Re: The GR metric in LeSagian Exponential Form...

carlip-nospam_at_physics.ucdavis.edu
Date: 10/21/04 

Date: Thu, 21 Oct 2004 20:15:17 +0000 (UTC)

In sci.physics Paul Stowe <ps@acompletelyjunkaddress.net> wrote:
 
[...]
> Ds^2 = exp(-2GM/rc^2)dt^2 - exp(2GM/rc^2)dr^2 - r^2d(theta)^2

[...]
> I want to revisit this in light of LeSagian theory, in which,
> since G is defined by an linear attenuation process, this would
> seem to be the native form of the equivalent LeSagian Metric.
> My question becomes, in the context of current observational
> limitations, could one discriminate between the normal form and
> this form and how???

The first thing to note is that general relativity is not the same
as the Schwarzschild metric. The assumption of such a metric for a
particular situation (a static, spherically symmetric source) simply
does not address many of the observational tests of GR (de Sitter
precession, gravitational radiation reaction, precession of the
perihelion in neutron star-neutron star binaries, the recent LAGEOS
measurement of frame-dragging) or the important future tests (details
of gravitational radiation, for instance).

There are two places where a metric of this form would be testable:
the Solar System, and astrophysical observations of black hole
candidates. For Solar System tests, the exponential metric differs
from the Schwarzschild metric at order (v/c)^4. There are not yet
any observations accurate enough to discriminate at this order, though
there are proposed experiments that will do so if they get funded --
LATOR, a Mercury orbiter or lander, ASTROD, GAIA. (The term to look
up in the technical literature is "post-post-Newtonian approximation.")

For black hole candidates, if your metric describes the exterior
of a collapsing/collapsed object, then presumably it should change
at some boundary to an interior metric describing the interior of
the remaining matter. For a general relativistic black hole, this
doesn't matter so much, because the transition takes place inside
the horizon, and is unobservable to those outside. Your metric,
on the other hand, has no horizon, so the "surface" of the collapsed
object is not invisible. This means that infalling matter should
hit this surface.

There are two pieces of observational evidence against this that
I know of. Neither is conclusive, but both strongly suggest that
the conventional black hole picture is right.

The first of these is apparent observation of "advection-dominated
accretion flow," or ADAF. As a gas falls into a black hole, it
releases a large amount of gravitational potential energy. Under
many circumstances, this energy is radiated away; this is what
astronomers "see" when they talk about observing a black hole. But
there is another possible flow, in which the energy is stored as
heat, with only a small amount of radiation.

Under such an advection-dominated flow, the gas becomes extremely hot.
One can then ask what happens to the energy. If the gas eventually
hits a surface, the energy will be released; this is observed for
flows onto neutron stars. If the object is a black hole, on the other
hand, the energy will be lost behind the horizon and will not come out
again. This is also observed, but only for gas flowing onto objects
that are predicted from mass observations to be black holes. While
I think there is still some controversy over details of ADAF, these
observations certainly provide some evidence of a horizon. See, for
example, http://cfa-www.harvard.edu/blackhole/release.html, or
Narayan et al., Ap. J. 478 (1997) L79.

A second argument has to do with the observation (and nonobservation)
of type I X-ray bursts, which are the result of thermonuclear explosions
when gas accretes onto the surface of a compact star and ignites. It
seems to be systematically true that such bursts are observed from
objects whose mass is low enough that they ought to be neutron stars,
and are *not* observed from objects whose mass is lowhigh enough that
they ought to be black holes. This is again evidence that the black
hole candidates have no visible "surface" on which the gas can collect.
There's a nice, not-too-technical lecture by Narayan on this on the
arXiv, astro-ph/0310692, which also discusses possible loopholes.

These observations are certainly not conclusive; it might well be
possible to cook up a theory without an event horizon that still
agrees with what we have seen so far. (Note, again, that a crucial
element is something *not* included in your metric -- in this case,
the question of what matter looks like on the "inside.") Observations
of gravitational radiation from colliding black holes and from objects
falling into black holes is probably not *too* far off, and this will
eventually allow a detailed investigation of the metric. But the
existing evidence *does* show that there are strong differences
between collapsed objects with neutron-star masses and those with
black-hole masses, and that these differences have to do with the
question of whether infalling matter hits a surface and releases energy
that then escapes.

Steve Carlip

Relevant Pages

  • Re: Two Schwarzschild radii
    ... radius of a black hole, on the other hand, can never move outward at ... So far the observations match the predictions of alternative models well. ... radius, rather than an event horizon, then relative to that surface, ... certainly have a very large energy. ...
    (sci.physics.relativity)
  • Re: The GR metric in LeSagian Exponential Form...
    ... > of gravitational radiation, for instance). ... For a general relativistic black hole, ... > releases a large amount of gravitational potential energy. ... > Under such an advection-dominated flow, the gas becomes extremely hot. ...
    (sci.physics)
  • Re: The GR metric in LeSagian Exponential Form...
    ... > of gravitational radiation, for instance). ... For a general relativistic black hole, ... > releases a large amount of gravitational potential energy. ... > Under such an advection-dominated flow, the gas becomes extremely hot. ...
    (sci.physics.relativity)
  • Re: GR THEORY IS NOT EVEN FALSE!
    ... The first point to keep in mind is that energy is relative. ... The energy of light falling into a black hole is infinite only ... requires infinite acceleration to remain at rest at the horizon. ...
    (sci.physics.relativity)
  • Re: General relativity versus black holes
    ... For a general relativistic black hole, ... accretion flow," or ADAF. ... releases a large amount of gravitational potential energy. ... the gas becomes extremely hot. ...
    (sci.physics.research)
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