Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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Transformation laws of
redshift, flux and luminosity in
generic spacetimes
Maurício O. Calvão*, B. L. Lago**, R. R. R. Reis* & B. B. Siffert*
*IF-UFRJ **CEFET-RJ
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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I. INTRODUCTION
redshift: Doppler, gravitational, cosmological
I.1. MOTIVATION
Wright (2013)] Schombert (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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flux and luminosities
[Whitle (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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I.2. BASIC CONCEPTS
instantaneous observer local Lorentz boost
[Calvão (2013)]
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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observer frame of reference
[Calvão (2013)][Calvão (2013)]
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II. REDSHIFT
II.1. LOCAL (OR POINTWISE)
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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II. REDSHIFT
II.1. LOCAL (OR POINTWISE)
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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II. REDSHIFT
II.1. LOCAL (OR POINTWISE)
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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II.2. GLOBAL (OR AT A DISTANCE)
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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II.2. GLOBAL (OR AT A DISTANCE)
generic redshift law:
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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II.2. GLOBAL (OR AT A DISTANCE)
in particular, for any spacetime:
challenge to expanding space paradigm!
basis for consistent definition of absolute magnitude!
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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II.3. DOPPLER FACTOR
[Calvão (2013)]
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II.3. DOPPLER FACTOR
[Calvão (2013)]
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II.3. DOPPLER FACTOR
[Calvão (2013)][Calvão (2013)]
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II.3. REDSHIFT TRANSFORMATION
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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II.3. REDSHIFT TRANSFORMATION
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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III. FLUX
III.1. DEFINITION
geometrical optics (eikonal) approximation
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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III.2. FLUX TRANSFORMATION
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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III.2. FLUX TRANSFORMATION
[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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III.2. FLUX TRANSFORMATION
[Calvão (2013)][Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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IV. LUMINOSITYIV. LUMINOSITIES
angular distribution of emitted (source) power, or simply angular emitted power
angular distribution of received (detector) power, or simply angular received power
IV.1. DEFINITIONS
[Rybicki (1979)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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[Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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[Calvão (2013)] [Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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emitted (source) power
received (detector) power
isotropic case:
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IV.1. TRANSFORMATION LAWS
[Calvão (2013)]
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IV.1. TRANSFORMATION LAWS
[Calvão (2013)]
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IV.1. TRANSFORMATION LAWS
[Calvão (2013)] [Calvão (2013)]
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IV.1. TRANSFORMATION LAWS
[Calvão (2013)]
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IV.1. TRANSFORMATION LAWS
[Calvão (2013)]
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IV.1. TRANSFORMATION LAWS
[Calvão (2013)][Calvão (2013)]
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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IV.1. TRANSFORMATION LAWS
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V. LUMINOSITY DISTANCES
V.1. DEFINITIONS
Vth Workshop “Challenges of New Physics in Space”, Rio de Janeiro, RJ, 28 April – 03 May 2013
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VI. CONCLUSION
● We clarified the notions related to redshift, flux, luminosities and luminosity distances in a generic spacetime for arbitrary instantaneous observers, essentially without any approximation, not perturbatively!
● All Doppler effects can be interpreted as purely kinematic ones, arising from the use of non-parallely transported instantaneous observers
● In particular, in any spacetime the redshift along a given null geodesic can always be made to vanish
● Flux is essentially the norm of the energy flux vector from the energy-momentum tensor and its transformation law is trivially obtained
● There are several consistent notions of (angular) luminosity and consequent luminosity distances
● Differences due to peculiar motions and/or anisotropies do arise and are not negligible at all!!
MAIN RESULTS:
