$ satisfy:
$\mu = \mu_0 \, \left( T/T_0 \right)^n, \; \; p = p_0 \, \left( T/T_0 \right)^{n+1}, \; \; \varepsilon = \mu + n \, p$
where $$\mu_0, \; p_0, \; \varepsilon_0$$ are respectively the central mass density, central pressure, and central mass-energy density.

7. the ratio of the central density to the average density (strictly speaking, this term requires some explanation because in curved spacetimes, "volume" may not scale with "surface area" as simply as it does in euclidean space!) can vary from about three for the Earth, to about one hundred for a star like our Sun, to about ten for a neutron star (we think)--- these figures are all very approximate but make the point that these models can accomodate a wide range of configurations.

Here, "in general" indicates that realistic models typically have the stated properties. However, some of these can be violated if one assumes an unrealistic equation of state or other unrealistic properties.

See for example M. Demianski, Relativistic Astrophysics, Pergamon, 1985, for more about Newtonian and relativistic polytropes. See for example Schutz, A First Course in General Relativity, for a bit about static spherically symmetric perfect fluid models in gtr.

To repeat something I noted recently in another post, in the past few years there have been some noteworthy developments in the theory of ssspf solutions in gtr; in a sense, these are now all known in closed form. More important, new techniques due to Visser and coworkers make it fairly easy to find new exact solutions of this kind in closed form. Other fairly recent techniques (e.g. Lake's algorithm) make it fairly straightforward to find solutions which are even physically reasonable, up to integrations which may be difficult to express in terms of standard special functions. Several dozen particularly simple ssspf solutions are well known; among the simplest, one of the best is the so-called Tolman IV ssspf from 1939. This admits an equation of state (not terribly well motivated but apparently not terribly unrealistic either) and performs suprisingly well in modeling neutron stars!

This pleasant situation is in stark contrast to the theory of rotating perfect fluid solutions, where despite much work it seems fair to say that really practical methods for finding exact rotating perfect fluid solutions remain to be found. (Nonetheless, some interesting examples are known, and there are fairly practical methods for useful approximate rotating perfect fluid solutions.)

Not sure what you mean by "quantum effects", but no-one said that nuclear physics does not require quantum theory--- since, of course, it does!.

Last edited: Dec 12, 2006