It may be useful

"Modern Cosmology", author: Scott Doldelson, page no: 155-160

Book Link:

http://www.lbreda.com/listing/fisica/Cosmologia/dodelson.pdf

Dear Abhijit,

That is most helpful - thanks!

If I understand correctly, these so-called 'gravity waves' are best described as (temporal) "tensor fluctuations in the gravitational metric" (spacetime coordinates). They are not the product of any strictly gravitational interaction...

in relativistic terms, it seems that these fluctuations are not necessarily associated with the propagation of any quantum particle (gravitons) - although quantum theorists apparently interpret them in that way...

James, As far as I can understand, size of the universe was small

at the time prior to inflation. I have got the following figure from

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/planck.html

Here I see that during initial periods of inflation length scale

was less that 10^-10 meters, so quantum theories was working

at that time. In the second part length scale rose to about 1 meters.

Therefore classical physics will be dominant at the end of inflation.

I am continuing with the previous post. For a considerable

part of the inflationary era quantum physics was the dominant

physics whereas for the later part classical physics took over.

During the quantum mechanical era the space time dependent

metric (a tensor field) must have fluctuated. It must also have

fluctuated in the later part of inflation when size of universe

rose to 1 meter giving classical fluctuations of the metric.

Point is that CMBR have experienced scattering with

the gravitational waves. Their de Broglie wavelengths

must be comparable.

My point ultimately is that for scattering to happen between the

gravity wave and CMBR, these two waves need to have

comparable de Broglie wavelengths.

Biswajoy,

"during initial periods of inflation length scale was less that 10^-10 meters, so quantum theories was working at that time."

I don't think there is any restriction that prevents "tensor fluctuations in the gravitational metric" (as Scott Doldelson says) at _quantum_ scales. Please review the Doldelson reference's discussion of primordial gravitational waves, including section 6.4.1 "Quantizing the Harmonic Oscilator" - I'm sure you can comprehend better than I, but the book makes no mention whatsoever of gravitons, for example...

What quantum theory do you suggest describes the tensor fluctuations of dimensional spacetime that purportedly caused the B mode polarization of CMB photons? I agree that if tensor fluctuations of spacetime did indeed cause the polarization of CMB light at the time of its emission then the spacetime fluctuations were oscillating at quantum scales, but i'm not aware of any quantum theory that describes the "gravitational metric" of dimensional spacetime.

Dear James,

Tensors have minimum two indices. A vector has one index.

A scalar has none. A tensor field in 4-D has 16 component fields

in general. These sixteen components are functions of coordinates.

When a such tensor field scatters microwave photons (vector fields)

then B modes are produced. The experimental discovery of B modes

in CMBR is therefore quite interesting. It means that before crossing

the surface of last scattering (when photons were in equilibrium

with matter) photons were scattered by some tensor fields.

(I hope the background issue of interstellar dust will be resolved)

I do not know whether these tensor fields signal existence of

gravity waves or not. This is another issue.

Dear Biswajoy,

"... It means that before crossing the surface of last scattering [...] photons were scattered by some tensor fields."

As I understand, only photons emitted beyond the surface of last scattering can be detected - those that were emitted before the decoupling of matter and radiation were absorbed... See http://en.wikipedia.org/wiki/Last_scattering_surface#Features

"According to the Big Bang model, the [CMB] radiation from the sky we measure today comes from a spherical surface called the surface of last scattering. This represents the set of locations in space at which the decoupling event is estimated to have occurred[20] and at a point in time such that the photons from that distance have just reached observers."

As I understand, the interaction between CMB photons and the proposed primordial gravitational waves, "tensor fluctuations in the gravitational metric", _must_ have occurred beyond the surface of last scattering.

If the non-cosmological potential sources of B mode polarization signals can be eliminated, then the CMB radiation may have been polarized as it was emitted.

"Tensors have minimum two indices. A vector has one index. A scalar has none. A tensor field in 4-D has 16 component fields in general. These sixteen components are functions of coordinates. When a such tensor field scatters microwave photons (vector fields) then B modes are produced."

Note: the B mode polarization of EMR has nothing to do with scattering photons. We can only identify polarization signals in photons that we detect. Please see the discussion in http://www.preposterousuniverse.com/blog/2014/03/16/gravitational-waves-in-the-cosmic-microwave-background/ beginning with the paragraph:

"Any kind of electromagnetic radiation, such as the microwaves we observe in the CMB, has a polarization. An electromagnetic wave is just a propagating ripple in the electric and magnetic fields, and we (somewhat arbitrarily) define the direction of polarization to be the direction in which the electric field is oscillating up and down."

Inflation has ended much before the time at which

CMBR photons crossed surface of last scattering.

The following picture shows time scales. I have got

it from the following link.

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec27.html

James,

Please see time scales in the picture in my last

post.

I am continuing with my previous post. If B-mode

polarizations in CMBR has been generated after CMBR

photons have crossed the surface of last scattering them

these B-mode polarizations cannot give any information

about the inflationary epoch.

Dear Biswajoy,

Please understand - the proposed primordial gravitational waves continued to propagate long after inflation ended! Eventually their energy dissipated so that they are no longer considered detectable, but when the CMB photons were emitted the proposed gravitational waves were energetic enough alternatingly stretch, then compress, the waves of CMB light, 'organizing' the otherwise random polarity of light, producing the reported B mode polarization signal.

See http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang#Dark_Ages

"Before decoupling occurred, most of the photons in the universe were interacting with electrons and protons in the photon–baryon fluid. The universe was opaque or "foggy" as a result. There was light but not light we can now observe through telescopes. The baryonic matter in the universe consisted of ionized plasma, and it only became neutral when it gained free electrons during "recombination", thereby releasing the photons creating the CMB. When the photons were released (or decoupled) the universe became transparent..."

Especially notice that, when protons and electrons interact with photons, the photons are _absorbed_. At the high temperatures of the early universe, new photons were soon re-emitted, but they could not freely propagate without being continuously absorbed and re-emitted. Only after recombination could the most recently re-emitted photons freely propagate through the suddenly transparent universe. Those photons constitute the CMB light, which is now proposed to have been initially polarized by still propagating gravitational waves.

I sincerely hope this helps.

Thank you for your post.

You are saying that photons of CMBR interacted with gravitational

waves after photons crossed the surface of last scattering. I

will look into technical papers in detail and examine this issue.

BTW, I'm also saying that, technically, effectively no photons 'crossed' the surface of last scattering - all the CMB photons we observe were emitted, at the earliest, during the recombination event.

Please also see the brief discussion at https://www.researchgate.net/post/Is_there_any_experimental_evidence_for_how_much_time_a_photon_takes_to_flow_from_the_core_to_the_surface_of_the_sun...

From the introduction part of bicep II paper.

http://arxiv.org/pdf/1403.4302v2.pdf, I am getting the following

discussion,

"In addition to this temperature signal, the CMB also pos-

sesses a small degree of polarization. This arises from Thom-

son scattering of photons from free electrons at the time

of decoupling in the presence of an anisotropic distribu-

tion of photons (Rees 1968). The largest component of po-

larization is a curl-free “ E -mode” pattern produced by the

same scalar density fluctuations that give rise to the CMB

temperature anisotropy. The scalar fluctuations are unable

to induce a pure-curl “ B -mode” polarization pattern in the

CMB, but B -modes can be produced by primordial gravita-

tional waves ( Seljak & Zaldarriaga 1997; Kamionkowski et al.

1997). These gravitational waves, or tensor fluctuations, are a

generic prediction of inflationary models (Starobinsky 1979;

Rubakov et al. 1982; Fabbri & Pollock 1983). The relative

amplitude, characterized by the tensor-to-scalar ratio

r(Lewis et al.2000; Leach et al. 2002), is a probe of the energy scale

of the physics behind inflation. The presence and amplitude

of primordial B -mode polarization is thus a key tool for un-

derstanding the inflationary epoch"

CMBR has a black-body spectrum. Which wavelength range is

measured by bicep2 ? Can anyone help ? Sorce of the following

diagram is http://hyperphysics.phy-astr.gsu.edu/hbase/bkg3k.html

Regarding 'Thompson scattering' mentioned in the BICEP-2 ref. (above),

"In addition to this temperature signal, the CMB also possesses a small degree of polarization. This arises from Thomson scattering of photons from free electrons at the time of _decoupling_..."

see http://en.wikipedia.org/wiki/Thomson_scattering#Introduction...

"In the low-energy limit, the electric field of the incident wave (photon) accelerates the charged particle, causing it, in turn, to _emit_ radiation at the same frequency as the incident wave, and thus the wave is scattered. Thomson scattering is an important phenomenon in plasma physics and was first explained by the physicist J. J. Thomson. As long as the motion of the particle is non-relativistic (i.e. its speed is much less than the speed of light), the main cause of the acceleration of the particle will be due to the electric field component of the incident wave, and the magnetic field can be neglected. The particle will move in the direction of the oscillating electric field, resulting in electromagnetic dipole radiation. The moving particle radiates most strongly in a direction perpendicular to its motion and that radiation will be polarized along the direction of its motion. Therefore, depending on where an observer is located, the light scattered from a small volume element may appear to be more or less polarized..."

[my emphasis added...]

I think this supports my contention that CMB photons were emitted at the time of photon _recombination_ or _decoupling_ from the hot proton-electron plasma, and that the CMB is thought to have been polarized by gravitational waves propagating long _after_ inflation ended.

See http://en.wikipedia.org/wiki/Big_bang#Cosmic_microwave_background_radiation

"The surface of last scattering corresponding to emission of the CMB occurs shortly after _recombination_, the epoch when neutral hydrogen becomes stable. Prior to this, the universe comprised a hot dense photon-baryon plasma sea where photons were quickly scattered from free charged particles."

Also see http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation#Relationship_to_the_Big_Bang...

"The CMB gives a snapshot of the universe when, according to standard cosmology, the temperature dropped enough to allow electrons and protons to form hydrogen atoms, thus making the universe transparent to radiation. When it originated some 380,000 years after the Big Bang—this time is generally known as the "time of last scattering" or the period of _recombination_ or _decoupling_..."

Also see http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation#Polarization...

"The cosmic microwave background is polarized at the level of a few microkelvin. There are two types of polarization, called E-modes and B-modes. This is in analogy to electrostatics, in which the electric field (E-field) has a vanishing curl and the magnetic field (B-field) has a vanishing divergence. The E-modes arise naturally from Thomson scattering in a heterogeneous plasma. The B-modes are not sourced by standard scalar type perturbations. Instead they can be sourced by two mechanisms: first one is by gravitational lensing of E-modes, which has been measured by South Pole Telescope in 2013.[70] Second one is from gravitational waves arising from cosmic inflation. Detecting the B-modes is extremely difficult, particularly as the degree of foreground contamination is unknown, and the weak gravitational lensing signal mixes the relatively strong E-mode signal with the B-mode signal.[71]"

Please let me know if this does not resolve this question.

Re. "Which wavelength range is measured by bicep2 ?"

The abstract of the paper you referenced - http://arxiv.org/abs/1403.4302 - states:

"In this paper we report on the design and performance of the instrument and on the three-year data set. BICEP2 completed three years of observation with 500 detectors at 150 GHz."

That is one of the issues with the BICEP2 results - the B-mode polarization signal could occur in a range of frequencies...

FYI - the BICEP2 primordial gravitational wave - CMB polarization results may be confirmed (or not) in Oct. See http://www.nature.com/news/milky-way-map-skirts-question-of-gravitational-waves-1.15181.

Thank you James. See that from above figure that

CMBR is emitted by a black body. Inside a black body

photons are in thermal equilibrium with the walls of a

box. This way they reach a thermal equilibrium.

Before decoupling following relations were true,

nb approx nbbar approx nphoton ----> (1)

(nb- nbbar)/nphoton approx 10^-10 ------->(2)

nb=number of baryons

nbbar=number of antibaryons

nphoton= number of photons

baryons and antibarons combined and formed

another nphoton number of photons, using (1).

So now there are approximately nphoton+nphoton

number of photons, half of them are formed by

recombination.

Photons which are generated by recombination

should come quickly into thermal equilibrium with

existing photons. Then they will fit into the black body

curve of 2.7 degree Kelvin.

See for example:

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

Biswajoy,

Sorry I can't follow the mathematics. I understood the question being discussed was whether the identified polarized CMB radiation had to have been emitted during the inflationary period (to be encoded with gravitational wave distortions) or whether gravitational waves are thought to have persisted until those CMB photons were emitted,

As I understand, any encoding of light polarization that might have been imparted prior to or during the 'dark ages' would have been erased by their continuous random scattering - absorption of 'old' photons and re-emission of new photons. As a result, a systematic encoding of CMB light had to occur after scattering subsided. This requires that any primordial gravitational wave polarization of CMB light had to occur _after_ the 'surface of last scattering'.

Regarding specifically the original question, a recent essay - http://www.gravityresearchfoundation.org/pdf/awarded/2014/Porto_2014.pdf. - states:

"At first glance, the (indirect) measurement of primordial tensor modes by the BICEP2 collaboration supports an inflationary paradigm for early universe cosmology together with quantum vacuum fluctuations (aka gravitons) as the origin of the spectrum. In this essay we argue the the observed signal may instead be a signature of semi-classical sources of perturbations during inflation. In this scenario, despite a large tensor-to-scalar ratio r ~ 0:2, it may be possible to write an effective field theory of a rolling scalar field without super Planckian excursions..."

James, I was looking up first three minutes by Steven Weinberg

to get some insights on the surface of last scattering. What he says

is that a system in THERMAL EQUILIBRIUM can be described by some

macroscopic parameters such as temperature. The system has

very little memory of its initial conditions prior to reaching the

equilibrium condition. If we take this view then photons of CMBR

which are produced at time =10^6 years, will retain very little memory of

inflation time with is time < 1 sec. Only its spectrum will be

fixed by the temperature of material in thermal equilibrium.

That is correct - as I've repeatedly stated, the CMBR photons DO NOT RETAIN ANY ENCODING IMPARTED PRIOR TO THEIR LAST SCATTERING.

The proposed propagating gravitational waves - oscillating perturbations of the (temporally varying) "tensor fluctuations in the gravitational metric" (spacetime dimensional coordinates) - continued to propagate right through the dark ages and the surface of last scattering. While they would continuously polarize any photons encountered - those photons would lose that polarization signal upon their next scattering (absorption & reemission). Only when photon scattering was discontinued would those now persistent (CMBR) photons retain the systematic polarization imparted by any gravitational waves propagatin from the time of inflation.

See http://arxiv.org/abs/1309.5343 - which states in its abstract:

"While many aspects of general relativity have been tested, and general principles of quantum dynamics demand its quantization, there is no direct evidence for that. It has been argued that development of detectors sensitive to individual gravitons is unlikely, and perhaps impossible. We argue here, however, that measurement of polarization of the Cosmic Microwave Background due to a long wavelength stochastic background of gravitational waves from Inflation in the Early Universe would firmly establish the quantization of gravity."

This is the proposition intended to be tested of the BICEP2 measurements - it conflicts with the proposition of the essay in my preceding comment. I cannot explain more clearly.

Because CMBR photons do not have any memory left prior

to the surface of last scattering, today, how can we observe

effects of inflationary gravity waves ? The answer lies the

propagation of gravity waves through the surface of

last scattering.

Gravitational waves are fluctuations in the metric. Therefore

it will also distort the surface of last scattering. Surface will not be

a perfect sphere: -- but there will be stretching and compressing

of the surface of last scattering itself. Distortion of geometry

of the surface of last scattering is creating B mode polarization.

This explanation sounds logical to me.

That's fine - that seems to be inconsistent with your position of 11 days - and 15 comments - ago that:

"... It means that before crossing the surface of last scattering [...] photons were scattered by some tensor fields."

and

"Inflation has ended much before the time at which CMBR photons crossed surface of last scattering."

As you selectively restated my counter-assertion:

"You are saying that photons of CMBR interacted with gravitational waves after photons crossed the surface of last scattering. I will look into technical papers in detail and examine this issue."

I must say that this little 'issue' has made this discussion very difficult and time consuming - IMO unnecessarily so.

I must apologize for that. I took me a while to understand

that surface of last scattering is undergoing stretching and

compression, which in turn is polarizing CMBR photons.

I have added another question on acoustic peaks in the

CMBR anisotropy spectrum. I guess that is also due to

some distortions in the surface of last scattering. But this

time it is not due to fluctuations of metric. I am not sure

what the answer is, let me see how that discussion proceeds.

For starters - see http://en.wikipedia.org/wiki/CMB#Relationship_to_the_Big_Bang and its referenced links,

A very nice paper on the BICEP2 results has just appeared on the arXiv eprint repository:

M. Mortonson & U. Seljak

A joint analysis of Planck and BICEP2 B modes including dust polarization uncertainty

http://arxiv.org/pdf/1405.5857v1.pdf

The good news about this paper is that they take as priors only what we know, on the basis of other experiments, regarding the contribution to the polarisation from dust at different angular scales. They get limits on the tensor to scalar ratio of r < 0.11 using BICEP2 and Planck data (see the paper for a precise statement).

At a first-read it seems like a constructive and objective paper and i will certainly read it in more detail. But if any experts out there would care to comment I am sure readers would be most interested to hear what they have to say.

Of course nothing is better than better data - but we have to wait for that.

Bernard:

Thank you very much for the reference.

I have taken a quick look at the reference. The main point

is that Bicep2 had insufficient knowledge about polarization

that may have been generated by foreground dust. If that

is high enough then tensor to scalar ratio is not a reliable

indicator because tensor polarization is not being generated

by inflation, it is only when CMBR photons travel to earth

they get polarized by scattering with interstellar dust. If

dust polarization background is taken out from signal

then r is consistent with zero under certain conditions.

I am quoting a few lines from their paper,

"We have assumed that we do not have a reliable prior

on the dust polarization in the BICEP2 field, so we perform

a pure power spectrum analysis. We find that under the

assumption of a dust polarization power spectrum with free

amplitude but known scaling with l, the BICEP2 data prefer

r= 0."

I agree that Bernard's recent reference is a fine analysis of the current state (prior to the full release of Planck dust map results, etc.), which remains "optimistic that future B mode polarization searches will provide powerful constraints on inflationary models." However, it states in summary (in its discussion on pages 8-9):

"This result does not automatically mean that BICEP2 has no evidence for primordial gravitational waves in its data. It does, however, mean that the case strongly relies on understanding the actual dust polarization contribution in the BICEP2 field, which at the moment is unavailable and possibly higher than the various estimates presented by the BICEP2 team. It is thus too early to celebrate the BICEP2 results as a definitive proof of inflation."

@James

Thanks for emphasizing that!

The polarization map shown recently by Planck notably had two polar regions where they are not showing the data. I wonder why?

Bernard,

Thanks! I think they're being extra-cautious in consideration of the hubbub raised by the high profile BICEP2 announcement. In http://www.nature.com/news/milky-way-map-skirts-question-of-gravitational-waves-1.15181 it's stated:

"The map released this week, however, focuses on the plane of the Galaxy and excludes the Southern Hole [the BICEP2 field of view] and other regions of high galactic latitude, “because our signal-to-noise ratio there is low and we do not yet fully [understand] the uncertainties in those regions,” says Jan Tauber, a Planck project scientist in Noordwijk, the Netherlands. The excluded regions, which amount to about 21% of the sky, will be included in Planck data released in October, he adds. Those data may also include findings from the Planck team’s attempt to search for the signature from gravitational waves."

Because it is always preferable to to keep us well informed about

latest experimental results, I was curious to know about current status

of LISA and LIGO experiments. These two experiments search for

gravity waves and they complement results of one another.

LISA experiment is done by three satellites forming an equilateral

triangle whose arms are five million kilometers, whereas, LIGO

is a ground based experiment. LISA uses interference of laser

beams to measure relative distances of these three satellites.

When a gravity wave passes through the array, one hopes to

measure its effect on relative distances.

Picture credit: http://science.nasa.gov/missions/lisa/

LIGO was in operation from 2002 to 2010, but is currently shut down for a multi-year, large scale upgrade - see http://blogs.nature.com/news/2014/05/rare-cosmic-blast-sends-astronomers-racing-to-telescopes.html.

The LISA program remains under consideration and is being reevaluated to reduce funding requirements (NASA seems to have dropped out) - see http://sci.esa.int/lisa/48728-mission-status/.

Of course, any primordial gravitational waves have dissipated long ago - these programs are intended to detect events such as nearby neutron star or black hole mergers - high amplitude oscillations in the curvature of local spacetime coordinates produced by the rapid juxtaposition of strong gravitational fields.

The original BICEP2 announcement is being criticized on many counts - it's reported:

"But James Bock, a physicist at the California Institute of Technology in Pasadena and a co-leader of the BICEP2 experiment, says that although his group’s main paper “has been revised based on many referee comments and resubmitted” for publication, the evidence for gravitational waves “is certainly not being retracted”."

See http://www.nature.com/news/gravitational-wave-discovery-faces-scrutiny-1.15248 and the more recent report (quoted above), http://www.nature.com/news/no-evidence-for-or-against-gravitational-waves-1.15322 - http://arxiv.org/abs/1405.5857 and http://arxiv.org/abs/1405.7351.

Most are still looking to the Planck team's final galactic dust map expected in Oct. to definitively determine the veracity of the BICEP2 results. Other experiments will also contribute additional observational evidence...

I suppose LIGO and LISA experiments will prove the existence of gravitational

waves. Is it experimentally proven whether gravity waves exist or not ?

Wikipedia gives following informations

"As of early 2014, no direct detection of gravitational waves has been

accomplished. However, a number of experiments have provided

evidence that gravitational waves do exist, notably the observation

of binary pulsars, the orbits of which evolve precisely matching the

predictions of general relativistic gravitational-wave emission. The

1993 Nobel Prize in Physics was awarded for this work"

IMO, the primary question in the direct detection of gravitational waves is not whether they can exist locally, but whether they independently propagate in a vacuum - as EM waves/photons do.

If, as I suspect, they are mechanical oscillations of the gravitational metric (produced by rapid juxtapositioning of gravitational fields), then their amplitude must diminish as a subfunction of the gravitational metric.

Also see http://en.wikipedia.org/wiki/Cooperstock's_energy-localization_hypothesis

https://www.researchgate.net/publication/231012063_The_localisation_of_energy_in_general_relativity

https://www.researchgate.net/publication/231027066_The_localisation_of_energy_in_general_relativity._II

http://link.springer.com/article/10.1007%2FBF00733393

Article The localisation of energy in general relativity

Article The localisation of energy in general relativity. II

I am quoting from the press release of 1993 Nobel prize.

Here an indirect *proof of existence* of gravitational waves

is discussed. Again this is not about primordial gravity waves

generated by inflation. The point I would like to stress is that

if gravity waves are a prediction of general relativity, we should also

observe gravitational waves originating from other possible

sources.

" A very important observation was made when the system had been

followed for some years. This followed theoretical predictions made

shortly after the original discovery of the pulsar. It was found that the

orbit period is declining: the two astronomical bodies are rotating

faster and faster about each other in an increasingly tight orbit. The

change is very small. It corresponds to a reduction of the orbit

period by about 75 millionths of a second per year, but, through

observation over sufficient time, it is nevertheless fully

measurable. This change was presumed to occur because

the system is emitting energy in the form of gravitational waves

in accordance with what Einstein in 1916 predicted should happen

to masses moving relatively to each other. According to the latest

data, the theoretically calculated value from the relativity theory agrees

to within about one half of a percent with the observed value. The first

report of this effect was made by Taylor and co-workers at the end of

1978, four years after the discovery of the binary pulsar was reported.

The good agreement between the observed value and the theoretically

calculated value of the orbital path can be seen as an indirect proof of

the existence of gravitational waves."

Biswajoy,

If you were responding to my comment, I see no contradictions - mechanical waves propagating in a medium also disperse energy... As I understand, it is the mass, proximity and rotation rate that _locally_ determines the energy dispersed. See http://en.wikipedia.org/wiki/Gravitational_wave#Radiation_from_other_sources

"The characteristics of their orbit can be deduced from the Doppler shifting of radio signals given off by the pulsar. Each of the stars has a mass about 1.4 times that of the Sun and the size of their orbit is about 1/75 of the Earth-Sun orbit. This means the distance between the two stars is just a few times larger than the diameter of our own Sun. The combination of greater masses and smaller separation means that the energy given off by the Hulse-Taylor binary will be far greater than the energy given off by the Earth-Sun system — roughly 10^22 times as much."

The issue I discussed is whether the radiated energy diminishes as a function of the strength of the gravitational field - whether we can detect remote gravitational waves or whether their energy is localized by the diminishing strength of the gravitational field.

Again, see http://en.wikipedia.org/wiki/Gravitational_wave#Sources_of_gravitational_waves.

- Two objects orbiting each other in a quasi-Keplerian planar orbit (basically, as a planet would orbit the Sun) will radiate.

- A spinning non-axisymmetric planetoid — say with a large bump or dimple on the equator — will radiate.

- A supernova will radiate _except_ in the unlikely event that the explosion is perfectly symmetric.

- An isolated non-spinning solid object moving at a constant velocity will _not_ radiate. This can be regarded as a consequence of the principle of conservation of linear momentum.

- A spinning disk will _not_ radiate. This can be regarded as a consequence of the principle of conservation of angular momentum. However, it will show gravitomagnetic effects.

- A spherically pulsating spherical star (non-zero monopole moment or mass, but zero quadrupole moment) will _not_ radiate, in agreement with Birkhoff's theorem.

It is the variations of gravitational fields in time that produces an oscillation of the gravitational metric that are described as gravitational waves - analogous to processes that produce waves in water, for example.