Quote:
Originally Posted by sjastro
The matter energy tensor (the right hand term) is not relevant if one wants to use black holes in the argument. This term is only applied when one is interested in external gravitational and/or electromagnetic fields acting on the field in question. It also applies to extended objects where matter is found in the field.
Gravitational waves are formed by variations of the field itself.
In other words you only need to consider the extension of the field into empty space and the propagation of gravitational waves into empty space.
The Einstein equation simply becomes Ricci Tensor=0.
Gravitational waves are derived mathematically by applying perturbation to the metric components of the Lorentzian metric. The components are time dependent indicating the field varies with time.
This is a solution to the equation.
You have lost me. If a gravitational field varies, the energy in the field is conserved by the radiation of gravity waves. That's the basis behind the existence of gravitational waves.
The mass alone (density) does not create gravitational waves. A static (Schwarzchild metric) black hole doesn't generate gravitational waves. A rotating (Kerr metrc) black hole can be a different matter. Since it rotates, there is centripetal force (with a non vanishing Christoffel) that adds to the field strength. By slowing down the rotation, the loss in rotational energy is taken up by the frequency of the emitted gravitational waves.
There is nothing devious about the maths unlike the manipulations that occur in Quantum Field Theory.
Regards
Steven
|
Hi Steven,
The mass energy tensor is as it says, it can be either energy as energy, or energy in the guise of mass, which is moving through a given spatial region over a temporal period. A black hole still has energy moving through given regions over a given periods, even if the mass energy tensor and [mathematical] dimensions breaks down in this environment. And this is one of my main points; hat breaks down here isn't reality at all, it’s still there, it's our mathematics and our understanding which does. The universe is doing what it has always done and doesn't need the math. This relates to the thread about Math Lingo, where math is manipulated to suit the observation (not necessarily the reality) and thus it is merely a descriptive language, NOT the be-all and end-all. But why do so many people tout it to be an absolute. This really needs to be understood by everyone; Newton was hailed as being correct, now not so correct, Einstein could well be next. My point here is simple; there are mathematical principles which merely describe reality, and there is reality. The two can and do conflict all, the time. The key difference is really simple; reality is what it is, reality. Mathematics is equally simple; it’s a visualization tool, a language, and nothing more!
My tutor spent his entire life working for NASA as an astrophysicist and lecturing at Cambridge, understanding how light is created within stars and logic in mathematics, and you should hear what he has to say about this topic. He was the one who showed me that there is a separation between math and reality that needs to be clearly understood. In one of my scanned notes, I wrote his words, “people these days run around talking about what light is, I’ve spent my entire life trying to understand what is light, and I haven’t a clue”.
Back to gravity: Gravitational waves are linked to the field, I agree, but they behave only in accordance with the [symmetric] metric tensor, and the Ricci and Scalar must be dropped in order to describe these waves (convenience of mathematics again). It takes all three to describe the gravitational field, therefore, gravity waves do not operate through the gravitational field, they have their own and they set-up the gravitational field (probably why we now need a Higgs field). We need to now drop mathematics entirely and look at gravitation as a physical form, two structures are present, a field which spreads out at the speed of light and for all we know, may well set-up of define the metric in some ether of energy, and a field which hold the interplay between energy and curved geodesics (Not curved space and time at all!) brought about from the negative divergence.
Without transferring understanding of gravitation from mathematics across to a physical mental picture, we are forever lost within the “tool”, the “language”.
"you only need to consider the extension of the field into empty space and the propagation of gravitational waves into empty space...the Einstein equation simply becomes Ricci Tensor=0."...yes, exactly!
There can be no conservation in a gravitational field since gravitational waves are radiating [sending out of the system] energy from the massed [energy dense] region where our star, or whatever, is. Again, my point is that gravity waves are a separate structure to the gravitational field, but there are linked. Einstein knew this and accounted for it. This is why he said that there is no background structure with which to measure against; even his evolution equations for quantum measurements hold an “all of universe” solution, “without a fixed background structure”. Ergo the importance of clocks (synchronicity).
I know what you're saying about black holes, and I agree, but there is a separation between the gravitational field and how the field is setup, a separation between math and the reality.
"There is nothing devious about the maths unlike the manipulations that occur in Quantum Field Theory."...yes there is. For example, every mathematician (Gauss, Riemann, Ricci, Minkowski, Christoffel, Einstein, all of them) played around with the math, creating variations in the chain rule for instance, until "hey presto", "that seems to match the observations or what we need". When we get to a black hole, all of a sudden we say that a new type of math needs to be derived in order to describe this region. Yet another variation in the language, yet reality chugs along in the background.
Again, mathematics is merely an aid in understanding what is happening in reality and not the contrary; reality is not the aid to understanding mathematics.
Anyway, I’ve said enough on this topic and I’m sure you get my point.
Cheers
Mark