11D Supergravity as a Gauge Theory for the MAlgebra

1
Centro de Estudios Científicos CECS-Valdivia-Chile
2
Gravitational Cheshire Effect 100 Years of
Relativity São Paulo, August 2005
J. Zanelli CECS - Valdivia

• In collaboration with
• Eloy Ayón-Beato
• Cristián Martínez
• Ricardo Troncoso
• Phys. Rev. D71 (2005) 104037 hep-th/0505086
• Gen. Rel. Grav. (in press) hep-th/0403228
• forthcoming preprints ...

3
1905 has been called Einsteins miraculous year.
However, what he did in 1915 showed that 1905 was
no miracle at all.
Perhaps we should take the occasion to celebrate
the 90 years of Einsteins greatest achievement.
. . . or perhaps we should have another
conference like this in ten years.
4
General Relativity (1915)
Gravity is a funny interaction that makes all
bodies to move in the same orbits.
Einsteins insight Gravity is an effect of the
geometry of spacetime.
Equivalence principle Spacetime is a
differentiable manifold endowed with a tangent
space identical to Minkowski space at each
point. In this way, GR generalizes Special
Relativity.
. . . and what determines the shape of the
spacetime?
5
However, this is not always true.
6

• These configurations are
• Non-perturbative, exact solutions of the coupled
  system
• Einstein Eqs. Self-interacting
  scalar field.
• Gravitationally undetectable (stealth fields).
• Back-reaction free.
• Have vanishing globally conserved charges

• Finite Euclidean action solution
  (instanton-like).

• Not admitted by all geometries.

7
The model
8

• Such field configurations could be taken as
  vacua and they do
• not curve spacetime.

• Is the new T derivable from an action principle?

9

• Is it logically necessary to allow for this
  extra term?

Yes.
10
The System
Scalar field Gravity
11
(No Transcript)
12
The Effect
13
In Euclidean space, the solution is an
instanton-like object

• Localized

• Finite action

14
Special Cases

15
Generalizations

• It is also possible to construct gravitationally
  undetectable
• time-dependent solutions, but only in 21
  dimensions.

A common feature of all these solutions is that
they exist in conformally flat spacetimes. We
conjecture this to be generic.
16
What is behind the trick?
But there are other options. . .
17
(No Transcript)
18
Summary

• In the presence of a pseudo conformal coupling,
  there exist
• non-trivial gravitationally undetectable
  (stealth) solutions.
• They are non perturbative and have finite
  action. They are
• instanton-like solutions in Euclidean space.
• They can be obtained by conformal
  transformations generated
• by harmonic functions. They only exist in
  certain special
• geometries. They are the scalar analogues of
  Killing spinors.
• More generally, one should not trust standard
  assumptions
• about the energy-momentum of scalar fields.
  There may be
• surprises even in flat space (Cheshire effect).
  Is there a lesson
• for cosmologists?

19
(No Transcript)